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christopher
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oeis

Dataset card Data Studio Files
xet
Community
2
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stringlengths
7
7
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4
573
sequence
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1
348
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score
int64
1
2.35k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
⌀
cross_references
listlengths
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128
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former_ids
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231
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timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-07-19 00:40:46
filename
stringlengths
29
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32
A382716
a(n) = n - A382715(n).
[ "1", "1", "4", "1", "1", "9", "1", "1", "-4", "1", "1", "1", "25", "-4", "1", "1", "1", "36", "-1", "-1", "-4", "-1", "4", "-4", "49", "4", "1", "1", "-1", "-1", "-1", "64", "4", "1", "1", "1", "1", "1", "1", "1", "1", "81", "1", "1", "1", "1", "1", "1", "1", "1", "100", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "121", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "144", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "-1", "-1", "-1", "-9", "4", "1", "1", "1", "1", "1", "1", "1", "196", "-1", "-4", "-1", "-1", "4", "-9" ]
[ "sign" ]
16
1
3
[ "A377091", "A379789", "A382715", "A382716", "A382717", "A382718" ]
null
N. J. A. Sloane, Apr 09 2025
2025-04-13T00:53:14
oeisdata/seq/A382/A382716.seq
ce7383fe47b4c64cdb90da42a9681e75
A382717
Square roots of record high points in A382716.
[ "1", "2", "3", "5", "6", "7", "8", "9", "10", "11", "12", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "46", "47", "48", "49", "50", "51", "52", "54", "55", "56", "57", "58", "59", "60", "61", "63", "64", "65", "66", "67", "68", "69", "70", "71", "73", "74", "75", "76", "77", "78", "79", "80", "82", "83", "85", "86", "87", "88", "89", "90", "91", "92", "93", "94", "95", "96", "97", "98", "99" ]
[ "nonn" ]
21
1
2
[ "A377091", "A379789", "A382715", "A382716", "A382717", "A382718" ]
null
N. J. A. Sloane, Apr 13 2025
2025-04-13T15:07:40
oeisdata/seq/A382/A382717.seq
584684b888a09896d9a0da4a308615b3
A382718
Numbers missing from A382717.
[ "4", "13", "25", "45", "53", "62", "72", "81", "84", "115", "118", "143", "145", "152", "161", "164", "170", "173", "182", "187", "192", "197", "214", "223", "228", "234", "248", "265", "272", "275", "283", "294", "302", "307", "312", "317", "319", "323", "329", "332", "341", "344", "350", "353", "355", "365", "375", "379", "382", "385", "400", "445", "455", "459", "462", "465", "480", "483", "487", "492" ]
[ "nonn" ]
26
1
1
[ "A377091", "A379789", "A382715", "A382716", "A382717", "A382718" ]
null
N. J. A. Sloane, Apr 13 2025
2025-04-27T16:55:56
oeisdata/seq/A382/A382718.seq
aa62c5d14fcec7200f50a9d0a28ebff7
A382719
Numerator of Sum_{i=1..n} 1/A348626(i)^2.
[ "0", "1", "1", "3", "31", "35", "1751", "2351", "115247", "416333389", "107225418168983", "562904175532925088592367", "1857180475556752726157213791943527783", "424594887903818740281781489141947299537771799837674380866823", "27616236678198713245845367246922973802897093015095664467076756280985616142084296233915021926355087" ]
[ "nonn", "frac" ]
5
0
4
[ "A348626", "A348640", "A348641", "A382719" ]
null
N. J. A. Sloane, Apr 21 2025
2025-04-21T11:18:59
oeisdata/seq/A382/A382719.seq
4a75cc7c712056d19516f4affd7615e8
A382720
Number of entries in the n-th row of Pascal's triangle not divisible by 7.
[ "1", "2", "3", "4", "5", "6", "7", "2", "4", "6", "8", "10", "12", "14", "3", "6", "9", "12", "15", "18", "21", "4", "8", "12", "16", "20", "24", "28", "5", "10", "15", "20", "25", "30", "35", "6", "12", "18", "24", "30", "36", "42", "7", "14", "21", "28", "35", "42", "49", "2", "4", "6", "8", "10", "12", "14", "4", "8", "12", "16", "20", "24", "28", "6", "12", "18", "24", "30", "36", "42", "8", "16", "24", "32", "40", "48", "56", "10", "20", "30", "40" ]
[ "nonn" ]
7
0
2
[ "A001316", "A006047", "A194459", "A382720", "A382721", "A382722" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T20:13:17
oeisdata/seq/A382/A382720.seq
4e1e6bbfbdea1bfbea692cde537d08b0
A382721
Number of entries in the n-th row of Pascal's triangle not divisible by 11.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "2", "4", "6", "8", "10", "12", "14", "16", "18", "20", "22", "3", "6", "9", "12", "15", "18", "21", "24", "27", "30", "33", "4", "8", "12", "16", "20", "24", "28", "32", "36", "40", "44", "5", "10", "15", "20", "25", "30", "35", "40", "45", "50", "55", "6", "12", "18", "24", "30", "36", "42", "48", "54", "60", "66", "7", "14", "21", "28", "35", "42", "49", "56", "63", "70", "77", "8", "16", "24", "32" ]
[ "nonn" ]
7
0
2
[ "A001316", "A006047", "A194459", "A382720", "A382721", "A382722" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T20:13:33
oeisdata/seq/A382/A382721.seq
44be03a897f9c4e44e1ebab3cdc76a58
A382722
Number of entries in the n-th row of Pascal's triangle not divisible by 13.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "2", "4", "6", "8", "10", "12", "14", "16", "18", "20", "22", "24", "26", "3", "6", "9", "12", "15", "18", "21", "24", "27", "30", "33", "36", "39", "4", "8", "12", "16", "20", "24", "28", "32", "36", "40", "44", "48", "52", "5", "10", "15", "20", "25", "30", "35", "40", "45", "50", "55", "60", "65", "6", "12", "18", "24", "30", "36", "42", "48", "54", "60", "66", "72", "78", "7", "14", "21" ]
[ "nonn" ]
7
0
2
[ "A001316", "A006047", "A194459", "A382720", "A382721", "A382722" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T20:13:52
oeisdata/seq/A382/A382722.seq
97226cdc5713189d4ed558d16f8b4116
A382723
Number of entries in the n-th row of Pascal's triangle not divisible by 4.
[ "1", "2", "3", "4", "3", "6", "6", "8", "3", "6", "8", "12", "6", "12", "12", "16", "3", "6", "8", "12", "8", "16", "16", "24", "6", "12", "16", "24", "12", "24", "24", "32", "3", "6", "8", "12", "8", "16", "16", "24", "8", "16", "20", "32", "16", "32", "32", "48", "6", "12", "16", "24", "16", "32", "32", "48", "12", "24", "32", "48", "24", "48", "48", "64", "3", "6", "8", "12", "8", "16", "16", "24", "8", "16", "20", "32", "16", "32", "32", "48", "8" ]
[ "nonn" ]
8
0
2
[ "A001316", "A006047", "A194459", "A382720", "A382723", "A382725" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T23:45:24
oeisdata/seq/A382/A382723.seq
b106dae4ef04499213be2831dbe448c7
A382724
Number of entries in the n-th row of Pascal's triangle not divisible by 6.
[ "1", "2", "3", "4", "4", "6", "5", "8", "9", "4", "6", "8", "6", "10", "14", "16", "12", "18", "5", "10", "11", "12", "16", "22", "11", "20", "27", "16", "10", "18", "18", "32", "12", "8", "14", "18", "6", "12", "16", "20", "18", "26", "18", "30", "36", "18", "24", "38", "14", "28", "38", "28", "38", "54", "17", "34", "15", "20", "26", "40", "23", "42", "45", "64", "12", "18", "14", "26", "36", "24", "38", "54", "11", "20", "29", "28", "38", "56", "37", "64", "81" ]
[ "nonn" ]
5
0
2
[ "A001316", "A006047", "A194459", "A382720", "A382724", "A382725" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T20:23:12
oeisdata/seq/A382/A382724.seq
ac4c93ff21329eece3c6d24da568a48d
A382725
Number of entries in the n-th row of Pascal's triangle not divisible by 8.
[ "1", "2", "3", "4", "5", "6", "7", "8", "5", "10", "9", "12", "11", "14", "14", "16", "5", "10", "13", "20", "13", "18", "20", "24", "11", "22", "20", "28", "22", "28", "28", "32", "5", "10", "13", "20", "17", "26", "28", "40", "13", "26", "26", "36", "28", "40", "40", "48", "11", "22", "28", "44", "28", "40", "44", "56", "22", "44", "40", "56", "44", "56", "56", "64", "5", "10", "13", "20", "17", "26", "28", "40", "17", "34", "34", "52", "36", "56", "56", "80", "13" ]
[ "nonn" ]
5
0
2
[ "A001316", "A006047", "A194459", "A382720", "A382724", "A382725" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T20:23:52
oeisdata/seq/A382/A382725.seq
ecf1b62069fba7845b01c77698b47927
A382726
Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 7.
[ "1", "3", "6", "10", "15", "21", "28", "30", "34", "40", "48", "58", "70", "84", "87", "93", "102", "114", "129", "147", "168", "172", "180", "192", "208", "228", "252", "280", "285", "295", "310", "330", "355", "385", "420", "426", "438", "456", "480", "510", "546", "588", "595", "609", "630", "658", "693", "735", "784", "786", "790", "796", "804", "814", "826", "840", "844", "852", "864", "880", "900", "924", "952", "958", "970", "988", "1012", "1042", "1078" ]
[ "nonn" ]
5
0
2
[ "A001316", "A006046", "A006048", "A194458", "A194459", "A382720", "A382726", "A382731" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T20:47:53
oeisdata/seq/A382/A382726.seq
37f290b8d86d645e627cea829c550e7d
A382727
Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 11.
[ "1", "3", "6", "10", "15", "21", "28", "36", "45", "55", "66", "68", "72", "78", "86", "96", "108", "122", "138", "156", "176", "198", "201", "207", "216", "228", "243", "261", "282", "306", "333", "363", "396", "400", "408", "420", "436", "456", "480", "508", "540", "576", "616", "660", "665", "675", "690", "710", "735", "765", "800", "840", "885", "935", "990", "996", "1008", "1026", "1050", "1080", "1116", "1158", "1206", "1260", "1320", "1386", "1393", "1407" ]
[ "nonn" ]
5
0
2
[ "A001316", "A006046", "A006048", "A194458", "A194459", "A382720", "A382727", "A382731" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T20:48:26
oeisdata/seq/A382/A382727.seq
9ce00bd605e9ecc90a48cb418304e389
A382728
Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 13.
[ "1", "3", "6", "10", "15", "21", "28", "36", "45", "55", "66", "78", "91", "93", "97", "103", "111", "121", "133", "147", "163", "181", "201", "223", "247", "273", "276", "282", "291", "303", "318", "336", "357", "381", "408", "438", "471", "507", "546", "550", "558", "570", "586", "606", "630", "658", "690", "726", "766", "810", "858", "910", "915", "925", "940", "960", "985", "1015", "1050", "1090", "1135", "1185", "1240", "1300", "1365", "1371", "1383", "1401" ]
[ "nonn" ]
5
0
2
[ "A001316", "A006046", "A006048", "A194458", "A194459", "A382720", "A382728", "A382731" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T20:48:53
oeisdata/seq/A382/A382728.seq
48381e8f1e2dc3b19b0fbd6057d0703f
A382729
Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 4.
[ "1", "3", "6", "10", "13", "19", "25", "33", "36", "42", "50", "62", "68", "80", "92", "108", "111", "117", "125", "137", "145", "161", "177", "201", "207", "219", "235", "259", "271", "295", "319", "351", "354", "360", "368", "380", "388", "404", "420", "444", "452", "468", "488", "520", "536", "568", "600", "648", "654", "666", "682", "706", "722", "754", "786", "834", "846", "870", "902", "950", "974", "1022", "1070", "1134", "1137", "1143", "1151" ]
[ "nonn" ]
3
0
2
[ "A001316", "A006046", "A006048", "A194458", "A194459", "A382720", "A382729", "A382731" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T20:51:20
oeisdata/seq/A382/A382729.seq
5466f8197e749955e81078827e0f9a72
A382730
Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 6.
[ "1", "3", "6", "10", "14", "20", "25", "33", "42", "46", "52", "60", "66", "76", "90", "106", "118", "136", "141", "151", "162", "174", "190", "212", "223", "243", "270", "286", "296", "314", "332", "364", "376", "384", "398", "416", "422", "434", "450", "470", "488", "514", "532", "562", "598", "616", "640", "678", "692", "720", "758", "786", "824", "878", "895", "929", "944", "964", "990", "1030", "1053", "1095", "1140", "1204", "1216", "1234", "1248", "1274" ]
[ "nonn" ]
3
0
2
[ "A001316", "A006046", "A006048", "A194458", "A194459", "A382720", "A382730", "A382731" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T20:53:17
oeisdata/seq/A382/A382730.seq
b0354a3ab65d1446e0f4138c8a307ac4
A382731
Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 8.
[ "1", "3", "6", "10", "15", "21", "28", "36", "41", "51", "60", "72", "83", "97", "111", "127", "132", "142", "155", "175", "188", "206", "226", "250", "261", "283", "303", "331", "353", "381", "409", "441", "446", "456", "469", "489", "506", "532", "560", "600", "613", "639", "665", "701", "729", "769", "809", "857", "868", "890", "918", "962", "990", "1030", "1074", "1130", "1152", "1196", "1236", "1292", "1336", "1392", "1448", "1512", "1517", "1527" ]
[ "nonn" ]
3
0
2
[ "A001316", "A006046", "A006048", "A194458", "A194459", "A382720", "A382730", "A382731" ]
null
N. J. A. Sloane, Apr 23 2025
2025-04-23T20:55:34
oeisdata/seq/A382/A382731.seq
8acf5240f87b107d5100f12114d04611
A382732
Number of proper hypercubic bipartitions of n.
[ "0", "0", "1", "1", "1", "2", "2", "1", "1", "2", "3", "3", "2", "2", "2", "1", "1", "2", "3", "3", "3", "4", "4", "3", "2", "2", "3", "3", "2", "2", "2", "1", "1", "2", "3", "3", "3", "4", "4", "3", "3", "4", "5", "5", "4", "4", "4", "3", "2", "2", "3", "3", "3", "4", "4", "3", "2", "2", "3", "3", "2", "2", "2", "1", "1", "2", "3", "3", "3", "4", "4", "3", "3", "4", "5", "5", "4", "4", "4", "3", "3", "4", "5", "5", "5", "6", "6", "5", "4", "4", "5", "5", "4", "4", "4", "3", "2", "2", "3", "3", "3" ]
[ "nonn" ]
56
0
6
[ "A000788", "A382732", "A382733" ]
null
Geir Agnarsson, Apr 03 2025
2025-04-17T09:38:42
oeisdata/seq/A382/A382732.seq
2e7f1f82dfb2cb0ac06d2ba8b26dca1e
A382733
Number of hypercubic bipartitions of n.
[ "1", "1", "2", "2", "2", "3", "3", "2", "2", "3", "4", "4", "3", "3", "3", "2", "2", "3", "4", "4", "4", "5", "5", "4", "3", "3", "4", "4", "3", "3", "3", "2", "2", "3", "4", "4", "4", "5", "5", "4", "4", "5", "6", "6", "5", "5", "5", "4", "3", "3", "4", "4", "4", "5", "5", "4", "3", "3", "4", "4", "3", "3", "3", "2", "2", "3", "4", "4", "4", "5", "5", "4", "4", "5", "6", "6", "5", "5", "5", "4", "4", "5", "6", "6", "6", "7", "7", "6", "5", "5", "6", "6", "5", "5", "5", "4", "3", "3", "4", "4" ]
[ "nonn" ]
30
0
3
[ "A000788", "A382732", "A382733" ]
null
Geir Agnarsson, Apr 03 2025
2025-04-17T08:09:18
oeisdata/seq/A382/A382733.seq
b0fadf0ddaa195b3192268bea3e80e62
A382734
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (exp(x) + exp(y) - exp(x+y))^2.
[ "1", "0", "0", "0", "2", "0", "0", "2", "2", "0", "0", "2", "14", "2", "0", "0", "2", "38", "38", "2", "0", "0", "2", "86", "254", "86", "2", "0", "0", "2", "182", "1118", "1118", "182", "2", "0", "0", "2", "374", "4142", "8654", "4142", "374", "2", "0", "0", "2", "758", "14078", "51662", "51662", "14078", "758", "2", "0", "0", "2", "1526", "45614", "267566", "467102", "267566", "45614", "1526", "2", "0" ]
[ "nonn", "tabl" ]
16
0
5
[ "A136126", "A371761", "A382734", "A382735", "A382736", "A382737", "A382740" ]
null
Seiichi Manyama, Apr 04 2025
2025-04-04T10:20:43
oeisdata/seq/A382/A382734.seq
980a939ca82aa8e6bd3e3121244f6e59
A382735
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (exp(x) + exp(y) - exp(x+y))^3.
[ "1", "0", "0", "0", "3", "0", "0", "3", "3", "0", "0", "3", "27", "3", "0", "0", "3", "75", "75", "3", "0", "0", "3", "171", "579", "171", "3", "0", "0", "3", "363", "2667", "2667", "363", "3", "0", "0", "3", "747", "10083", "22779", "10083", "747", "3", "0", "0", "3", "1515", "34635", "142923", "142923", "34635", "1515", "3", "0", "0", "3", "3051", "112899", "761211", "1396803", "761211", "112899", "3051", "3", "0" ]
[ "nonn", "tabl" ]
15
0
5
[ "A371761", "A382673", "A382734", "A382735", "A382736", "A382738", "A382741" ]
null
Seiichi Manyama, Apr 04 2025
2025-04-04T09:19:54
oeisdata/seq/A382/A382735.seq
8047b1989c79b92f5aed8105b9dd0f7b
A382736
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (exp(x) + exp(y) - exp(x+y))^4.
[ "1", "0", "0", "0", "4", "0", "0", "4", "4", "0", "0", "4", "44", "4", "0", "0", "4", "124", "124", "4", "0", "0", "4", "284", "1084", "284", "4", "0", "0", "4", "604", "5164", "5164", "604", "4", "0", "0", "4", "1244", "19804", "48044", "19804", "1244", "4", "0", "0", "4", "2524", "68524", "313804", "313804", "68524", "2524", "4", "0", "0", "4", "5084", "224284", "1707884", "3281404", "1707884", "224284", "5084", "4", "0" ]
[ "nonn", "tabl" ]
16
0
5
[ "A371761", "A382674", "A382734", "A382735", "A382736", "A382739", "A382742" ]
null
Seiichi Manyama, Apr 04 2025
2025-04-04T10:20:37
oeisdata/seq/A382/A382736.seq
c44d2cb2f8c7893392ca62e819f5fce9
A382737
a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling2(n,k)^2.
[ "1", "2", "14", "254", "8654", "467102", "36414734", "3862847774", "534433092494", "93409669590302", "20117959360842254", "5233190283794276894", "1617259866279958581134", "585633786711715561283102", "245587300036701328750786574", "118067003149791582488105955614", "64502003996859329263691323378574" ]
[ "nonn" ]
23
0
2
[ "A048144", "A382734", "A382737", "A382738", "A382739" ]
null
Seiichi Manyama, Apr 04 2025
2025-05-05T06:37:05
oeisdata/seq/A382/A382737.seq
0c9c0d32855151974ba56eb38eb1b96d
A382738
a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+2,2) * Stirling2(n,k)^2.
[ "1", "3", "27", "579", "22779", "1396803", "121998267", "14333812419", "2175860165499", "414000255441603", "96422983358827707", "26970211126038920259", "8918364340126714711419", "3440770498298077165166403", "1531504734740033368269820347", "778873986278207207346380124099" ]
[ "nonn" ]
16
0
2
[ "A048144", "A382676", "A382735", "A382737", "A382738", "A382739" ]
null
Seiichi Manyama, Apr 04 2025
2025-04-04T06:32:24
oeisdata/seq/A382/A382738.seq
21570cf04df1421f5e664fb4ab7219df
A382739
a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+3,3) * Stirling2(n,k)^2.
[ "1", "4", "44", "1084", "48044", "3281404", "316032044", "40592233084", "6687195379244", "1372291071723004", "342877475325619244", "102409872018962876284", "36014541870868393113644", "14724003012156426011095804", "6922777830859189006847193644", "3708347961746448904830944962684" ]
[ "nonn" ]
16
0
2
[ "A048144", "A382678", "A382736", "A382737", "A382738", "A382739" ]
null
Seiichi Manyama, Apr 04 2025
2025-04-04T06:32:48
oeisdata/seq/A382/A382739.seq
84df3f47477df92ab86cb8d7fe55298a
A382740
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/2) * (1 / (exp(x) + exp(y) - exp(x+y))^2 - 1).
[ "1", "1", "1", "1", "7", "1", "1", "19", "19", "1", "1", "43", "127", "43", "1", "1", "91", "559", "559", "91", "1", "1", "187", "2071", "4327", "2071", "187", "1", "1", "379", "7039", "25831", "25831", "7039", "379", "1", "1", "763", "22807", "133783", "233551", "133783", "22807", "763", "1", "1", "1531", "71839", "636679", "1748791", "1748791", "636679", "71839", "1531", "1" ]
[ "nonn", "tabl" ]
12
1
5
[ "A272644", "A382734", "A382740", "A382741", "A382742" ]
null
Seiichi Manyama, Apr 04 2025
2025-04-04T06:32:55
oeisdata/seq/A382/A382740.seq
8ae79e560e3987f4773afb963af31f21
A382741
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/3) * (1 / (exp(x) + exp(y) - exp(x+y))^3 - 1).
[ "1", "1", "1", "1", "9", "1", "1", "25", "25", "1", "1", "57", "193", "57", "1", "1", "121", "889", "889", "121", "1", "1", "249", "3361", "7593", "3361", "249", "1", "1", "505", "11545", "47641", "47641", "11545", "505", "1", "1", "1017", "37633", "253737", "465601", "253737", "37633", "1017", "1", "1", "2041", "118969", "1228249", "3657721", "3657721", "1228249", "118969", "2041", "1" ]
[ "nonn", "tabl" ]
10
1
5
[ "A272644", "A382735", "A382740", "A382741", "A382742" ]
null
Seiichi Manyama, Apr 04 2025
2025-04-04T06:31:21
oeisdata/seq/A382/A382741.seq
66319b01cd1b046e34be20c0ff404304
A382742
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/4) * (1 / (exp(x) + exp(y) - exp(x+y))^4 - 1).
[ "1", "1", "1", "1", "11", "1", "1", "31", "31", "1", "1", "71", "271", "71", "1", "1", "151", "1291", "1291", "151", "1", "1", "311", "4951", "12011", "4951", "311", "1", "1", "631", "17131", "78451", "78451", "17131", "631", "1", "1", "1271", "56071", "426971", "820351", "426971", "56071", "1271", "1", "1", "2551", "177691", "2093491", "6709651", "6709651", "2093491", "177691", "2551", "1" ]
[ "nonn", "tabl" ]
10
1
5
[ "A272644", "A382736", "A382740", "A382741", "A382742" ]
null
Seiichi Manyama, Apr 04 2025
2025-04-04T06:31:14
oeisdata/seq/A382/A382742.seq
99e33b27dec35cd9206c677592d098f3
A382743
Number of minimum total dominating sets in the n X n fiveleaper graph.
[ "0", "0", "0", "0", "0", "0", "0", "16", "16", "100", "40" ]
[ "nonn", "more" ]
4
1
8
null
null
Eric W. Weisstein, Apr 04 2025
2025-04-04T10:16:29
oeisdata/seq/A382/A382743.seq
da17723f82dd9525e09ea7251ae1ac88
A382744
If k appears, 5*k does not.
[ "1", "2", "3", "4", "6", "7", "8", "9", "11", "12", "13", "14", "16", "17", "18", "19", "21", "22", "23", "24", "25", "26", "27", "28", "29", "31", "32", "33", "34", "36", "37", "38", "39", "41", "42", "43", "44", "46", "47", "48", "49", "50", "51", "52", "53", "54", "56", "57", "58", "59", "61", "62", "63", "64", "66", "67", "68", "69", "71", "72", "73", "74", "75", "76", "77", "78", "79", "81", "82", "83", "84" ]
[ "nonn" ]
39
1
2
[ "A003159", "A007417", "A382744", "A382745", "A382746" ]
null
Jan Snellman, Apr 04 2025
2025-04-11T03:33:33
oeisdata/seq/A382/A382744.seq
c8526ec9f298887160e13d033858f584
A382745
If k appears, 7*k does not.
[ "1", "2", "3", "4", "5", "6", "8", "9", "10", "11", "12", "13", "15", "16", "17", "18", "19", "20", "22", "23", "24", "25", "26", "27", "29", "30", "31", "32", "33", "34", "36", "37", "38", "39", "40", "41", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "57", "58", "59", "60", "61", "62", "64", "65", "66", "67", "68", "69", "71", "72", "73", "74", "75", "76", "78", "79", "80", "81", "82", "83", "85" ]
[ "nonn", "easy" ]
32
1
2
[ "A003159", "A007417", "A382744", "A382745", "A382746" ]
null
Jan Snellman, Apr 04 2025
2025-04-11T03:34:38
oeisdata/seq/A382/A382745.seq
8c60c6fd75239371c48fa1288653dc88
A382746
If k appears, 8*k does not.
[ "1", "2", "3", "4", "5", "6", "7", "9", "10", "11", "12", "13", "14", "15", "17", "18", "19", "20", "21", "22", "23", "25", "26", "27", "28", "29", "30", "31", "33", "34", "35", "36", "37", "38", "39", "41", "42", "43", "44", "45", "46", "47", "49", "50", "51", "52", "53", "54", "55", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70", "71", "73", "74", "75", "76", "77", "78", "79" ]
[ "nonn", "easy" ]
35
1
2
[ "A003159", "A007417", "A382744", "A382745", "A382746" ]
null
Jan Snellman, Apr 04 2025
2025-05-31T06:49:54
oeisdata/seq/A382/A382746.seq
8b226903aa0655742589f71c0be6fdb8
A382747
Greedy partition of the positive integers into arithmetic progressions of length at most 4.
[ "1", "2", "3", "4", "5", "10", "15", "20", "6", "12", "18", "24", "7", "14", "21", "28", "8", "16", "0", "0", "9", "0", "0", "0", "11", "22", "33", "44", "13", "26", "39", "52", "17", "34", "51", "68", "19", "38", "57", "76", "23", "46", "69", "92", "25", "50", "75", "100", "27", "54", "81", "108", "29", "58", "87", "116", "30", "60", "90", "120", "31", "62", "93", "124", "32", "64", "96", "128", "35", "70", "105", "140", "36", "72", "0", "0", "37", "74", "111", "148", "40", "80", "0", "0" ]
[ "nonn", "tabf", "easy" ]
44
1
2
[ "A036552", "A382747", "A382748", "A382749" ]
null
Jan Snellman, Apr 23 2025
2025-05-12T10:13:48
oeisdata/seq/A382/A382747.seq
1898bbe3ff9cbd581c975ae554783e17
A382748
Primitive exponents for the greedy convolution of length 4.
[ "1", "5", "6", "7", "8", "9", "11", "13", "17", "19", "23", "25", "27", "29", "30", "31", "32", "35", "36", "37", "40", "41", "42", "43", "45", "47", "48", "49", "53", "55", "56", "59", "61", "63", "65", "66", "67", "71", "73", "77", "78", "79", "83", "85", "88", "89", "91", "95", "97", "99", "101", "102", "103", "104", "107", "109", "113", "114", "115", "117", "119", "121", "125", "127", "131", "133", "135", "136", "137", "138", "139" ]
[ "nonn", "easy" ]
26
1
2
[ "A121537", "A382747", "A382748" ]
null
Jan Snellman, Apr 24 2025
2025-05-14T13:27:31
oeisdata/seq/A382/A382748.seq
76d111d2ea6ddcf420f85881cdc39301
A382749
Position in block for greedy partition of length 4.
[ "1", "2", "3", "4", "1", "1", "1", "1", "1", "2", "1", "2", "1", "2", "3", "2", "1", "3", "1", "4", "3", "2", "1", "4", "1", "2", "1", "4", "1", "1", "1", "1", "3", "2", "1", "1", "1", "2", "3", "1", "1", "1", "1", "4", "1", "2", "1", "1", "1", "2", "3", "4", "1", "2", "1", "1", "3", "2", "1", "2", "1", "2", "1", "2", "1", "1", "1", "4", "3", "2", "1", "2", "1", "2", "3", "4", "1", "1", "1", "2", "3", "2", "1", "2", "1", "2", "3", "1", "1", "3", "1", "4", "3", "2", "1", "3", "1", "2", "1", "4" ]
[ "nonn" ]
17
1
2
[ "A382747", "A382748", "A382749" ]
null
Jan Snellman, Apr 24 2025
2025-05-05T19:41:30
oeisdata/seq/A382/A382749.seq
26d3613ddfd27aa7a077383546828e58
A382750
If k appears, 9*k does not.
[ "1", "2", "3", "4", "5", "6", "7", "8", "10", "11", "12", "13", "14", "15", "16", "17", "19", "20", "21", "22", "23", "24", "25", "26", "28", "29", "30", "31", "32", "33", "34", "35", "37", "38", "39", "40", "41", "42", "43", "44", "46", "47", "48", "49", "50", "51", "52", "53", "55", "56", "57", "58", "59", "60", "61", "62", "64", "65", "66", "67", "68", "69", "70", "71", "73", "74", "75", "76", "77", "78", "79", "80", "81" ]
[ "nonn", "easy" ]
58
1
2
[ "A003159", "A007417", "A382744", "A382745", "A382746", "A382750" ]
null
Jan Snellman, May 09 2025
2025-05-26T11:47:01
oeisdata/seq/A382/A382750.seq
61fbc49d2fddcf61fb3c583cd0730e55
A382752
Numbers k such that A000005(k) = A065295(k).
[ "6", "7", "8", "9", "10", "13", "19", "23", "29", "32", "37", "47", "54", "71", "109", "149", "167", "173", "223", "229", "263", "283", "359", "383", "479", "503", "509", "653", "659", "719", "739", "773", "839", "863", "887", "971", "983", "1229", "1319", "1367", "1439", "1487", "1493", "1637", "1699", "1823", "1949", "1997", "2039", "2063", "2207", "2309", "2411", "2447" ]
[ "nonn" ]
16
1
1
[ "A000005", "A065295", "A382752" ]
null
Juri-Stepan Gerasimov, Jun 02 2025
2025-06-09T17:20:38
oeisdata/seq/A382/A382752.seq
e2f24c21e969f0459528ca5018c0c688
A382753
Expansion of e.g.f. 3/(5 - 2*exp(3*x)).
[ "1", "2", "14", "138", "1806", "29562", "580734", "13309578", "348611886", "10272416922", "336326121054", "12112707922218", "475894244100366", "20255443904321082", "928448378212678974", "45597074777924954058", "2388608236671667179246", "132947999835258872046042", "7835059049893316949502494" ]
[ "nonn" ]
18
0
2
[ "A004123", "A094417", "A201367", "A216794", "A326324", "A382753", "A384435", "A384521" ]
null
Seiichi Manyama, Jun 03 2025
2025-06-03T08:43:08
oeisdata/seq/A382/A382753.seq
eb78a016cf043f490cf914b2ecd98459
A382754
List of unlabeled simple graphs, encoded as integers (see comments).
[ "0", "1", "2", "3", "8", "9", "11", "15", "64", "65", "67", "71", "75", "76", "77", "79", "94", "95", "127", "1024", "1025", "1027", "1031", "1039", "1043", "1044", "1045", "1047", "1052", "1053", "1055", "1078", "1079", "1082", "1083", "1086", "1087", "1150", "1151", "1207", "1208", "1209", "1211", "1215", "1231", "1244", "1245", "1247", "1278", "1279", "1519", "1535", "2047" ]
[ "nonn", "tabf" ]
7
0
3
[ "A000088", "A000120", "A000523", "A002024", "A076184", "A382754", "A382755", "A382756", "A382757", "A382758", "A382759", "A382760", "A382761", "A382762", "A382763", "A382764" ]
null
Pontus von Brömssen, Apr 04 2025
2025-04-06T15:03:43
oeisdata/seq/A382/A382754.seq
69b2322fbdc7b6c25818c221198aa511
A382755
Irregular triangle read by rows: Let k encode the edges of an n-vertex graph by taking edges (u,v), with u < v, in lexicographic order ((0,1), ..., (0,n-1), (1,2), ..., (1,n-1), ..., (n-1,n)) and adding each edge to the graph if the corresponding binary digit of k (starting with the least significant digit) is 1. T(n,k) is the smallest nonnegative integer that encodes the same unlabeled n-vertex graph as k, 0 <= k < n*(n-1)/2.
[ "0", "0", "0", "1", "0", "1", "1", "3", "1", "3", "3", "7", "0", "1", "1", "3", "1", "3", "3", "7", "1", "3", "3", "11", "12", "13", "13", "15", "1", "3", "12", "13", "3", "11", "13", "15", "3", "7", "13", "15", "13", "15", "30", "31", "1", "12", "3", "13", "3", "13", "11", "15", "3", "13", "7", "15", "13", "30", "15", "31", "3", "13", "13", "30", "7", "15", "15", "31", "11", "15", "15", "31", "15", "31", "31", "63" ]
[ "nonn", "tabf" ]
5
0
8
[ "A382281", "A382754", "A382755" ]
null
Pontus von Brömssen, Apr 04 2025
2025-04-06T15:03:55
oeisdata/seq/A382/A382755.seq
f56f96253bac9b338846c64cc79697d2
A382756
a(n) is the graph corresponding to A076184(n), encoded as in A382754.
[ "1", "3", "11", "15", "71", "76", "77", "79", "94", "95", "127", "1039", "1052", "1053", "1055", "1082", "1083", "1086", "1087", "1208", "1209", "1211", "1215", "1150", "1151", "1231", "1244", "1245", "1247", "1278", "1279", "1519", "1535", "2047", "32799", "32828", "32829", "32831", "32888", "32889", "32890", "32891", "32894", "32895", "33400" ]
[ "nonn", "tabf" ]
4
1
2
[ "A002494", "A076184", "A382754", "A382756", "A382757" ]
null
Pontus von Brömssen, Apr 04 2025
2025-04-06T15:04:08
oeisdata/seq/A382/A382756.seq
04ef9e5daf5c3a84bf33c08e55176ddd
A382757
a(n) is the graph corresponding to A382754(n), encoded as in A076184.
[ "0", "0", "1", "0", "1", "3", "7", "0", "1", "3", "11", "7", "12", "13", "15", "30", "31", "63", "0", "1", "3", "11", "75", "7", "12", "13", "15", "76", "77", "79", "30", "31", "86", "87", "94", "95", "222", "223", "63", "116", "117", "119", "127", "235", "236", "237", "239", "254", "255", "507", "511", "1023", "0", "1", "3", "11", "75", "1099", "7", "12", "13", "15", "76", "77", "79" ]
[ "nonn", "tabf" ]
4
1
6
[ "A000088", "A076184", "A382754", "A382756", "A382757" ]
null
Pontus von Brömssen, Apr 04 2025
2025-04-06T15:04:17
oeisdata/seq/A382/A382757.seq
d3afccf246788068d98452043454de80
A382758
Number of edges of the graph encoded by A382754(n).
[ "0", "0", "0", "1", "0", "1", "2", "3", "0", "1", "2", "3", "3", "2", "3", "4", "4", "5", "6", "0", "1", "2", "3", "4", "3", "2", "3", "4", "3", "4", "5", "4", "5", "4", "5", "5", "6", "6", "7", "6", "4", "5", "6", "7", "6", "5", "6", "7", "7", "8", "8", "9", "10", "0", "1", "2", "3", "4", "5", "3", "2", "3", "4", "3", "4", "5", "4", "5", "6", "4", "5", "4", "5", "5", "6", "4", "5", "5", "6", "6", "7", "6", "7", "6", "7", "7", "8" ]
[ "nonn", "tabf" ]
4
0
7
[ "A000088", "A000120", "A382191", "A382754", "A382758" ]
null
Pontus von Brömssen, Apr 04 2025
2025-04-06T15:04:26
oeisdata/seq/A382/A382758.seq
5c50b0aeaeeac9dbf6fb62eb88eb2035
A382759
Number of connected components of the graph encoded by A382754(n).
[ "0", "1", "2", "1", "3", "2", "1", "1", "4", "3", "2", "1", "2", "2", "1", "1", "1", "1", "1", "5", "4", "3", "2", "1", "3", "3", "2", "2", "2", "1", "1", "2", "2", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "6", "5", "4", "3", "2", "1", "4", "4", "3", "3", "3", "2", "2", "2", "1", "1", "3", "3", "2", "2", "2", "2", "2", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1" ]
[ "nonn", "tabf" ]
4
0
3
[ "A000088", "A382192", "A382754", "A382759" ]
null
Pontus von Brömssen, Apr 04 2025
2025-04-06T15:04:33
oeisdata/seq/A382/A382759.seq
0fb691788b3c642153a7205aa926dc65
A382760
Independence number of the graph encoded by A382754(n).
[ "0", "1", "2", "1", "3", "2", "2", "1", "4", "3", "3", "3", "2", "2", "2", "2", "2", "2", "1", "5", "4", "4", "4", "4", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "1", "6", "5", "5", "5", "5", "5", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4" ]
[ "nonn", "tabf" ]
6
0
3
[ "A000088", "A002024", "A065120", "A382754", "A382760" ]
null
Pontus von Brömssen, Apr 04 2025
2025-04-06T15:04:41
oeisdata/seq/A382/A382760.seq
bf5370ef22969e9762685cd1ad82a554
A382761
List of graphs that are squares, encoded as in A382754.
[ "0", "1", "2", "3", "8", "9", "15", "64", "65", "75", "76", "95", "127", "1024", "1025", "1043", "1044", "1079", "1207", "1208", "1247", "1279", "1535", "2047", "32768", "32769", "32803", "32804", "32871", "33383", "33384", "33424", "33455", "33519", "33689", "34543", "34687", "36863", "38639", "38640", "38673", "38711", "38719", "38783", "38911", "39423", "39935", "40959", "48638", "48639", "49151", "65535" ]
[ "nonn", "tabf" ]
5
0
3
[ "A382181", "A382194", "A382754", "A382761", "A382762", "A382763" ]
null
Pontus von Brömssen, Apr 05 2025
2025-04-06T15:04:50
oeisdata/seq/A382/A382761.seq
fc86078c36004e045b389fb992b1af75
A382762
List of graphs that are squares, encoded by their indices in A382754.
[ "0", "1", "2", "3", "4", "5", "7", "8", "9", "12", "13", "17", "18", "19", "20", "24", "25", "32", "39", "40", "47", "49", "51", "52", "53", "54", "59", "60", "70", "89", "90", "99", "107", "117", "127", "144", "160", "170", "171", "172", "177", "182", "186", "191", "193", "195", "201", "204", "205", "206", "207", "208" ]
[ "nonn", "tabf" ]
4
0
3
[ "A382181", "A382194", "A382754", "A382761", "A382762", "A382764" ]
null
Pontus von Brömssen, Apr 05 2025
2025-04-10T06:47:18
oeisdata/seq/A382/A382762.seq
f86530a5a5af6163a3e05d8070360466
A382763
a(n) is the code (in the encoding given by A382754) of the square of the graph with code A382754(n).
[ "0", "1", "2", "3", "8", "9", "15", "15", "64", "65", "75", "127", "75", "76", "95", "127", "127", "127", "127", "1024", "1025", "1043", "1207", "2047", "1043", "1044", "1079", "1207", "1208", "1279", "2047", "1207", "1207", "1247", "1535", "1535", "2047", "2047", "2047", "1207", "1208", "1279", "1535", "2047", "2047", "2047", "2047", "2047", "2047", "2047", "2047", "2047", "2047" ]
[ "nonn", "tabf" ]
5
0
3
[ "A000088", "A382195", "A382754", "A382761", "A382763", "A382764" ]
null
Pontus von Brömssen, Apr 05 2025
2025-04-10T06:47:32
oeisdata/seq/A382/A382763.seq
e58a0f2f0097ae3c9dda98156fbc3ce2
A382764
a(n) is the index in A382754 of the square of the graph with code A382754(n).
[ "0", "1", "2", "3", "4", "5", "7", "7", "8", "9", "12", "18", "12", "13", "17", "18", "18", "18", "18", "19", "20", "24", "39", "52", "24", "25", "32", "39", "40", "49", "52", "39", "39", "47", "51", "51", "52", "52", "52", "39", "40", "49", "51", "52", "52", "52", "52", "52", "52", "52", "52", "52", "52" ]
[ "nonn", "tabf" ]
4
0
3
[ "A000088", "A382195", "A382754", "A382762", "A382763", "A382764" ]
null
Pontus von Brömssen, Apr 05 2025
2025-04-10T06:47:39
oeisdata/seq/A382/A382764.seq
07be2f9760a88c747b93f4276a4d9d07
A382765
Primes that can be expressed using exactly one of each of the prime digits 2, 3, 5, 7, using concatenation and the arithmetic operations +,-,*,/,^.
[ "2", "3", "5", "7", "11", "13", "17", "19", "23", "29", "31", "37", "41", "43", "47", "53", "59", "61", "67", "71", "73", "79", "83", "89", "103", "107", "113", "139", "149", "151", "163", "167", "173", "181", "197", "211", "223", "227", "229", "257", "263", "311", "353", "359", "367", "373", "379", "389", "479", "569", "571", "643", "691", "727", "733", "751", "877", "1019", "1091", "1699", "2239", "2357", "2749", "2753" ]
[ "nonn", "base", "fini", "full" ]
32
1
1
[ "A382765", "A382901" ]
null
Zak Seidov and Robert Israel, Apr 10 2025
2025-04-17T09:51:15
oeisdata/seq/A382/A382765.seq
a60a16e4405b5ffe904cd52760e9a82e
A382766
Odd primes p such that p + 4, p + 6 and p + 8 are composite.
[ "113", "137", "139", "179", "181", "197", "199", "211", "239", "241", "281", "283", "293", "317", "337", "409", "419", "421", "467", "509", "521", "523", "547", "577", "617", "619", "631", "659", "661", "691", "709", "773", "787", "797", "809", "811", "827", "829", "839", "863", "887", "919", "953", "997", "1019", "1021", "1039", "1049", "1051", "1069" ]
[ "nonn" ]
42
1
1
[ "A049591", "A067774", "A083371", "A124582", "A382765", "A382766" ]
null
Michel Eduardo Beleza Yamagishi, Apr 04 2025
2025-05-29T06:28:36
oeisdata/seq/A382/A382766.seq
611c4daa70c3d762389839b96b7fc147
A382767
Smallest number k that is powerful but not a prime power that is also coprime to n.
[ "36", "225", "100", "225", "36", "1225", "36", "225", "100", "441", "36", "1225", "36", "225", "196", "225", "36", "1225", "36", "441", "100", "225", "36", "1225", "36", "225", "100", "225", "36", "5929", "36", "225", "100", "225", "36", "1225", "36", "225", "100", "441", "36", "3025", "36", "225", "196", "225", "36", "1225", "36", "441", "100", "225", "36", "1225" ]
[ "nonn", "easy" ]
8
1
1
[ "A002110", "A007947", "A053669", "A286708", "A380539", "A381805", "A382248", "A382767" ]
null
Michael De Vlieger, Apr 04 2025
2025-04-05T10:58:23
oeisdata/seq/A382/A382767.seq
2e749809498da608f071cdd7b110af51
A382768
Number of k < n that are coprime to n and neither squarefree nor prime powers.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "2", "0", "1", "0", "3", "0", "3", "0", "1", "0", "5", "0", "5", "0", "2", "0", "3", "0", "6", "0", "2", "0", "7", "0", "7", "0", "2", "1", "9", "0", "9", "0", "5", "1", "12", "0", "8", "1", "7", "1", "14", "0", "15", "1", "5", "2", "10", "0", "16", "2", "8", "0", "17", "0", "18", "2", "5", "3", "16", "0", "20", "1", "10", "3", "21", "0" ]
[ "nonn", "easy" ]
8
1
19
[ "A002110", "A073311", "A126706", "A139555", "A382248", "A382768" ]
null
Michael De Vlieger, Apr 04 2025
2025-04-22T09:00:47
oeisdata/seq/A382/A382768.seq
88088e5db6bf4b068a7426fe1bca9636
A382769
Largest k < n such that gcd(k,n) > 1 and rad(k) does not divide n, where rad = A007947, or 0 if k does not exist.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "6", "0", "10", "0", "12", "12", "0", "0", "15", "0", "18", "18", "20", "0", "22", "0", "24", "0", "26", "0", "28", "0", "0", "30", "30", "30", "34", "0", "36", "36", "38", "0", "40", "0", "42", "42", "44", "0", "46", "0", "48", "48", "50", "0", "52", "50", "54", "54", "56", "0", "58", "0", "60", "60", "0", "60", "63", "0", "66", "66", "68", "0", "70", "0", "72" ]
[ "nonn", "easy" ]
4
1
10
[ "A000961", "A024619", "A096014", "A272619", "A382769" ]
null
Michael De Vlieger, Apr 04 2025
2025-04-05T10:58:53
oeisdata/seq/A382/A382769.seq
df633f3783264bfacaf15467d8485d52
A382770
Number of powerful k < n such that k and n are coprime.
[ "0", "1", "1", "1", "2", "1", "2", "1", "3", "2", "4", "1", "4", "2", "3", "2", "5", "1", "5", "2", "4", "2", "5", "1", "5", "3", "5", "4", "7", "1", "7", "4", "6", "4", "7", "2", "9", "4", "6", "3", "9", "2", "9", "4", "5", "4", "9", "2", "9", "4", "7", "5", "10", "3", "9", "4", "7", "5", "10", "2", "10", "5", "6", "5", "10", "3", "11", "5", "8", "3", "11", "3", "12", "5", "7", "5", "11", "3", "12", "4", "8", "6", "13", "2" ]
[ "nonn", "easy" ]
7
1
5
[ "A001694", "A304574", "A382770" ]
null
Michael De Vlieger, Apr 05 2025
2025-04-12T12:46:18
oeisdata/seq/A382/A382770.seq
79707dc6218b25a276946e2cb0c146e0
A382771
Number of ways to permute the prime indices of n so that the run-lengths are all different.
[ "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "2", "1", "0", "0", "1", "1", "2", "1", "2", "0", "0", "1", "2", "1", "0", "1", "2", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "2", "1", "0", "1", "2", "2", "0", "1", "2", "1", "2", "0", "2", "1", "2", "0", "2", "0", "0", "1", "0", "1", "0", "2", "1", "0", "0", "1", "2", "0", "0", "1", "2", "1", "0", "2", "2", "0", "0", "1", "2", "1", "0", "1", "0", "0", "0", "0" ]
[ "nonn" ]
16
1
12
[ "A000720", "A000961", "A001221", "A001222", "A003242", "A044813", "A048767", "A051903", "A051904", "A055396", "A056239", "A061395", "A098859", "A112798", "A130091", "A238130", "A239455", "A242882", "A329738", "A329739", "A335407", "A351013", "A351202", "A351293", "A351294", "A351295", "A351596", "A353744", "A381432", "A381433", "A382771", "A382772", "A382773", "A382774", "A382857", "A382858", "A382876", "A382877", "A382878", "A382879", "A383113" ]
null
Gus Wiseman, Apr 07 2025
2025-04-21T10:47:19
oeisdata/seq/A382/A382771.seq
052b93fa0d2e49610dd459f73dad2650
A382772
Set of positions of first appearances in A382771 (permutations of prime indices with distinct run-lengths).
[ "1", "6", "12", "96", "360", "1536", "3456", "5184", "5760", "6144", "7776", "13824", "23040", "24576", "55296", "62208", "92160" ]
[ "nonn", "more" ]
7
1
2
[ "A000720", "A001221", "A001222", "A003242", "A044813", "A048767", "A055396", "A056239", "A061395", "A098859", "A112798", "A130091", "A140690", "A164707", "A238130", "A239455", "A242882", "A305936", "A328592", "A329738", "A329739", "A351013", "A351202", "A351293", "A351294", "A351295", "A351596", "A353744", "A381432", "A381433", "A382771", "A382772", "A382773", "A382857", "A382876", "A382878", "A382879" ]
null
Gus Wiseman, Apr 09 2025
2025-04-09T23:39:22
oeisdata/seq/A382/A382772.seq
ce6d231bd13f6c57f035ba1169f847ff
A382773
Number of ways to permute a multiset whose multiplicities are the prime indices of n so that the run-lengths are all different.
[ "1", "1", "1", "0", "1", "2", "1", "0", "0", "2", "1", "0", "1", "2", "2", "0", "1", "0", "1", "0", "4", "4", "1", "0", "4", "4", "0", "0", "1", "6", "1", "0", "4", "6", "4", "0", "1", "6", "4", "0", "1", "6", "1", "0", "0", "8", "1", "0", "4", "0", "6", "0", "1", "0", "6", "0", "6", "8", "1", "0", "1", "10", "0", "0", "8", "6", "1", "0", "8", "6", "1", "0", "1", "10", "0", "0", "6", "6", "1", "0", "0", "12", "1", "0", "16" ]
[ "nonn" ]
7
1
6
[ "A000670", "A000720", "A003242", "A008578", "A044813", "A048767", "A055396", "A056239", "A061395", "A098859", "A112798", "A130091", "A140690", "A181821", "A238130", "A239455", "A242882", "A305936", "A329738", "A329739", "A335125", "A335407", "A351013", "A351202", "A351293", "A351294", "A351295", "A351596", "A353744", "A381432", "A381433", "A382771", "A382772", "A382773", "A382774", "A382857", "A382858", "A382876", "A382879", "A382912", "A382913" ]
null
Gus Wiseman, Apr 09 2025
2025-04-09T23:39:26
oeisdata/seq/A382/A382773.seq
49d3696dd4db07de054d7373166d0f7e
A382774
Number of ways to permute the prime indices of n! so that the run-lengths are all different.
[ "1", "1", "1", "0", "2", "0", "6", "0", "0", "0", "96", "0" ]
[ "nonn", "more" ]
8
0
5
[ "A000142", "A000720", "A001221", "A001222", "A003242", "A022559", "A044813", "A048767", "A056239", "A081401", "A098859", "A112798", "A130091", "A140690", "A164707", "A181821", "A239455", "A242882", "A328592", "A329738", "A329739", "A335125", "A335407", "A351013", "A351202", "A351293", "A351294", "A351295", "A351596", "A353744", "A360015", "A381432", "A381433", "A382771", "A382773", "A382774", "A382857", "A382858", "A382879" ]
null
Gus Wiseman, Apr 09 2025
2025-04-10T23:22:43
oeisdata/seq/A382/A382774.seq
6599ffa2ea4f437fa1d9ce460f27eddc
A382775
Least number appearing n times in A048767 (rank of Look-and-Say partition of prime indices).
[ "6", "1", "8", "32", "64", "128", "256", "6144", "512", "27648", "1024", "73728", "2048", "147456", "165888", "4096", "248832", "196608", "8192", "497664", "1119744", "393216", "16384", "2239488" ]
[ "nonn", "more" ]
6
0
1
[ "A003557", "A047966", "A048767", "A048768", "A051903", "A051904", "A055396", "A056239", "A061395", "A066328", "A071178", "A112798", "A116861", "A122111", "A130091", "A217605", "A239455", "A239964", "A351293", "A351294", "A351295", "A381431", "A381432", "A381433", "A381436", "A381440", "A381540", "A382525", "A382775" ]
null
Gus Wiseman, Apr 11 2025
2025-04-13T21:08:57
oeisdata/seq/A382/A382775.seq
ef98fe7d63c2f23b9d95918e45836c43
A382776
Triangle read by rows: T(n,k) is the number of ways to place 2*n rooks on a (n+k) X (2*n-k) board so that there is at least one rook in every column and row and so that each rook is defended by another.
[ "1", "1", "1", "6", "9", "6", "90", "180", "180", "90", "2520", "6300", "8100", "6300", "2520", "113400", "340200", "529200", "529200", "340200", "113400", "7484400", "26195400", "47628000", "57153600", "47628000", "26195400", "7484400", "681080400", "2724321600", "5658206400", "7858620000", "7858620000", "5658206400", "2724321600", "681080400" ]
[ "nonn", "tabl" ]
13
0
4
[ "A000680", "A382776", "A382777" ]
null
Andrew Howroyd, Apr 04 2025
2025-04-05T12:01:44
oeisdata/seq/A382/A382776.seq
9ae4c510d4a3da46d8be2dbb9119157b
A382777
Number of minimum total dominating sets in the (3n)-triangular honeycomb bishop graph.
[ "1", "2", "21", "540", "25740", "1965600", "219769200", "33844456800", "6868433880000", "1776393899280000", "570349326947400000", "222585024290428800000", "103769138324197906560000", "56957727035726406489600000", "36357688414546530128697600000", "26705308554813693259046592000000", "22364482036994885663848836864000000" ]
[ "nonn" ]
6
0
2
[ "A304564", "A382776", "A382777" ]
null
Andrew Howroyd, Apr 04 2025
2025-04-05T12:01:48
oeisdata/seq/A382/A382777.seq
f1298391a961cab610fb6bdccd8fb3cd
A382778
Decimal expansion of 6*log(3)/(3*log(3) - 3).
[ "2", "2", "2", "8", "1", "4", "4", "7", "9", "5", "1", "4", "9", "4", "3", "2", "1", "5", "6", "0", "3", "9", "6", "2", "0", "6", "7", "4", "1", "5", "8", "5", "8", "5", "3", "2", "3", "3", "4", "6", "8", "9", "2", "4", "9", "0", "7", "8", "1", "5", "0", "1", "3", "5", "9", "1", "8", "8", "5", "6", "5", "3", "2", "7", "9", "8", "9", "9", "4", "6", "4", "4", "9", "3", "5", "9", "3", "4", "0", "1", "4", "5", "4", "5", "5", "6", "3", "5", "2", "3", "0", "4", "4", "7", "4", "9", "9", "4", "4", "6" ]
[ "nonn", "cons" ]
10
2
1
[ "A002391", "A016650", "A382497", "A382778", "A383822", "A383824" ]
null
Stefano Spezia, May 11 2025
2025-05-12T00:26:28
oeisdata/seq/A382/A382778.seq
e41fcd525f42dee85ecd31128fc6972c
A382779
a(n) = Sum_{0<=i<=k<=n} 2^(4*(n-k)) * binomial(2*i,i)^2 * binomial(2*n-2*i,n-i) * binomial(2*k-2*i,k-i) * binomial(2*k,k)^2 * binomial(2*n-2*k,n-k).
[ "1", "96", "14944", "2743296", "547115616", "114691716096", "24855999978496", "5516395226824704", "1246310097807086176", "285511424277840331776", "66136775263705972306944", "15459962390271174936920064", "3641349843333453310791883776", "863175698505287814277639471104", "205741271729612742942836920909824" ]
[ "nonn" ]
13
0
2
[ "A000984", "A001025", "A002894", "A106187", "A382779" ]
null
Stefano Spezia, May 11 2025
2025-05-22T20:57:18
oeisdata/seq/A382/A382779.seq
32baf364a64af68f02843d8e2e596e2a
A382780
Sum of the orders of all permutations of [n] with distinct cycle lengths.
[ "1", "1", "2", "12", "48", "360", "2520", "22680", "221760", "2298240", "28425600", "385862400", "5269017600", "80951270400", "1347631084800", "21565729785600", "413922526617600", "8409043612569600", "172028224598630400", "3765253760710041600", "84080417596471296000", "1935910813364656128000" ]
[ "nonn" ]
13
0
3
[ "A000142", "A000793", "A007838", "A060014", "A382780", "A382781" ]
null
Alois P. Heinz, May 11 2025
2025-05-13T11:21:24
oeisdata/seq/A382/A382780.seq
c7b547b81d0ee2dd527a4d7859f4b20a
A382781
Sum of GCD of cycle lengths over all permutations of [n] with distinct cycle lengths.
[ "0", "1", "2", "9", "32", "170", "1164", "7434", "62880", "582336", "5875200", "60041520", "841501440", "9440926560", "141618778560", "2222190784800", "34862691548160", "543348318159360", "11173101312844800", "186494289764106240", "4219768887634944000", "86094733814301542400", "1834643656963469721600" ]
[ "nonn" ]
12
0
3
[ "A000142", "A007838", "A346066", "A382780", "A382781" ]
null
Alois P. Heinz, May 11 2025
2025-05-13T11:17:44
oeisdata/seq/A382/A382781.seq
3e63835bd41c731d3089da00eb71b034
A382782
Irregular triangle T(n,k) read by rows of the reduced coefficients of Pi^(2*k) in the expansion of Sum_{k>=1} (1 / (4*k^2-1)^n).
[ "1", "-8", "1", "32", "-3", "-384", "30", "1", "1536", "-105", "-5", "-30720", "1890", "105", "2", "61440", "-3465", "-210", "-7", "-10321920", "540540", "34650", "1512", "17", "4587520", "-225225", "-15015", "-770", "-17", "-1486356480", "68918850", "4729725", "270270", "8415", "62", "2972712960", "-130945815", "-9189180", "-567567", "-21879", "-341" ]
[ "sign", "tabf" ]
14
1
2
[ "A123092", "A248895", "A248896", "A382782", "A382783", "A382784" ]
null
Sean A. Irvine, Apr 04 2025
2025-04-14T07:39:01
oeisdata/seq/A382/A382782.seq
fa16884113f9a6e6dca6beb631d69cc6
A382783
Denominators arising in the expansion of Sum_{k>=1} (1/(4k^2-1)^n) in even powers of Pi.
[ "2", "16", "64", "768", "3072", "61440", "122880", "20643840", "9175040", "2972712960", "5945425920", "2615987404800", "5231974809600", "816188070297600", "108825076039680", "2742391916199936000", "10969567664799744000", "745930601206382592000", "1491861202412765184000", "2040866124900662771712000" ]
[ "nonn" ]
4
1
1
[ "A382782", "A382783" ]
null
Sean A. Irvine, Apr 04 2025
2025-04-05T17:26:45
oeisdata/seq/A382/A382783.seq
70789f5dadbe9f8657101db72b5b8943
A382784
Irregular triangle T(n,k) read by rows of the coefficients of Pi^(2k) in the expansion of Sum_{k>=1} (1 / (4k^2-1)^n) with denominator 2^(2n)*(n-1)!.
[ "2", "-8", "1", "64", "-6", "-768", "60", "2", "12288", "-840", "-40", "-245760", "15120", "840", "16", "5898240", "-332640", "-20160", "-672", "-165150720", "8648640", "554400", "24192", "272", "5284823040", "-259459200", "-17297280", "-887040", "-19584", "-190253629440", "8821612800", "605404800", "34594560", "1077120", "7936", "7610145177600", "-335221286400", "-23524300800", "-1452971520", "-56010240", "-872960" ]
[ "sign" ]
4
1
1
[ "A123092", "A248895", "A248896", "A382782", "A382784" ]
null
Sean A. Irvine, Apr 04 2025
2025-04-05T17:26:41
oeisdata/seq/A382/A382784.seq
a4e56a44b44827fa18192db4b8d54636
A382785
a(n) is the least multiple of the n-th primorial such that both a(n)-1 and a(n)+1 are prime and the prime factors of a(n) do not exceed prime(n).
[ "4", "6", "30", "420", "2310", "180180", "4084080", "106696590", "892371480", "103515091680", "4412330782860", "29682952539240", "22514519501013540", "313986271960080720", "22750921955774182170", "912496437361321252440", "26918644902158976946980", "1290172194953476680815970", "1901713815361424627522739780" ]
[ "nonn" ]
53
1
1
[ "A000040", "A002110", "A060255", "A060256", "A088256", "A088257", "A382785" ]
null
Rory Pulvino, Apr 04 2025
2025-05-10T11:29:50
oeisdata/seq/A382/A382785.seq
2e24a6add58f3736b66d87921a60fb3a
A382786
Numbers k such that 5^k + k is prime.
[ "7954", "22102", "33054", "135156" ]
[ "nonn", "hard", "more" ]
47
1
1
[ "A052007", "A057900", "A057909", "A058046", "A104745", "A382786" ]
null
Nico Puada, Apr 24 2025
2025-05-04T10:00:38
oeisdata/seq/A382/A382786.seq
9a3235dbc9270791997f1fe8755f84c3
A382787
The product of exponents in the prime factorization of the numbers whose prime factorization contains exponents that are either 1 or even.
[ "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "4", "1", "2", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "4", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "4", "2", "2", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "2", "6", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "4", "4", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1" ]
[ "nonn", "easy" ]
7
1
4
[ "A005361", "A013661", "A065465", "A335275", "A368473", "A382787" ]
null
Amiram Eldar, Apr 05 2025
2025-04-05T09:10:42
oeisdata/seq/A382/A382787.seq
a42cef6e5f17334ef9bfcc0b9860a60a
A382788
The sum of divisors of n that are numbers whose number of divisors is a power of 2.
[ "1", "3", "4", "3", "6", "12", "8", "11", "4", "18", "12", "12", "14", "24", "24", "11", "18", "12", "20", "18", "32", "36", "24", "44", "6", "42", "31", "24", "30", "72", "32", "11", "48", "54", "48", "12", "38", "60", "56", "66", "42", "96", "44", "36", "24", "72", "48", "44", "8", "18", "72", "42", "54", "93", "72", "88", "80", "90", "60", "72", "62", "96", "32", "11", "84", "144", "68", "54" ]
[ "nonn", "easy", "mult" ]
16
1
2
[ "A000523", "A033634", "A036537", "A353900", "A372379", "A372380", "A382788" ]
null
Amiram Eldar, Apr 05 2025
2025-04-26T03:33:14
oeisdata/seq/A382/A382788.seq
7c35bc9b5a6ae05409612576569d0792
A382789
The number of prime factors of Euler phi of the n-th primorial number, counted with multiplicity.
[ "0", "0", "1", "3", "5", "7", "10", "14", "17", "19", "22", "25", "29", "33", "36", "38", "41", "43", "47", "50", "53", "58", "61", "63", "67", "73", "77", "80", "82", "87", "92", "96", "99", "103", "106", "109", "113", "117", "122", "124", "127", "129", "134", "137", "144", "148", "152", "156", "159", "161", "165", "169", "172", "178", "182", "190", "192", "195", "200", "204" ]
[ "nonn", "easy" ]
7
0
4
[ "A000010", "A001222", "A002110", "A023508", "A055768", "A055769", "A382789" ]
null
Amiram Eldar, Apr 05 2025
2025-04-05T09:10:10
oeisdata/seq/A382/A382789.seq
c2566bd13d8e8415785d7f8c45e5b413
A382790
a(n) is the (2^n)-th powerful number.
[ "1", "4", "9", "32", "121", "392", "1352", "5000", "18432", "69192", "265837", "1024144", "3968064", "15523600", "60972500", "240413400", "950612224", "3767130288", "14959246864", "59495990724", "236902199076", "944193944097", "3765996039168", "15029799230264", "60010866324576", "239700225078125", "957712290743329" ]
[ "nonn" ]
12
0
2
[ "A001694", "A062762", "A090699", "A376092", "A382790" ]
null
Amiram Eldar, Apr 05 2025
2025-04-15T11:58:39
oeisdata/seq/A382/A382790.seq
6d6888784a9b318c099505695ac0f3d9
A382791
Carmichael numbers with exactly 3 prime factors, p*q*r, such that p-1, q-1 and r-1 have an equal 2-adic valuation.
[ "8911", "29341", "314821", "410041", "1024651", "1152271", "5481451", "10267951", "14913991", "15247621", "36765901", "64377991", "67902031", "133800661", "139952671", "178482151", "188516329", "299736181", "362569201", "368113411", "395044651", "532758241", "579606301", "612816751", "620169409", "625482001", "652969351" ]
[ "nonn" ]
9
1
1
[ "A002997", "A007814", "A087788", "A329799", "A382791" ]
null
Amiram Eldar, Apr 05 2025
2025-04-05T09:10:49
oeisdata/seq/A382/A382791.seq
c5e5a9992dea6c80f2ebd41824957ef4
A382792
a(n) = Sum_{k=0..n} (Stirling1(n,k) * k!)^2.
[ "1", "1", "5", "76", "2392", "126676", "10057204", "1114096320", "163918005696", "30894047577216", "7254176241285504", "2075722128162164736", "710883208780304954112", "287061726161439955116288", "134961239570613490548986112", "73079781978184515947237031936", "45150931601954398539342470578176" ]
[ "nonn" ]
16
0
3
[ "A006252", "A007840", "A047796", "A048144", "A379821", "A382792", "A382794" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-05T16:09:44
oeisdata/seq/A382/A382792.seq
5dffef11d84abce61635cc7605d92b92
A382793
a(n) = Sum_{k=0..n} (-1)^k * (Stirling2(n,k) * k!)^2.
[ "1", "-1", "3", "-1", "-525", "21599", "-575757", "-11712961", "4147828275", "-478419026401", "27474795508083", "3849481231073279", "-1772585499434165325", "366912253456842693599", "-26525609280231515934477", "-17189616925094873258825281", "10414911263566240831226298675", "-3136992122810471155294591778401" ]
[ "sign" ]
5
0
3
[ "A047797", "A048144", "A192552", "A382793" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-05T10:24:32
oeisdata/seq/A382/A382793.seq
0f21af10ba94996b5972f2b99cef6df7
A382794
a(n) = Sum_{k=0..n} Stirling1(n,k) * Stirling2(n,k) * (k!)^2.
[ "1", "1", "3", "2", "-418", "-14676", "-234344", "18565056", "2659703616", "169046742960", "-6539356064736", "-4061128974843744", "-672969012637199040", "-19289566159655581440", "27323548725052131528960", "10157639436460221570630144", "1433264952547826545065237504", "-520046813680980959472490690560" ]
[ "sign" ]
6
0
3
[ "A000670", "A006252", "A047792", "A048144", "A064618", "A192554", "A192564", "A382792", "A382794" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-05T10:24:29
oeisdata/seq/A382/A382794.seq
69fed55eda2da0ab8bb1875228463953
A382795
Number of minimum total dominating sets in the n-odd graph.
[ "0", "3", "10", "3570", "52920" ]
[ "nonn", "more" ]
4
1
2
null
null
Eric W. Weisstein, Apr 05 2025
2025-04-05T09:10:01
oeisdata/seq/A382/A382795.seq
5ac4cdab73596d3dc82aa5ee5470bc93
A382796
Numbers that can be represented as the sum of two distinct Ulam numbers in more than one way.
[ "5", "7", "9", "10", "12", "14", "15", "17", "19", "20", "21", "22", "24", "27", "29", "30", "31", "32", "34", "37", "39", "40", "41", "42", "44", "46", "49", "50", "51", "52", "54", "55", "56", "58", "59", "60", "61", "63", "64", "65", "66", "68", "70", "71", "73", "74", "75", "76", "78", "79", "80", "81", "83", "84", "85", "86", "88", "89", "90", "91", "93", "95", "98", "100", "101" ]
[ "nonn" ]
10
1
1
[ "A002858", "A033629", "A138892", "A382796" ]
null
Shyam Sunder Gupta, Apr 05 2025
2025-04-06T15:00:52
oeisdata/seq/A382/A382796.seq
0b97d060dac370945bfb1d6fe7ca1cb0
A382797
Odd Ulam numbers.
[ "1", "3", "11", "13", "47", "53", "57", "69", "77", "87", "97", "99", "131", "145", "155", "175", "177", "189", "197", "209", "219", "221", "241", "243", "253", "273", "309", "319", "339", "341", "363", "409", "429", "431", "441", "451", "483", "485", "497", "585", "605", "607", "627", "673", "685", "695", "739", "751", "781", "783", "847", "849", "861", "891" ]
[ "nonn" ]
12
1
2
[ "A002858", "A005408", "A382797" ]
null
Shyam Sunder Gupta, Apr 05 2025
2025-04-06T15:01:23
oeisdata/seq/A382/A382797.seq
66f6d19c888921d6d23e384c5490621e
A382798
Even Ulam numbers.
[ "2", "4", "6", "8", "16", "18", "26", "28", "36", "38", "48", "62", "72", "82", "102", "106", "114", "126", "138", "148", "180", "182", "206", "236", "238", "258", "260", "282", "316", "324", "356", "358", "370", "382", "390", "400", "402", "412", "414", "434", "456", "502", "522", "524", "544", "546", "566", "568", "602", "612", "624", "646", "668", "688", "690" ]
[ "nonn" ]
11
1
1
[ "A002858", "A005843", "A382798" ]
null
Shyam Sunder Gupta, Apr 05 2025
2025-04-06T15:01:34
oeisdata/seq/A382/A382798.seq
1fcd1f711f6ce57ca2d1b04df730908d
A382799
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (1 - log(1-x) * log(1-y))^2.
[ "1", "0", "0", "0", "2", "0", "0", "2", "2", "0", "0", "4", "14", "4", "0", "0", "12", "40", "40", "12", "0", "0", "48", "144", "260", "144", "48", "0", "0", "240", "648", "1284", "1284", "648", "240", "0", "0", "1440", "3528", "6936", "9588", "6936", "3528", "1440", "0", "0", "10080", "22608", "42744", "65928", "65928", "42744", "22608", "10080", "0", "0", "80640", "166896", "300240", "476808", "581952", "476808", "300240", "166896", "80640", "0" ]
[ "nonn", "tabl" ]
12
0
5
[ "A379821", "A382734", "A382799", "A382800", "A382801", "A382804" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T16:10:01
oeisdata/seq/A382/A382799.seq
546673794533efca1758854f2daa0099
A382800
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (1 - log(1-x) * log(1-y))^3.
[ "1", "0", "0", "0", "3", "0", "0", "3", "3", "0", "0", "6", "27", "6", "0", "0", "18", "78", "78", "18", "0", "0", "72", "282", "588", "282", "72", "0", "0", "360", "1272", "2988", "2988", "1272", "360", "0", "0", "2160", "6936", "16344", "24612", "16344", "6936", "2160", "0", "0", "15120", "44496", "101448", "175632", "175632", "101448", "44496", "15120", "0" ]
[ "nonn", "tabl" ]
13
0
5
[ "A379821", "A382735", "A382799", "A382800", "A382802", "A382806" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T16:09:57
oeisdata/seq/A382/A382800.seq
2323130a644a87822a720f595f1cbab0
A382801
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/2) * (1 / (1 - log(1-x) * log(1-y))^2 - 1).
[ "1", "1", "1", "2", "7", "2", "6", "20", "20", "6", "24", "72", "130", "72", "24", "120", "324", "642", "642", "324", "120", "720", "1764", "3468", "4794", "3468", "1764", "720", "5040", "11304", "21372", "32964", "32964", "21372", "11304", "5040", "40320", "83448", "150120", "238404", "290976", "238404", "150120", "83448", "40320" ]
[ "nonn", "tabl" ]
14
1
4
[ "A382740", "A382799", "A382801" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T23:17:14
oeisdata/seq/A382/A382801.seq
011b1d98eb23517f5ae0d41409253c95
A382802
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/3) * (1 / (1 - log(1-x) * log(1-y))^3 - 1).
[ "1", "1", "1", "2", "9", "2", "6", "26", "26", "6", "24", "94", "196", "94", "24", "120", "424", "996", "996", "424", "120", "720", "2312", "5448", "8204", "5448", "2312", "720", "5040", "14832", "33816", "58544", "58544", "33816", "14832", "5040", "40320", "109584", "238656", "431632", "556376", "431632", "238656", "109584", "40320" ]
[ "nonn", "tabl" ]
16
1
4
[ "A382741", "A382800", "A382802" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T23:17:20
oeisdata/seq/A382/A382802.seq
6882964a02cc16788fc9d6bd554c5b38
A382803
Positive integers m such that phi(m) and phi(m+1) are both powers of 2.
[ "1", "2", "3", "4", "5", "15", "16", "255", "256", "65535", "65536", "4294967295" ]
[ "nonn", "hard" ]
41
1
2
[ "A000010", "A000215", "A003401", "A019434", "A051179", "A382519", "A382803" ]
null
Caleb Stanford, Apr 05 2025
2025-04-18T21:29:29
oeisdata/seq/A382/A382803.seq
59c822e0c0f6e28996b7cec45a0a8c45
A382804
a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling1(n,k)^2.
[ "1", "2", "14", "260", "9588", "581952", "52096512", "6423520896", "1041005447424", "214260350714496", "54547409318781312", "16820040059243046144", "6175245603727007034624", "2661063379044058584861696", "1329787781176741647226481664", "762665713456216694195942866944" ]
[ "nonn" ]
14
0
2
[ "A382737", "A382792", "A382799", "A382804", "A382806" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T16:09:35
oeisdata/seq/A382/A382804.seq
8720814927f72dfd3a3893d63957b14b
A382805
a(n) = Sum_{k=0..n} (-1)^(n-k) * (Stirling1(n,k) * k!)^2.
[ "1", "1", "3", "4", "-272", "-8524", "-96596", "9634752", "983055168", "36429411456", "-4303305703296", "-1051644384152064", "-89651253435644160", "10632887072757561600", "5599203549778990667520", "914684633796830925275136", "-89559567563652079025946624", "-104514775371103880549281775616" ]
[ "sign" ]
4
0
3
[ "A006252", "A007840", "A047796", "A048144", "A192554", "A320502", "A382792", "A382793", "A382805" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-06T14:56:50
oeisdata/seq/A382/A382805.seq
dc99617f175f826a5f374546bf0b1702
A382806
a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+2,2) * Stirling1(n,k)^2.
[ "1", "3", "27", "588", "24612", "1669128", "165049224", "22269896064", "3918921022656", "870149951146944", "237662482188210624", "78249086559726140160", "30547324837444471084800", "13946361918619108837939200", "7359961832428044552536217600", "4444946383758589481684168540160" ]
[ "nonn" ]
9
0
2
[ "A382738", "A382792", "A382800", "A382804", "A382806" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T16:09:31
oeisdata/seq/A382/A382806.seq
fd4a27d1e0aeb9f3d9652fb57fa5ae9e
A382807
a(n) = Sum_{k=0..n} (Stirling1(n,k) * k!)^3.
[ "1", "1", "7", "8", "-22400", "-3821176", "733375592", "1324952888832", "521577465629184", "-1322687167356985344", "-3493561791052460040192", "83811280007607865122816", "33603928402796871413168222208", "112696506862115060894313558528000", "-389416384673353674591900391305326592" ]
[ "sign" ]
5
0
3
[ "A006252", "A242280", "A382792", "A382807", "A382808" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-06T14:57:01
oeisdata/seq/A382/A382807.seq
ec9c4e9f5a7e8ff6799810c8d39198ce
A382808
a(n) = Sum_{k=0..n} (|Stirling1(n,k)| * k!)^3.
[ "1", "1", "9", "440", "71344", "25826824", "17321581592", "19304140340736", "33142988156751360", "82906630912116006912", "289508760665893747703808", "1364207202603804952193826816", "8438589244471363680258331914240", "66972265137135031645961782287814656", "668922701586813036491303458870218731520" ]
[ "nonn" ]
7
0
3
[ "A007840", "A242280", "A382792", "A382807", "A382808" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-06T05:52:03
oeisdata/seq/A382/A382808.seq
445fce080d911cd74b83b87767a6716c
A382809
a(n) = (6*n + 1)*(12*n + 1)*(18*n + 1).
[ "1", "1729", "12025", "38665", "89425", "172081", "294409", "464185", "689185", "977185", "1335961", "1773289", "2296945", "2914705", "3634345", "4463641", "5410369", "6482305", "7687225", "9032905", "10527121", "12177649", "13992265", "15978745", "18144865", "20498401", "23047129", "25798825", "28761265", "31942225", "35349481" ]
[ "nonn", "easy", "changed" ]
15
0
2
[ "A002476", "A002997", "A016921", "A017533", "A033502", "A046025", "A068228", "A161705", "A382809" ]
null
Stefano Spezia, Apr 05 2025
2025-07-18T10:32:53
oeisdata/seq/A382/A382809.seq
912bcb82256abd55715683560a0580ec
A382810
Primes p such that p + 6, p + 10 and p + 16 are also primes.
[ "7", "13", "31", "37", "73", "97", "157", "223", "373", "433", "1087", "1291", "1423", "1483", "1543", "1861", "1987", "2341", "2383", "2677", "2683", "3313", "3607", "4441", "4507", "4783", "4993", "5641", "5851", "6037", "6961", "7237", "7867", "8731", "9613", "9733", "10723", "13093", "13681", "14143", "14731", "16057", "16411", "16921", "17377" ]
[ "nonn" ]
22
1
1
[ "A000040", "A001223", "A023200", "A031924", "A033451", "A078852", "A078856", "A078858", "A382810" ]
null
Alexander Yutkin, Apr 05 2025
2025-05-06T06:53:27
oeisdata/seq/A382/A382810.seq
c17e4e283af12512d621aa5108250447
A382811
Integers k such that d*2^k - 1 is prime for some divisor d of k.
[ "2", "3", "4", "5", "6", "7", "10", "12", "13", "16", "17", "18", "19", "21", "28", "30", "31", "36", "42", "46", "54", "60", "61", "63", "75", "81", "88", "89", "99", "102", "104", "106", "107", "108", "115", "123", "126", "127", "132", "133", "204", "214", "216", "225", "249", "264", "270", "286", "304", "306", "324", "330", "342", "352", "362", "384", "390" ]
[ "nonn" ]
40
1
1
[ "A000043", "A002234", "A382811" ]
null
Juri-Stepan Gerasimov, Apr 15 2025
2025-04-25T15:56:15
oeisdata/seq/A382/A382811.seq
97e26d82366ed1677838f51b3cbd08b7
A382812
Numerator of the n-th partial sum of the squares of the harmonic numbers.
[ "1", "13", "119", "1577", "3233", "8867", "141563", "2844129", "28119709", "335676251", "3968696491", "55023970333", "758025067309", "799020611041", "1676892996083", "59597395635137", "351844709221043", "2314823924364859", "9114392136427625", "628176680098075", "216039223801697", "5117413095318143", "363066107054194281", "27957386425926920257" ]
[ "nonn", "frac" ]
33
1
2
[ "A001008", "A002805", "A027611", "A027612", "A382812", "A382813" ]
null
Gary Detlefs, Apr 05 2025
2025-04-25T17:15:55
oeisdata/seq/A382/A382812.seq
1498f8bdd18ffff33c20d15050a5be4a
A382813
Denominator of the n-th partial sum of the squares of the harmonic numbers.
[ "1", "4", "18", "144", "200", "400", "4900", "78400", "635040", "6350400", "64033200", "768398400", "9275666400", "8657288640", "16232416200", "519437318400", "2779951574400", "16679709446400", "60213751101504", "3823095308032", "1216439416192", "26761667156224", "1769615240705312", "127412297330782464", "3062795608913040000" ]
[ "nonn", "frac" ]
29
1
2
[ "A001008", "A002805", "A027611", "A027612", "A382812", "A382813" ]
null
Gary Detlefs, Apr 05 2025
2025-04-25T17:15:32
oeisdata/seq/A382/A382813.seq
5f5396292237a039452d7abfc424697a
A382814
Number of nachos that the first player gets when playing the "Fibonachos" game starting with n nachos.
[ "1", "1", "2", "3", "3", "4", "3", "4", "4", "5", "6", "8", "8", "9", "9", "9", "10", "10", "12", "8", "9", "9", "10", "11", "11", "12", "11", "12", "12", "13", "14", "16", "21", "21", "22", "22", "22", "23", "23", "25", "25", "26", "26", "26", "25", "26", "26", "27", "28", "28", "29", "28", "33", "21", "22", "22", "23", "24", "24", "25", "24", "25", "25", "26", "27", "29", "29", "30", "30", "30" ]
[ "nonn" ]
10
1
3
[ "A000045", "A280521", "A382814" ]
null
Peter Kagey, Apr 05 2025
2025-04-12T12:38:46
oeisdata/seq/A382/A382814.seq
c5af6fe02fde0ade8bc0eb903b4aaf2a
A382815
Positive numbers k such that abs((sin k)^k) sets a new record.
[ "1", "8", "11", "51464", "51819", "52174", "573204", "37362253", "42781604", "122925461", "534483448", "3083975227" ]
[ "nonn", "more" ]
59
1
2
[ "A004112", "A382815", "A383540" ]
null
Jwalin Bhatt, Apr 28 2025
2025-05-07T10:38:29
oeisdata/seq/A382/A382815.seq
0e45265517e4e9205444051318e22278
A382816
a(n) = number of occurrences of n in A008949.
[ "1", "1", "2", "1", "1", "2", "2", "1", "1", "2", "1", "1", "1", "2", "3", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "2", "1", "2", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "2", "3", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn" ]
13
2
3
[ "A007318", "A008949", "A382816", "A382817" ]
null
Clark Kimberling, Apr 07 2025
2025-04-13T11:47:20
oeisdata/seq/A382/A382816.seq
036378d16591fd1757c4435100853370