sequence_id
stringlengths 7
7
| sequence_name
stringlengths 4
573
| sequence
listlengths 1
348
| keywords
listlengths 1
8
| score
int64 1
2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
int64 0
635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
| filename
stringlengths 29
29
| hash
stringlengths 32
32
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A013901
|
a(n) = 21^(5*n + 4).
|
[
"194481",
"794280046581",
"3243919932521508681",
"13248496640331026125580781",
"54108198377272584130510593262881",
"220983347100817338120002444455525554981",
"902518308877795191433240103403256374623457081",
"3685975927806112219127687339549342762856035687969181"
] |
[
"nonn"
] | 19 | 0 | 1 |
[
"A009965",
"A013901"
] | null |
N. J. A. Sloane
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013901.seq
|
7b747dc64f0f767ad87e4d828aa1585e
|
A013902
|
a(n) = 22^(5*n + 1).
|
[
"22",
"113379904",
"584318301411328",
"3011361496339065143296",
"15519448971100888972574851072",
"79981528839832616637508874879893504",
"412195366437884247746798137865015318806528",
"2124303230726006271483826780841554627491524509696",
"10947877107572929152919737180202022857988400441953615872"
] |
[
"nonn"
] | 21 | 0 | 1 |
[
"A009966",
"A013902"
] | null |
N. J. A. Sloane
| 2024-05-25T22:50:45 |
oeisdata/seq/A013/A013902.seq
|
c56ce9bef0c4ed88da8f4f6bd8579f2f
|
A013903
|
a(n) = 22^(5*n + 2).
|
[
"484",
"2494357888",
"12855002631049216",
"66249952919459433152512",
"341427877364219557396646723584",
"1759593634476317566025195247357657088",
"9068298061633453450429559033030337013743616",
"46734671075972137972644189178514201804813539213312"
] |
[
"nonn"
] | 18 | 0 | 1 |
[
"A009966",
"A013903"
] | null |
N. J. A. Sloane
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013903.seq
|
80cf3d0fad975ef60861d06c0e172184
|
A013904
|
a(n) = 22^(5*n + 3).
|
[
"10648",
"54875873536",
"282810057883082752",
"1457498964228107529355264",
"7511413302012830262726227918848",
"38711059958478986452554295441868455936",
"199502557355935975909450298726667414302359552",
"1028162763671387035398172161927312439705897862692864"
] |
[
"nonn"
] | 16 | 0 | 1 |
[
"A009966",
"A013904"
] | null |
N. J. A. Sloane
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013904.seq
|
ad144a6fc283cee1cdb5cfc42396ab3e
|
A013905
|
22^(5n+4).
|
[
"234256",
"1207269217792",
"6221821273427820544",
"32064977213018365645815808",
"165251092644282265779977014214656",
"851643319086537701956194499721106030592",
"4389056261830591470007906571986683114651910144",
"22619580800770514778759787562400873673529752979243008"
] |
[
"nonn",
"easy"
] | 17 | 0 | 1 | null | null |
N. J. A. Sloane, Dec 11 1996
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013905.seq
|
b221ef0f6f007b44dea79db5a9fa7441
|
A013906
|
a(n) = 23^(5*n + 1).
|
[
"23",
"148035889",
"952809757913927",
"6132610415680998648961",
"39471584120695485887249589623",
"254052654154149545721997685422868689",
"1635170022196481349560959748587682926364327",
"10524515126174167358877236351104092889324551536161",
"67739389260745218861137988047774370539553852007909099223"
] |
[
"nonn"
] | 22 | 0 | 1 |
[
"A009967",
"A013906",
"A016861"
] | null |
N. J. A. Sloane
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013906.seq
|
bbcba11cdd8d65d978bab4ec73022192
|
A013907
|
a(n) = 23^(5*n + 2).
|
[
"529",
"3404825447",
"21914624432020321",
"141050039560662968926103",
"907846434775996175406740561329",
"5843211045545439551605946764725979847",
"37608910510519071039902074217516707306379521",
"242063847902005849254176436075394136454464685331703"
] |
[
"nonn"
] | 22 | 0 | 1 |
[
"A009967",
"A013907"
] | null |
N. J. A. Sloane
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013907.seq
|
ed91fa973b5af2a0fa54245d3a8e1320
|
A013908
|
a(n) = 23^(5*n + 3).
|
[
"12167",
"78310985281",
"504036361936467383",
"3244150909895248285300369",
"20880467999847912034355032910567",
"134393854047545109686936775588697536481",
"865004941741938633917747707002884268046728983",
"5567468501746134532846058029734065138452687762629169"
] |
[
"nonn"
] | 16 | 0 | 1 |
[
"A009967",
"A013908"
] | null |
N. J. A. Sloane
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013908.seq
|
8f76f7ca951c4180db825cba5fa8c187
|
A013909
|
a(n) = 23^(5*n + 4).
|
[
"279841",
"1801152661463",
"11592836324538749809",
"74615470927590710561908487",
"480250763996501976790165756943041",
"3091058643093537522799545838540043339063",
"19895113660064588580108197261066338165074766609",
"128051775540161094255459334683883498184411818540470887"
] |
[
"nonn"
] | 18 | 0 | 1 |
[
"A009967",
"A013909"
] | null |
N. J. A. Sloane
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013909.seq
|
d0d99de285c75c1d03860fcc3345656f
|
A013910
|
a(n) = 24^(5*n + 1).
|
[
"24",
"191102976",
"1521681143169024",
"12116574790945106558976",
"96479729228174488169059713024",
"768231807465763655682670928358014976",
"6117141027690268863066571918245810640257024"
] |
[
"nonn"
] | 28 | 0 | 1 |
[
"A009968",
"A013910"
] | null |
N. J. A. Sloane
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013910.seq
|
bfa03c81da7c02c93c085d2581745ff3
|
A013911
|
a(n) = 24^(5*n + 2).
|
[
"576",
"4586471424",
"36520347436056576",
"290797794982682557415424",
"2315513501476187716057433112576",
"18437563379178327736384102280592359424",
"146811384664566452713597726037899455366168576",
"1169003855003308785972158379694803112885582691303424"
] |
[
"nonn",
"easy"
] | 28 | 0 | 1 |
[
"A009968",
"A013911"
] | null |
N. J. A. Sloane
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013911.seq
|
9223ea1266d7127e0a53c017ed68ffbb
|
A013912
|
a(n) = 24^(5*n + 3).
|
[
"13824",
"110075314176",
"876488338465357824",
"6979147079584381377970176",
"55572324035428505185378394701824",
"442501521100279865673218454734216626176",
"3523473231949594865126345424909586928788045824",
"28056092520079410863331801112675274709253984591282176"
] |
[
"nonn",
"easy"
] | 31 | 0 | 1 |
[
"A009968",
"A013912"
] | null |
N. J. A. Sloane
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013912.seq
|
3bb30f700563dae391fe234128346ea7
|
A013913
|
a(n) = 24^(5*n + 4).
|
[
"331776",
"2641807540224",
"21035720123168587776",
"167499529910025153071284224",
"1333735776850284124449081472843776",
"10620036506406716776157242913621199028224",
"84563357566790276763032290197830086290913099776",
"673346220481905860719963226704206593022095630190772224"
] |
[
"nonn",
"easy"
] | 38 | 0 | 1 | null | null |
N. J. A. Sloane
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013913.seq
|
d8f68de2309d361f2ef48b4c5e5712c1
|
A013914
|
Number of distinct nonzero absolute values of Sum_{j=1..n} sigma_j * exp(i * Pi * j / n) where sigma_j = +- 1.
|
[
"1",
"1",
"1",
"2",
"3",
"4",
"8",
"12",
"16",
"33",
"62",
"67",
"186",
"316",
"280",
"1040",
"1963",
"1702",
"6830",
"10751",
"8679",
"45838",
"88255",
"56292",
"264838",
"624778",
"348817",
"2208496",
"4526585"
] |
[
"nonn",
"nice"
] | 9 | 1 | 4 | null | null |
David Broadhurst
| 2018-08-24T20:19:54 |
oeisdata/seq/A013/A013914.seq
|
7068d5db1bf061e67b859aa33f7d6959
|
A013915
|
a(n) = F(n) + L(n) + n, where F(n) (A000045) and L(n) (A000204) are Fibonacci and Lucas numbers respectively.
|
[
"3",
"3",
"7",
"10",
"16",
"24",
"37",
"57",
"89",
"140",
"222",
"354",
"567",
"911",
"1467",
"2366",
"3820",
"6172",
"9977",
"16133",
"26093",
"42208",
"68282",
"110470",
"178731",
"289179",
"467887",
"757042",
"1224904",
"1981920",
"3206797",
"5188689",
"8395457",
"13584116",
"21979542",
"35563626",
"57543135"
] |
[
"nonn",
"easy"
] | 22 | 0 | 1 | null | null |
Mohammad K. Azarian
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013915.seq
|
994311a60b33e82a7e73d424ba1a02ff
|
A013916
|
Numbers k such that the sum of the first k primes is prime.
|
[
"1",
"2",
"4",
"6",
"12",
"14",
"60",
"64",
"96",
"100",
"102",
"108",
"114",
"122",
"124",
"130",
"132",
"146",
"152",
"158",
"162",
"178",
"192",
"198",
"204",
"206",
"208",
"214",
"216",
"296",
"308",
"326",
"328",
"330",
"332",
"334",
"342",
"350",
"356",
"358",
"426",
"446",
"458",
"460",
"464",
"480",
"484",
"488",
"512",
"530",
"536",
"548",
"568",
"620",
"630",
"676",
"680"
] |
[
"nonn",
"nice"
] | 57 | 1 | 2 |
[
"A007504",
"A013916",
"A013917",
"A013918"
] | null |
N. J. A. Sloane, Renaud Lifchitz (100637.64(AT)CompuServe.COM)
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013916.seq
|
3b3c7d5c9cb84db98659f39bc40f42d8
|
A013917
|
a(n) is prime and sum of all primes <= a(n) is prime.
|
[
"2",
"3",
"7",
"13",
"37",
"43",
"281",
"311",
"503",
"541",
"557",
"593",
"619",
"673",
"683",
"733",
"743",
"839",
"881",
"929",
"953",
"1061",
"1163",
"1213",
"1249",
"1277",
"1283",
"1307",
"1321",
"1949",
"2029",
"2161",
"2203",
"2213",
"2237",
"2243",
"2297",
"2357",
"2393",
"2411",
"2957",
"3137",
"3251",
"3257",
"3301",
"3413",
"3461",
"3491"
] |
[
"nonn"
] | 25 | 1 | 1 |
[
"A013916",
"A013917",
"A013918"
] | null |
N. J. A. Sloane, Renaud Lifchitz (100637.64(AT)CompuServe.COM)
| 2021-10-19T11:21:39 |
oeisdata/seq/A013/A013917.seq
|
41279352b50eaed02a9af7f10f0bce8e
|
A013918
|
Primes equal to the sum of the first k primes for some k.
|
[
"2",
"5",
"17",
"41",
"197",
"281",
"7699",
"8893",
"22039",
"24133",
"25237",
"28697",
"32353",
"37561",
"38921",
"43201",
"44683",
"55837",
"61027",
"66463",
"70241",
"86453",
"102001",
"109147",
"116533",
"119069",
"121631",
"129419",
"132059",
"263171",
"287137",
"325019",
"329401",
"333821",
"338279",
"342761"
] |
[
"nonn"
] | 51 | 1 | 1 |
[
"A000040",
"A007504",
"A010051",
"A013916",
"A013917",
"A013918",
"A189153"
] | null |
N. J. A. Sloane, Renaud Lifchitz (100637.64(AT)CompuServe.COM)
| 2024-12-24T22:12:13 |
oeisdata/seq/A013/A013918.seq
|
ab220d7d2a2dfcc06cacf63d0f0ee9a7
|
A013919
|
Numbers n such that sum of first n composites is composite.
|
[
"1",
"2",
"3",
"4",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"15",
"16",
"18",
"19",
"21",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"32",
"33",
"34",
"38",
"39",
"40",
"41",
"42",
"44",
"45",
"46",
"49",
"50",
"51",
"52",
"55",
"56",
"57",
"58",
"59",
"60",
"61",
"62",
"65",
"66",
"67",
"69",
"70",
"71",
"72",
"76",
"77",
"78",
"79",
"80",
"81",
"82",
"83",
"84",
"85",
"87",
"88",
"89",
"90",
"91",
"92",
"93"
] |
[
"nonn"
] | 15 | 1 | 2 |
[
"A013919",
"A013920",
"A013921"
] | null |
N. J. A. Sloane, Henri Lifchitz
| 2013-10-16T17:44:05 |
oeisdata/seq/A013/A013919.seq
|
666452a2bb8417782edfcbf7b043fd9b
|
A013920
|
Composite numbers k such that the sum of all composites <= k is composite.
|
[
"4",
"6",
"8",
"9",
"12",
"14",
"15",
"16",
"18",
"20",
"21",
"22",
"25",
"26",
"28",
"30",
"33",
"34",
"35",
"36",
"38",
"39",
"40",
"42",
"44",
"45",
"46",
"48",
"49",
"50",
"55",
"56",
"57",
"58",
"60",
"63",
"64",
"65",
"69",
"70",
"72",
"74",
"77",
"78",
"80",
"81",
"82",
"84",
"85",
"86",
"90",
"91",
"92",
"94",
"95",
"96",
"98",
"104",
"105",
"106",
"108",
"110",
"111",
"112",
"114",
"115",
"116",
"118",
"119"
] |
[
"nonn"
] | 12 | 1 | 1 |
[
"A013919",
"A013920",
"A013921"
] | null |
N. J. A. Sloane, Henri Lifchitz
| 2021-10-02T15:14:35 |
oeisdata/seq/A013/A013920.seq
|
cc9e398602817d65aaa0a6f4e92d7f23
|
A013921
|
Composite numbers that are equal to the sum of the first k composites for some k.
|
[
"4",
"10",
"18",
"27",
"49",
"63",
"78",
"94",
"112",
"132",
"153",
"175",
"224",
"250",
"305",
"335",
"400",
"434",
"469",
"505",
"543",
"582",
"622",
"664",
"708",
"753",
"799",
"847",
"896",
"946",
"1158",
"1214",
"1271",
"1329",
"1389",
"1514",
"1578",
"1643",
"1846",
"1916",
"1988",
"2062",
"2290",
"2368",
"2448",
"2529",
"2611",
"2695",
"2780",
"2866"
] |
[
"nonn"
] | 24 | 1 | 1 |
[
"A013919",
"A013920",
"A013921",
"A053767"
] | null |
N. J. A. Sloane, Henri Lifchitz
| 2022-11-26T13:21:03 |
oeisdata/seq/A013/A013921.seq
|
f514fa8f5cb50f72abfa48f1377ad224
|
A013922
|
Number of labeled connected graphs with n nodes and 0 cutpoints (blocks or nonseparable graphs).
|
[
"0",
"1",
"1",
"10",
"238",
"11368",
"1014888",
"166537616",
"50680432112",
"29107809374336",
"32093527159296128",
"68846607723033232640",
"290126947098532533378816",
"2417684612523425600721132544",
"40013522702538780900803893881856"
] |
[
"nonn",
"easy",
"nice"
] | 39 | 1 | 4 |
[
"A002218",
"A004115",
"A013922",
"A095983",
"A123534"
] | null |
Stanley Selkow (sms(AT)owl.WPI.EDU)
| 2020-12-27T19:25:53 |
oeisdata/seq/A013/A013922.seq
|
33db29fbd0089c308880ce48ac7f77a6
|
A013923
|
Number of labeled connected graphs with n vertices and 1 cutpoint.
|
[
"3",
"16",
"250",
"8496",
"540568",
"61672192",
"12608406288",
"4697459302400",
"3256012245850496",
"4276437400678311936",
"10796431791679078528256",
"52955364458428847588956160",
"508511231062550463852707804160",
"9611398894866376672902234634977280"
] |
[
"nonn"
] | 17 | 3 | 1 |
[
"A013923",
"A370064"
] | null |
Stanley Selkow (sms(AT)owl.WPI.EDU)
| 2024-02-26T01:21:46 |
oeisdata/seq/A013/A013923.seq
|
be3ea88ae265aa303f81758c9bb491be
|
A013924
|
Number of labeled connected graphs with n nodes and 2 cutpoints.
|
[
"12",
"180",
"4560",
"211680",
"17186624",
"2416430016",
"597615868800",
"266262716016000",
"218583901063537152",
"336744209796848156160",
"987653716558634390487040",
"5576385411303897176201779200",
"61117320790343064985205192540160"
] |
[
"nonn"
] | 18 | 4 | 1 |
[
"A013924",
"A370064"
] | null |
Stanley Selkow (sms(AT)owl.WPI.EDU)
| 2024-02-26T01:20:57 |
oeisdata/seq/A013/A013924.seq
|
fd3e206bafae05d0d85fed2970a00d69
|
A013925
|
Number of labeled connected graphs with n nodes and 3 cutpoints.
|
[
"60",
"1920",
"75600",
"4663680",
"469336896",
"79132032000",
"23121510192000",
"12082931084928000",
"11564306171310537216",
"20625639730671895535616",
"69501783433272242637312000",
"447403458171641201324598067200",
"5550030610876067133522251137105920"
] |
[
"nonn"
] | 19 | 5 | 1 |
[
"A013925",
"A370064"
] | null |
Stanley Selkow (sms(AT)owl.WPI.EDU)
| 2024-02-26T01:21:30 |
oeisdata/seq/A013/A013925.seq
|
13c9d771892c1e04849c127233da26a1
|
A013926
|
a(n) = (2*n)! * D_{2*n}, where D_{2*n} = (1/Pi) * Integral_{x=0..oo} [1 - x^(2*n) / Product_{j=1..n} (x^2+j^2)] dx.
|
[
"1",
"28",
"1434",
"118960",
"14611150",
"2494744728",
"565526968692",
"164368956804288",
"59603021615454678",
"26379919529434077640",
"13996517446366589638636",
"8769645281519454489332448",
"6406629794568469259015608204"
] |
[
"nonn"
] | 11 | 1 | 2 | null | null |
Micha Hofri (hofri(AT)cs.rice.edu)
| 2025-06-29T07:15:48 |
oeisdata/seq/A013/A013926.seq
|
8b6c6eab7d61cb6bd430b5fbc78d6e7e
|
A013927
|
Begin with 2n cards in n piles of 2, the piles being {1,1},{2,2},{3,3},...,{n,n}. How many transpositions of adjacent (single) cards are needed to reverse the order of the piles?
|
[
"0",
"2",
"5",
"10",
"15",
"23",
"31",
"40"
] |
[
"nonn",
"more"
] | 20 | 1 | 2 | null | null |
N. J. A. Sloane
| 2023-05-12T12:05:54 |
oeisdata/seq/A013/A013927.seq
|
384c716c8525fc1985d4a454e156f870
|
A013928
|
Number of (positive) squarefree numbers < n.
|
[
"0",
"1",
"2",
"3",
"3",
"4",
"5",
"6",
"6",
"6",
"7",
"8",
"8",
"9",
"10",
"11",
"11",
"12",
"12",
"13",
"13",
"14",
"15",
"16",
"16",
"16",
"17",
"17",
"17",
"18",
"19",
"20",
"20",
"21",
"22",
"23",
"23",
"24",
"25",
"26",
"26",
"27",
"28",
"29",
"29",
"29",
"30",
"31",
"31",
"31",
"31",
"32",
"32",
"33",
"33",
"34",
"34",
"35",
"36",
"37",
"37",
"38",
"39",
"39",
"39",
"40",
"41",
"42",
"42",
"43",
"44",
"45",
"45",
"46",
"47",
"47",
"47",
"48",
"49",
"50",
"50",
"50",
"51"
] |
[
"nonn",
"easy",
"changed"
] | 108 | 1 | 3 |
[
"A000720",
"A002321",
"A005117",
"A013928",
"A057627",
"A066779",
"A081239",
"A107079",
"A158819",
"A179211",
"A179215",
"A284584"
] | null |
Henri Lifchitz
| 2025-07-15T15:38:32 |
oeisdata/seq/A013/A013928.seq
|
09d37d4cb96c7222802c874ede588cac
|
A013929
|
Numbers that are not squarefree. Numbers that are divisible by a square greater than 1. The complement of A005117.
|
[
"4",
"8",
"9",
"12",
"16",
"18",
"20",
"24",
"25",
"27",
"28",
"32",
"36",
"40",
"44",
"45",
"48",
"49",
"50",
"52",
"54",
"56",
"60",
"63",
"64",
"68",
"72",
"75",
"76",
"80",
"81",
"84",
"88",
"90",
"92",
"96",
"98",
"99",
"100",
"104",
"108",
"112",
"116",
"117",
"120",
"121",
"124",
"125",
"126",
"128",
"132",
"135",
"136",
"140",
"144",
"147",
"148",
"150",
"152",
"153",
"156",
"160"
] |
[
"nonn",
"easy"
] | 239 | 1 | 1 |
[
"A001694",
"A005117",
"A008683",
"A013929",
"A034444",
"A038109",
"A114374",
"A130897",
"A190641",
"A256012",
"A332785",
"A351381",
"A353282"
] | null |
Henri Lifchitz
| 2025-02-16T08:32:32 |
oeisdata/seq/A013/A013929.seq
|
e03b3c65e8fc35cff5dede1d5b7dbb84
|
A013930
|
Sum of first a(n) squarefrees is squarefree.
|
[
"1",
"2",
"3",
"4",
"5",
"7",
"9",
"11",
"13",
"15",
"17",
"19",
"20",
"23",
"25",
"26",
"27",
"29",
"32",
"34",
"37",
"40",
"41",
"42",
"43",
"44",
"46",
"47",
"49",
"50",
"51",
"53",
"54",
"56",
"58",
"60",
"61",
"63",
"64",
"65",
"69",
"70",
"71",
"74",
"76",
"77",
"79",
"80",
"81",
"82",
"83",
"84",
"86",
"88",
"89",
"90",
"92",
"94",
"95",
"96",
"98",
"100",
"102",
"103",
"104",
"106",
"107",
"108",
"110",
"111"
] |
[
"nonn"
] | 14 | 1 | 2 |
[
"A005117",
"A013930",
"A013931",
"A013932"
] | null |
Henri Lifchitz
| 2021-03-07T03:14:12 |
oeisdata/seq/A013/A013930.seq
|
13d989145d67fa100ff8e4c505d5c2dd
|
A013931
|
a(n) is squarefree and sum of all squarefrees <= a(n) is squarefree.
|
[
"1",
"2",
"3",
"5",
"6",
"10",
"13",
"15",
"19",
"22",
"26",
"30",
"31",
"35",
"38",
"39",
"41",
"43",
"51",
"55",
"59",
"65",
"66",
"67",
"69",
"70",
"73",
"74",
"78",
"79",
"82",
"85",
"86",
"89",
"93",
"95",
"97",
"102",
"103",
"105",
"110",
"111",
"113",
"118",
"122",
"123",
"129",
"130",
"131",
"133",
"134",
"137",
"139",
"142",
"143",
"145",
"149",
"154",
"155",
"157",
"159",
"163",
"166",
"167"
] |
[
"nonn"
] | 17 | 1 | 2 |
[
"A005117",
"A013930",
"A013931",
"A013932"
] | null |
Henri Lifchitz
| 2021-03-07T03:13:59 |
oeisdata/seq/A013/A013931.seq
|
b9dfeb971d5ab600f7b3ad0761edcf0f
|
A013932
|
Integers that are squarefree and also the sum of first k squarefrees for some k.
|
[
"1",
"3",
"6",
"11",
"17",
"34",
"58",
"87",
"123",
"166",
"215",
"274",
"305",
"407",
"482",
"521",
"562",
"647",
"791",
"899",
"1073",
"1261",
"1327",
"1394",
"1463",
"1533",
"1677",
"1751",
"1906",
"1985",
"2067",
"2235",
"2321",
"2497",
"2681",
"2870",
"2967",
"3170",
"3273",
"3378",
"3810",
"3921",
"4034",
"4381",
"4622",
"4745",
"5001",
"5131",
"5262"
] |
[
"nonn"
] | 19 | 1 | 2 |
[
"A005117",
"A013930",
"A013931",
"A013932",
"A173143"
] | null |
Henri Lifchitz
| 2021-03-07T03:13:36 |
oeisdata/seq/A013/A013932.seq
|
d81fcbdadc8186a60825c6aab4a64c3a
|
A013933
|
Numbers k such that the sum of the first k nonsquarefree numbers is nonsquarefree.
|
[
"1",
"2",
"5",
"9",
"15",
"16",
"17",
"24",
"25",
"26",
"27",
"29",
"31",
"32",
"33",
"35",
"37",
"40",
"41",
"43",
"44",
"45",
"49",
"50",
"51",
"58",
"59",
"61",
"64",
"66",
"69",
"72",
"76",
"77",
"79",
"80",
"81",
"82",
"83",
"84",
"85",
"88",
"89",
"93",
"94",
"95",
"99",
"101",
"102",
"103",
"104",
"108",
"109",
"110",
"111",
"116",
"117",
"118",
"120",
"133",
"134",
"137",
"142",
"146",
"147",
"149"
] |
[
"nonn"
] | 16 | 1 | 2 |
[
"A013929",
"A013933",
"A013934",
"A013935"
] | null |
Henri Lifchitz
| 2021-02-11T03:32:43 |
oeisdata/seq/A013/A013933.seq
|
a4792f49acf1097ec63985b623939f70
|
A013934
|
Nonsquarefree numbers k such that the sum of all nonsquarefree numbers <= k is nonsquarefree.
|
[
"4",
"8",
"16",
"25",
"44",
"45",
"48",
"63",
"64",
"68",
"72",
"76",
"81",
"84",
"88",
"92",
"98",
"104",
"108",
"116",
"117",
"120",
"126",
"128",
"132",
"150",
"152",
"156",
"164",
"169",
"175",
"184",
"196",
"198",
"204",
"207",
"208",
"212",
"216",
"220",
"224",
"232",
"234",
"243",
"244",
"245",
"256",
"261",
"264",
"268",
"270",
"279",
"280",
"284",
"288",
"297",
"300",
"304"
] |
[
"nonn"
] | 16 | 1 | 1 |
[
"A013929",
"A013933",
"A013934",
"A013935"
] | null |
Henri Lifchitz
| 2021-02-11T03:32:39 |
oeisdata/seq/A013/A013934.seq
|
2ce65722b3ed9b0e364348c363e71cad
|
A013935
|
a(n) is nonsquarefree and is sum of first k nonsquarefrees for some k.
|
[
"4",
"12",
"49",
"136",
"343",
"388",
"436",
"820",
"884",
"952",
"1024",
"1175",
"1336",
"1420",
"1508",
"1690",
"1884",
"2187",
"2295",
"2523",
"2640",
"2760",
"3256",
"3384",
"3516",
"4516",
"4668",
"4977",
"5463",
"5800",
"6318",
"6858",
"7623",
"7821",
"8225",
"8432",
"8640",
"8852",
"9068",
"9288",
"9512",
"10197",
"10431",
"11392"
] |
[
"nonn"
] | 18 | 1 | 1 |
[
"A013929",
"A013933",
"A013934",
"A013935"
] | null |
Henri Lifchitz
| 2017-06-13T02:11:33 |
oeisdata/seq/A013/A013935.seq
|
b19655b00adafacead0d83ec6c3b1240
|
A013936
|
a(n) = Sum_{k=1..n} floor(n/k^2).
|
[
"1",
"2",
"3",
"5",
"6",
"7",
"8",
"10",
"12",
"13",
"14",
"16",
"17",
"18",
"19",
"22",
"23",
"25",
"26",
"28",
"29",
"30",
"31",
"33",
"35",
"36",
"38",
"40",
"41",
"42",
"43",
"46",
"47",
"48",
"49",
"53",
"54",
"55",
"56",
"58",
"59",
"60",
"61",
"63",
"65",
"66",
"67",
"70",
"72",
"74",
"75",
"77",
"78",
"80",
"81",
"83",
"84",
"85",
"86",
"88",
"89",
"90",
"92",
"96",
"97",
"98",
"99",
"101",
"102",
"103"
] |
[
"nonn"
] | 38 | 1 | 2 |
[
"A013936",
"A046951"
] | null |
N. J. A. Sloane, Henri Lifchitz
| 2021-08-19T11:00:07 |
oeisdata/seq/A013/A013936.seq
|
e85e6df86c7098adc877b0ce433277ec
|
A013937
|
a(n) = Sum_{k=1..n} floor(n/k^3).
|
[
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"16",
"18",
"19",
"20",
"21",
"22",
"23",
"24",
"25",
"27",
"28",
"29",
"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",
"62",
"63",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"72",
"75",
"76",
"77",
"78",
"79",
"80",
"81",
"82"
] |
[
"nonn"
] | 32 | 0 | 3 |
[
"A005187",
"A006218",
"A011371",
"A013936",
"A013937",
"A013939"
] | null |
N. J. A. Sloane, Henri Lifchitz
| 2021-05-26T09:40:00 |
oeisdata/seq/A013/A013937.seq
|
5af86a34b02f3460c196ebf39354b6e6
|
A013938
|
a(n) = Sum_{k=1..n} floor(n/k^4).
|
[
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"32",
"34",
"35",
"36",
"37",
"38",
"39",
"40",
"41",
"42",
"43",
"44",
"45",
"46",
"47",
"48",
"49",
"51",
"52",
"53",
"54",
"55",
"56",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"64",
"65",
"66",
"68",
"69",
"70",
"71",
"72",
"73",
"74",
"75",
"76",
"77",
"78",
"79",
"80",
"81",
"82",
"83",
"85",
"87"
] |
[
"nonn"
] | 21 | 1 | 2 |
[
"A013936",
"A013937",
"A013938"
] | null |
N. J. A. Sloane, Henri Lifchitz
| 2021-05-26T13:03:51 |
oeisdata/seq/A013/A013938.seq
|
bdb795b973895ce937245df91875009d
|
A013939
|
Partial sums of sequence A001221 (number of distinct primes dividing n).
|
[
"0",
"1",
"2",
"3",
"4",
"6",
"7",
"8",
"9",
"11",
"12",
"14",
"15",
"17",
"19",
"20",
"21",
"23",
"24",
"26",
"28",
"30",
"31",
"33",
"34",
"36",
"37",
"39",
"40",
"43",
"44",
"45",
"47",
"49",
"51",
"53",
"54",
"56",
"58",
"60",
"61",
"64",
"65",
"67",
"69",
"71",
"72",
"74",
"75",
"77",
"79",
"81",
"82",
"84",
"86",
"88",
"90",
"92",
"93",
"96",
"97",
"99",
"101",
"102",
"104",
"107",
"108",
"110",
"112"
] |
[
"nonn",
"easy",
"nice"
] | 100 | 1 | 3 |
[
"A000040",
"A001222",
"A005187",
"A006218",
"A011371",
"A013936",
"A013939",
"A022559",
"A027748",
"A048803",
"A048865",
"A077761",
"A082287",
"A093614",
"A346617"
] | null |
N. J. A. Sloane, Henri Lifchitz
| 2025-06-01T18:06:39 |
oeisdata/seq/A013/A013939.seq
|
3485fe332633fbf80411e96a268bfa42
|
A013940
|
a(n) = Sum_{k=1..n} floor(n/prime(k)^2).
|
[
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"2",
"3",
"3",
"3",
"4",
"4",
"4",
"4",
"5",
"5",
"6",
"6",
"7",
"7",
"7",
"7",
"8",
"9",
"9",
"10",
"11",
"11",
"11",
"11",
"12",
"12",
"12",
"12",
"14",
"14",
"14",
"14",
"15",
"15",
"15",
"15",
"16",
"17",
"17",
"17",
"18",
"19",
"20",
"20",
"21",
"21",
"22",
"22",
"23",
"23",
"23",
"23",
"24",
"24",
"24",
"25",
"26",
"26",
"26",
"26",
"27",
"27",
"27",
"27",
"29"
] |
[
"nonn"
] | 34 | 1 | 8 |
[
"A013940",
"A085548"
] | null |
N. J. A. Sloane, Henri Lifchitz, Dec 11 1996
| 2022-09-08T08:44:38 |
oeisdata/seq/A013/A013940.seq
|
9222f4e90c8515924dcc0d4eab478a2a
|
A013941
|
a(n) = Sum_{k = 1..n} floor(n/prime(k)^3).
|
[
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"3",
"3",
"3",
"4",
"4",
"4",
"4",
"4",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"7",
"7",
"7",
"7",
"7",
"7",
"8",
"8",
"9",
"9",
"9",
"9",
"9",
"9",
"9",
"9",
"10",
"10",
"10",
"10",
"10",
"10",
"10",
"10",
"11",
"11",
"11",
"11"
] |
[
"nonn",
"easy"
] | 23 | 1 | 16 |
[
"A013940",
"A013941",
"A295659"
] | null |
N. J. A. Sloane, Henri Lifchitz
| 2022-06-26T22:45:58 |
oeisdata/seq/A013/A013941.seq
|
890ce3deed9047a2bd5c16aac77bbae8
|
A013942
|
Triangle of numbers T(n,k) = floor(2n/k), k=1..2n, read by rows.
|
[
"2",
"1",
"4",
"2",
"1",
"1",
"6",
"3",
"2",
"1",
"1",
"1",
"8",
"4",
"2",
"2",
"1",
"1",
"1",
"1",
"10",
"5",
"3",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"12",
"6",
"4",
"3",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"14",
"7",
"4",
"3",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"16",
"8",
"5",
"4",
"3",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"18",
"9",
"6",
"4",
"3",
"3",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"20",
"10",
"6",
"5",
"4",
"3"
] |
[
"nonn",
"tabf",
"easy",
"nice"
] | 30 | 1 | 1 |
[
"A005843",
"A010766",
"A013942",
"A062550"
] | null |
Clark Kimberling
| 2022-09-26T09:20:48 |
oeisdata/seq/A013/A013942.seq
|
fbbe23dc29cde1043872511a2a5e3e2c
|
A013943
|
Period of continued fraction for sqrt(m), m = n-th nonsquare.
|
[
"1",
"2",
"1",
"2",
"4",
"2",
"1",
"2",
"2",
"5",
"4",
"2",
"1",
"2",
"6",
"2",
"6",
"6",
"4",
"2",
"1",
"2",
"4",
"5",
"2",
"8",
"4",
"4",
"4",
"2",
"1",
"2",
"2",
"2",
"3",
"2",
"10",
"8",
"6",
"12",
"4",
"2",
"1",
"2",
"6",
"5",
"6",
"4",
"2",
"6",
"7",
"6",
"4",
"11",
"4",
"2",
"1",
"2",
"10",
"2",
"8",
"6",
"8",
"2",
"7",
"5",
"4",
"12",
"6",
"4",
"4",
"2",
"1",
"2",
"2",
"5",
"10",
"2",
"6",
"5",
"2",
"8",
"8",
"10",
"16",
"4",
"4",
"11",
"4",
"2",
"1",
"2",
"12",
"2",
"2",
"9",
"6",
"8",
"15",
"2",
"6",
"6"
] |
[
"nonn",
"easy"
] | 35 | 1 | 2 |
[
"A003285",
"A013943",
"A035015"
] | null |
Clark Kimberling
| 2025-02-16T08:32:32 |
oeisdata/seq/A013/A013943.seq
|
c451434b48f03877decbe3afa81bab4e
|
A013944
|
Sum of terms in period of continued fraction for square root of the n-th nonsquare.
|
[
"2",
"3",
"4",
"6",
"7",
"5",
"6",
"9",
"8",
"10",
"10",
"7",
"8",
"12",
"17",
"10",
"14",
"18",
"13",
"9",
"10",
"15",
"18",
"16",
"12",
"25",
"13",
"14",
"16",
"11",
"12",
"18",
"16",
"15",
"16",
"14",
"29",
"20",
"20",
"34",
"19",
"13",
"14",
"21",
"26",
"22",
"26",
"20",
"16",
"22",
"20",
"27",
"18",
"36",
"22",
"15",
"16",
"24",
"41",
"20",
"34",
"24",
"33",
"18",
"30",
"20",
"19",
"40"
] |
[
"nonn"
] | 11 | 1 | 1 | null | null |
Clark Kimberling
| 2024-07-21T03:36:11 |
oeisdata/seq/A013/A013944.seq
|
9ab4c7ad527fd65f198b4974fdec7440
|
A013945
|
Least d such that period of continued fraction for sqrt(d) contains n (n^2+2 if n odd, (n/2)^2+1 if n even).
|
[
"3",
"2",
"11",
"5",
"27",
"10",
"51",
"17",
"83",
"26",
"123",
"37",
"171",
"50",
"227",
"65",
"291",
"82",
"363",
"101",
"443",
"122",
"531",
"145",
"627",
"170",
"731",
"197",
"843",
"226",
"963",
"257",
"1091",
"290",
"1227",
"325",
"1371",
"362",
"1523",
"401",
"1683",
"442",
"1851",
"485",
"2027",
"530",
"2211",
"577",
"2403",
"626",
"2603",
"677",
"2811"
] |
[
"nonn",
"easy"
] | 19 | 1 | 1 |
[
"A002522",
"A013945",
"A164897"
] | null |
Clark Kimberling
| 2017-08-09T09:20:23 |
oeisdata/seq/A013/A013945.seq
|
453e25b85747c1f9fccb6575b87fb60b
|
A013946
|
Least d for which the number with continued fraction [n,n,n,n...] is in Q(sqrt(d)).
|
[
"5",
"2",
"13",
"5",
"29",
"10",
"53",
"17",
"85",
"26",
"5",
"37",
"173",
"2",
"229",
"65",
"293",
"82",
"365",
"101",
"445",
"122",
"533",
"145",
"629",
"170",
"733",
"197",
"5",
"226",
"965",
"257",
"1093",
"290",
"1229",
"13",
"1373",
"362",
"61",
"401",
"1685",
"442",
"1853",
"485",
"2029",
"530",
"2213",
"577",
"2405",
"626",
"2605",
"677",
"2813",
"730",
"3029",
"785",
"3253"
] |
[
"nonn"
] | 30 | 1 | 1 |
[
"A002878",
"A013946",
"A077444"
] | null |
Clark Kimberling
| 2024-03-25T12:05:58 |
oeisdata/seq/A013/A013946.seq
|
ff389bb48fa2cd341098e66f7d9c75a5
|
A013947
|
Positions of 1's in Kolakoski sequence (A000002).
|
[
"1",
"4",
"5",
"7",
"10",
"13",
"14",
"16",
"17",
"20",
"22",
"23",
"25",
"28",
"29",
"31",
"32",
"34",
"37",
"40",
"41",
"43",
"46",
"48",
"49",
"51",
"52",
"55",
"58",
"59",
"61",
"64",
"67",
"68",
"70",
"71",
"73",
"76",
"78",
"79",
"82",
"85",
"86",
"88",
"91",
"94",
"95",
"97",
"98",
"101",
"103",
"104",
"106",
"109",
"112",
"113",
"115",
"116",
"118",
"121",
"122",
"124",
"125",
"128",
"130",
"131",
"133"
] |
[
"nonn",
"easy"
] | 15 | 1 | 2 |
[
"A000002",
"A013947",
"A013948",
"A022297",
"A156077"
] | null |
Clark Kimberling
| 2022-07-27T16:35:57 |
oeisdata/seq/A013/A013947.seq
|
610eb756f44a0dbe51b6cc90e5950dc3
|
A013948
|
Positions of 2's in Kolakoski sequence (A000002).
|
[
"2",
"3",
"6",
"8",
"9",
"11",
"12",
"15",
"18",
"19",
"21",
"24",
"26",
"27",
"30",
"33",
"35",
"36",
"38",
"39",
"42",
"44",
"45",
"47",
"50",
"53",
"54",
"56",
"57",
"60",
"62",
"63",
"65",
"66",
"69",
"72",
"74",
"75",
"77",
"80",
"81",
"83",
"84",
"87",
"89",
"90",
"92",
"93",
"96",
"99",
"100",
"102",
"105",
"107",
"108",
"110",
"111",
"114",
"117",
"119",
"120",
"123",
"126",
"127",
"129",
"132",
"135"
] |
[
"nonn",
"easy"
] | 11 | 1 | 1 |
[
"A000002",
"A013947",
"A013948",
"A054353",
"A078649"
] | null |
Clark Kimberling
| 2022-07-27T16:35:30 |
oeisdata/seq/A013/A013948.seq
|
ae51fe37b68b2bedc5affce99f6826c4
|
A013949
|
Start with 1, apply 1->12, 21->21, 22->21, 2->2 (for final 2), take limit.
|
[
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2"
] |
[
"nonn",
"easy"
] | 4 | 1 | 2 | null | null |
Clark Kimberling
| 2012-03-30T18:55:49 |
oeisdata/seq/A013/A013949.seq
|
4935e1258adb072081c8b28a4e0e6f67
|
A013950
|
Start with 1, apply 1->12, 21->21, 22->21, 2->2 (for final 2); a(n) = length of n-th term.
|
[
"1",
"2",
"3",
"4",
"6",
"9",
"12",
"16",
"22",
"31",
"42",
"56",
"76",
"105",
"142",
"190",
"258",
"353",
"476",
"640",
"870",
"1183",
"1594",
"2152",
"2924",
"3961",
"5342",
"7230",
"9810",
"13265",
"17916",
"24272",
"32886",
"44447",
"60106",
"81432",
"110220",
"149001",
"201646",
"273086",
"369442",
"499649",
"676380",
"915616",
"1238534"
] |
[
"nonn"
] | 4 | 1 | 2 |
[
"A013949",
"A013950"
] | null |
Clark Kimberling
| 2012-03-30T18:55:49 |
oeisdata/seq/A013/A013950.seq
|
1c2cc628a0be13dfc1908bd8f3e4013b
|
A013951
|
Start with 1, apply 1->12, 21->21, 22->21, 2->2 (for final 2); take limit; note positions of 1's.
|
[
"1",
"4",
"5",
"7",
"10",
"12",
"13",
"16",
"17",
"20",
"21",
"23",
"26",
"27",
"29",
"32",
"34",
"35",
"37",
"40",
"42",
"43",
"46",
"47",
"50",
"52",
"53",
"56",
"57",
"60",
"61",
"63",
"66",
"67",
"70",
"71",
"74",
"75",
"77",
"80",
"81",
"83",
"86",
"88",
"89",
"91",
"94",
"95",
"97",
"100",
"101",
"103",
"106",
"108",
"109",
"111",
"114",
"116",
"117",
"120"
] |
[
"nonn"
] | 7 | 1 | 2 |
[
"A013949",
"A013951"
] | null |
Clark Kimberling
| 2018-09-02T02:16:59 |
oeisdata/seq/A013/A013951.seq
|
baf015fca26ca39b8baf0b57f5bcbf4b
|
A013952
|
Start with 1, apply 1->12, 21->21, 22->21, 2->2 (for final 2); take limit; note positions of 2's.
|
[
"2",
"3",
"6",
"8",
"9",
"11",
"14",
"15",
"18",
"19",
"22",
"24",
"25",
"28",
"30",
"31",
"33",
"36",
"38",
"39",
"41",
"44",
"45",
"48",
"49",
"51",
"54",
"55",
"58",
"59",
"62",
"64",
"65",
"68",
"69",
"72",
"73",
"76",
"78",
"79",
"82",
"84",
"85",
"87",
"90",
"92",
"93",
"96",
"98",
"99",
"102",
"104",
"105",
"107",
"110",
"112",
"113",
"115",
"118",
"119"
] |
[
"nonn"
] | 7 | 1 | 1 |
[
"A013949",
"A013952"
] | null |
Clark Kimberling
| 2018-09-02T03:03:36 |
oeisdata/seq/A013/A013952.seq
|
88009aa019d98d6120d5563454f7aa16
|
A013953
|
Expansion of the modular form of level 4 and weight 1/2.
|
[
"1",
"0",
"0",
"4",
"-240",
"0",
"0",
"26760",
"-85995",
"0",
"0",
"1707264",
"-4096240",
"0",
"0",
"44330496",
"-91951146",
"0",
"0",
"708938760",
"-1343913984",
"0",
"0",
"8277534720",
"-14733025125",
"0",
"0",
"77092288000",
"-130880766192",
"0",
"0",
"604139268096",
"-988226335125",
"0",
"0",
"4125992712192",
"-6548115718144",
"0",
"0",
"25168873498760"
] |
[
"sign",
"changed"
] | 29 | -3 | 4 |
[
"A000025",
"A013953",
"A192732"
] | null |
N. J. A. Sloane
| 2025-07-08T02:51:09 |
oeisdata/seq/A013/A013953.seq
|
5eedb1b6139c54a341a3ac4fc5460322
|
A013954
|
a(n) = sigma_6(n), the sum of the 6th powers of the divisors of n.
|
[
"1",
"65",
"730",
"4161",
"15626",
"47450",
"117650",
"266305",
"532171",
"1015690",
"1771562",
"3037530",
"4826810",
"7647250",
"11406980",
"17043521",
"24137570",
"34591115",
"47045882",
"65019786",
"85884500",
"115151530",
"148035890",
"194402650",
"244156251",
"313742650",
"387952660",
"489541650",
"594823322",
"741453700"
] |
[
"nonn",
"mult",
"easy"
] | 44 | 1 | 2 |
[
"A000203",
"A001014",
"A001157",
"A001160",
"A013665",
"A013954",
"A013955",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2025-06-29T05:30:07 |
oeisdata/seq/A013/A013954.seq
|
110d1305dc95448ca31343877436385d
|
A013955
|
a(n) = sigma_7(n), the sum of the 7th powers of the divisors of n.
|
[
"1",
"129",
"2188",
"16513",
"78126",
"282252",
"823544",
"2113665",
"4785157",
"10078254",
"19487172",
"36130444",
"62748518",
"106237176",
"170939688",
"270549121",
"410338674",
"617285253",
"893871740",
"1290094638",
"1801914272",
"2513845188",
"3404825448",
"4624699020",
"6103593751",
"8094558822",
"10465138360"
] |
[
"nonn",
"easy",
"mult"
] | 65 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013666",
"A013954",
"A013955",
"A013972",
"A017665",
"A017712",
"A087115"
] | null |
N. J. A. Sloane
| 2023-10-29T02:34:55 |
oeisdata/seq/A013/A013955.seq
|
4be284f4bd5ba2ff35125805bf331c22
|
A013956
|
a(n) = sigma_8(n), the sum of the 8th powers of the divisors of n.
|
[
"1",
"257",
"6562",
"65793",
"390626",
"1686434",
"5764802",
"16843009",
"43053283",
"100390882",
"214358882",
"431733666",
"815730722",
"1481554114",
"2563287812",
"4311810305",
"6975757442",
"11064693731",
"16983563042",
"25700456418",
"37828630724",
"55090232674",
"78310985282",
"110523825058",
"152588281251"
] |
[
"nonn",
"mult",
"easy"
] | 46 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013667",
"A013954",
"A013956",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2025-06-29T05:30:22 |
oeisdata/seq/A013/A013956.seq
|
a656e478a0226d2b54cae999e9b7d6f2
|
A013957
|
a(n) = sigma_9(n), the sum of the 9th powers of the divisors of n.
|
[
"1",
"513",
"19684",
"262657",
"1953126",
"10097892",
"40353608",
"134480385",
"387440173",
"1001953638",
"2357947692",
"5170140388",
"10604499374",
"20701400904",
"38445332184",
"68853957121",
"118587876498",
"198756808749",
"322687697780",
"513002215782",
"794320419872",
"1209627165996",
"1801152661464"
] |
[
"nonn",
"mult",
"easy"
] | 54 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013667",
"A013668",
"A013954",
"A013957",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2023-10-29T02:57:22 |
oeisdata/seq/A013/A013957.seq
|
7bacab62bf9c055504a80c6f8c9e2eed
|
A013958
|
a(n) = sigma_10(n), the sum of the 10th powers of the divisors of n.
|
[
"1",
"1025",
"59050",
"1049601",
"9765626",
"60526250",
"282475250",
"1074791425",
"3486843451",
"10009766650",
"25937424602",
"61978939050",
"137858491850",
"289537131250",
"576660215300",
"1100586419201",
"2015993900450",
"3574014537275",
"6131066257802",
"10250010815226",
"16680163512500",
"26585860217050"
] |
[
"nonn",
"mult",
"easy"
] | 43 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013669",
"A013954",
"A013958",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2025-06-29T05:29:47 |
oeisdata/seq/A013/A013958.seq
|
190635a497e9b96be120573e929835ed
|
A013959
|
a(n) = sigma_11(n), the sum of the 11th powers of the divisors of n.
|
[
"1",
"2049",
"177148",
"4196353",
"48828126",
"362976252",
"1977326744",
"8594130945",
"31381236757",
"100048830174",
"285311670612",
"743375541244",
"1792160394038",
"4051542498456",
"8649804864648",
"17600780175361",
"34271896307634",
"64300154115093",
"116490258898220",
"204900053024478"
] |
[
"nonn",
"mult",
"easy"
] | 74 | 1 | 2 |
[
"A000203",
"A000594",
"A001157",
"A001160",
"A013670",
"A013954",
"A013959",
"A013972",
"A017665",
"A017712",
"A027860",
"A046694"
] | null |
N. J. A. Sloane
| 2025-06-29T05:29:21 |
oeisdata/seq/A013/A013959.seq
|
7a1b91c48183a4a9de93f67ddd918a86
|
A013960
|
a(n) = sigma_12(n), the sum of the 12th powers of the divisors of n.
|
[
"1",
"4097",
"531442",
"16781313",
"244140626",
"2177317874",
"13841287202",
"68736258049",
"282430067923",
"1000244144722",
"3138428376722",
"8918294543346",
"23298085122482",
"56707753666594",
"129746582562692",
"281543712968705",
"582622237229762",
"1157115988280531",
"2213314919066162"
] |
[
"nonn",
"mult",
"easy"
] | 48 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013671",
"A013954",
"A013960",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2023-10-29T02:37:09 |
oeisdata/seq/A013/A013960.seq
|
443e9bd67f1a01303b195830e57ea772
|
A013961
|
a(n) = sigma_13(n), the sum of the 13th powers of the divisors of n.
|
[
"1",
"8193",
"1594324",
"67117057",
"1220703126",
"13062296532",
"96889010408",
"549822930945",
"2541867422653",
"10001220711318",
"34522712143932",
"107006334784468",
"302875106592254",
"793811662272744",
"1946196290656824",
"4504149450301441",
"9904578032905938",
"20825519793796029",
"42052983462257060"
] |
[
"nonn",
"mult",
"easy"
] | 57 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013672",
"A013954",
"A013961",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2025-01-15T04:18:38 |
oeisdata/seq/A013/A013961.seq
|
5a5f0cfd1a650e4921256abeb97cd4da
|
A013962
|
a(n) = sigma_14(n), the sum of the 14th powers of the divisors of n.
|
[
"1",
"16385",
"4782970",
"268451841",
"6103515626",
"78368963450",
"678223072850",
"4398314962945",
"22876797237931",
"100006103532010",
"379749833583242",
"1283997101947770",
"3937376385699290",
"11112685048647250",
"29192932133689220",
"72061992352890881",
"168377826559400930"
] |
[
"nonn",
"mult",
"easy"
] | 47 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013673",
"A013954",
"A013962",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2024-12-30T04:18:01 |
oeisdata/seq/A013/A013962.seq
|
4d24fed36b5b67272c937a672f3da3ab
|
A013963
|
a(n) = sigma_15(n), the sum of the 15th powers of the divisors of n.
|
[
"1",
"32769",
"14348908",
"1073774593",
"30517578126",
"470199366252",
"4747561509944",
"35185445863425",
"205891146443557",
"1000030517610894",
"4177248169415652",
"15407492847694444",
"51185893014090758",
"155572843119354936",
"437893920912786408",
"1152956690052710401",
"2862423051509815794"
] |
[
"nonn",
"mult",
"easy"
] | 39 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013674",
"A013954",
"A013963",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2023-10-29T02:38:19 |
oeisdata/seq/A013/A013963.seq
|
30743c7f450cffa99f275bd29f52090a
|
A013964
|
a(n) = sigma_16(n), the sum of the 16th powers of the divisors of n.
|
[
"1",
"65537",
"43046722",
"4295032833",
"152587890626",
"2821153019714",
"33232930569602",
"281479271743489",
"1853020231898563",
"10000152587956162",
"45949729863572162",
"184887084343023426",
"665416609183179842",
"2177986570740006274",
"6568408508343827972",
"18447025552981295105"
] |
[
"nonn",
"mult",
"easy"
] | 42 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013675",
"A013954",
"A013964",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2023-10-29T02:38:40 |
oeisdata/seq/A013/A013964.seq
|
26bf6e2e41d7a0c84c0d6e45bc195f0b
|
A013965
|
a(n) = sigma_17(n), the sum of the 17th powers of the divisors of n.
|
[
"1",
"131073",
"129140164",
"17180000257",
"762939453126",
"16926788715972",
"232630513987208",
"2251816993685505",
"16677181828806733",
"100000762939584198",
"505447028499293772",
"2218628050709022148",
"8650415919381337934",
"30491579359845314184",
"98526126098761952664"
] |
[
"nonn",
"easy",
"mult"
] | 49 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013676",
"A013954",
"A013965",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2023-10-29T02:39:02 |
oeisdata/seq/A013/A013965.seq
|
18c85b7a69e2b937a95ed62ad8227c14
|
A013966
|
a(n) = sigma_18(n), the sum of the 18th powers of the divisors of n.
|
[
"1",
"262145",
"387420490",
"68719738881",
"3814697265626",
"101560344351050",
"1628413597910450",
"18014467229220865",
"150094635684419611",
"1000003814697527770",
"5559917313492231482",
"26623434909949071690",
"112455406951957393130",
"426880482624234915250",
"1477891883850485076740"
] |
[
"nonn",
"mult",
"easy"
] | 45 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013677",
"A013954",
"A013966",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2023-10-29T02:33:32 |
oeisdata/seq/A013/A013966.seq
|
5536c47a865e79b374919a0161e58dbd
|
A013967
|
a(n) = sigma_19(n), the sum of the 19th powers of the divisors of n.
|
[
"1",
"524289",
"1162261468",
"274878431233",
"19073486328126",
"609360902796252",
"11398895185373144",
"144115462954287105",
"1350851718835253557",
"10000019073486852414",
"61159090448414546292",
"319480609006403630044",
"1461920290375446110678",
"5976315357844100294616"
] |
[
"nonn",
"easy",
"mult"
] | 34 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013678",
"A013954",
"A013967",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2023-10-29T02:39:13 |
oeisdata/seq/A013/A013967.seq
|
256a88eb7f29b43a765509c6ea9d056e
|
A013968
|
a(n) = sigma_20(n), the sum of the 20th powers of the divisors of n.
|
[
"1",
"1048577",
"3486784402",
"1099512676353",
"95367431640626",
"3656161927895954",
"79792266297612002",
"1152922604119523329",
"12157665462543713203",
"100000095367432689202",
"672749994932560009202",
"3833763649708914645906",
"19004963774880799438802",
"83668335217551100221154"
] |
[
"nonn",
"easy",
"mult"
] | 38 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013954",
"A013968",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2023-10-29T08:36:37 |
oeisdata/seq/A013/A013968.seq
|
c9469ce21fe7f8fc60aa3a2b4fe68024
|
A013969
|
a(n) = sigma_21(n), the sum of the 21st powers of the divisors of n.
|
[
"1",
"2097153",
"10460353204",
"4398048608257",
"476837158203126",
"21936961102828212",
"558545864083284008",
"9223376434903384065",
"109418989141972712413",
"1000000476837160300278",
"7400249944258160101212",
"46005141850728850805428",
"247064529073450392704414",
"1171356134499851307229224"
] |
[
"nonn",
"easy",
"mult"
] | 38 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013954",
"A013969",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2023-10-29T08:36:41 |
oeisdata/seq/A013/A013969.seq
|
c260ccb4c806d20cf3a6b7ba6b5a4f26
|
A013970
|
a(n) = sigma_22(n), the sum of the 22nd powers of the divisors of n.
|
[
"1",
"4194305",
"31381059610",
"17592190238721",
"2384185791015626",
"131621735227521050",
"3909821048582988050",
"73786993887028445185",
"984770902214992292491",
"10000002384185795209930",
"81402749386839761113322",
"552061570551763831158810",
"3211838877954855105157370"
] |
[
"nonn",
"easy",
"mult"
] | 35 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013954",
"A013970",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2023-10-29T08:36:44 |
oeisdata/seq/A013/A013970.seq
|
c1c16875096e4467c2423bd53937db87
|
A013971
|
a(n) = sigma_23(n), the sum of the 23rd powers of the divisors of n.
|
[
"1",
"8388609",
"94143178828",
"70368752566273",
"11920928955078126",
"789730317205170252",
"27368747340080916344",
"590295880727458217985",
"8862938119746644274757",
"100000011920928963466734",
"895430243255237372246532",
"6624738056749922960468044",
"41753905413413116367045798"
] |
[
"nonn",
"easy",
"mult"
] | 45 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013954",
"A013971",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2023-10-29T08:36:57 |
oeisdata/seq/A013/A013971.seq
|
618b7bdd431c9315ed08a392a96dc4ef
|
A013972
|
a(n) = sigma_24(n), the sum of the 24th powers of the divisors of n.
|
[
"1",
"16777217",
"282429536482",
"281474993487873",
"59604644775390626",
"4738381620767930594",
"191581231380566414402",
"4722366764344638701569",
"79766443077154939399843",
"1000000059604644792167842",
"9849732675807611094711842",
"79496851942053939878082786",
"542800770374370512771595362"
] |
[
"nonn",
"mult",
"easy"
] | 51 | 1 | 2 |
[
"A000203",
"A001157",
"A001160",
"A013954",
"A013972",
"A017665",
"A017712"
] | null |
N. J. A. Sloane
| 2025-06-29T05:29:35 |
oeisdata/seq/A013/A013972.seq
|
3a734f5791906828e2b67133de34c1b9
|
A013973
|
Expansion of Eisenstein series E_6(q) (alternate convention E_3(q)).
|
[
"1",
"-504",
"-16632",
"-122976",
"-532728",
"-1575504",
"-4058208",
"-8471232",
"-17047800",
"-29883672",
"-51991632",
"-81170208",
"-129985632",
"-187132176",
"-279550656",
"-384422976",
"-545530104",
"-715608432",
"-986161176",
"-1247954400",
"-1665307728",
"-2066980608",
"-2678616864",
"-3243917376",
"-4159663200"
] |
[
"sign",
"easy"
] | 78 | 0 | 2 |
[
"A001160",
"A004009",
"A006352",
"A008410",
"A013973",
"A013974",
"A029828",
"A029829",
"A029830",
"A029831",
"A058550",
"A145095",
"A286346",
"A286399"
] | null |
N. J. A. Sloane
| 2025-02-16T08:32:32 |
oeisdata/seq/A013/A013973.seq
|
8891db2db1a212e4b7f99230475db810
|
A013974
|
Eisenstein series E_10(q) (alternate convention E_5(q)).
|
[
"1",
"-264",
"-135432",
"-5196576",
"-69341448",
"-515625264",
"-2665843488",
"-10653352512",
"-35502821640",
"-102284205672",
"-264515760432",
"-622498190688",
"-1364917062432",
"-2799587834736",
"-5465169838656",
"-10149567696576",
"-18177444679944"
] |
[
"sign"
] | 35 | 0 | 2 |
[
"A004009",
"A006352",
"A008410",
"A013973",
"A013974",
"A029828",
"A029829",
"A029830",
"A029831",
"A058550"
] | null |
N. J. A. Sloane
| 2025-02-16T08:32:32 |
oeisdata/seq/A013/A013974.seq
|
def35782bdf6f200972177db30e32cf9
|
A013975
|
Modular form of level 4 and weight 1/2.
|
[
"1",
"0",
"0",
"0",
"6",
"504",
"0",
"0",
"143388",
"565760",
"0",
"0",
"18473000",
"51180024",
"0",
"0",
"818626500",
"1912896000",
"0",
"0",
"20556578700",
"43222528000",
"0",
"0",
"357139677440",
"697599931392",
"0",
"0",
"4764286992816",
"8806299845112",
"0",
"0",
"51954490735875",
"91956846489088",
"0",
"0"
] |
[
"nonn",
"changed"
] | 7 | -4 | 5 | null | null |
N. J. A. Sloane
| 2025-07-08T02:51:15 |
oeisdata/seq/A013/A013975.seq
|
1a761211222210e30cfce8728c839594
|
A013976
|
Number of tournaments on n nodes with a unique winner.
|
[
"1",
"2",
"6",
"32",
"600",
"20544",
"1218224",
"160241152",
"42129744768",
"21293228876800",
"22220602090444032",
"45959959305969143808",
"188702851949391611599872",
"1566370829898884830446395392",
"25801614282517307546368494213120",
"851300764257208779000509484701188096"
] |
[
"nonn",
"nice"
] | 20 | 1 | 2 |
[
"A013976",
"A125031"
] | null |
Michael Stob (stob(AT)udu.calvin.edu)
| 2022-09-09T22:27:19 |
oeisdata/seq/A013/A013976.seq
|
6d7f85a32458db96c52e0ad577a16a60
|
A013977
|
Molien series of 4-dimensional representation of u.g.g.r. #9.
|
[
"1",
"10",
"40",
"130",
"283",
"513",
"883",
"1372",
"1994",
"2836",
"3853",
"5059",
"6565",
"8302",
"10284",
"12646",
"15295",
"18245",
"21655",
"25408",
"29518",
"34168",
"39217",
"44679",
"50761",
"57298",
"64304",
"72010",
"80227",
"88969",
"98491",
"108580",
"119250",
"130780",
"142933",
"155723",
"169453",
"183862",
"198964",
"215086",
"231943",
"249549",
"268255",
"287752"
] |
[
"nonn",
"changed"
] | 28 | 0 | 2 | null | null |
N. J. A. Sloane
| 2025-07-08T02:51:22 |
oeisdata/seq/A013/A013977.seq
|
acd2b11ae2a01563e258aa2d613dee17
|
A013978
|
Molien series of 4-dimensional representation of u.g.g.r. #8.
|
[
"1",
"0",
"10",
"20",
"40",
"75",
"130",
"179",
"283",
"383",
"513",
"678",
"883",
"1078",
"1372",
"1658",
"1994",
"2385",
"2836",
"3273",
"3853",
"4421",
"5059",
"5772",
"6565",
"7340",
"8302",
"9248",
"10284",
"11415",
"12646",
"13855",
"15295",
"16715",
"18245",
"19890"
] |
[
"nonn",
"easy",
"changed"
] | 23 | 0 | 3 | null | null |
N. J. A. Sloane
| 2025-07-08T02:51:28 |
oeisdata/seq/A013/A013978.seq
|
3dad8557fd7a6796612b963c35c60f38
|
A013979
|
Expansion of 1/(1 - x^2 - x^3 - x^4) = 1/((1 + x)*(1 - x - x^3)).
|
[
"1",
"0",
"1",
"1",
"2",
"2",
"4",
"5",
"8",
"11",
"17",
"24",
"36",
"52",
"77",
"112",
"165",
"241",
"354",
"518",
"760",
"1113",
"1632",
"2391",
"3505",
"5136",
"7528",
"11032",
"16169",
"23696",
"34729",
"50897",
"74594",
"109322",
"160220",
"234813",
"344136",
"504355",
"739169",
"1083304",
"1587660",
"2326828",
"3410133",
"4997792",
"7324621"
] |
[
"nonn",
"easy"
] | 105 | 0 | 5 |
[
"A000045",
"A000930",
"A001634",
"A006498",
"A013979",
"A023435",
"A060945",
"A071675",
"A077889",
"A078012",
"A097333",
"A107458"
] | null |
N. J. A. Sloane
| 2025-01-25T02:11:22 |
oeisdata/seq/A013/A013979.seq
|
71cfa3b1fc4c26240ce2373fdbcb2ea1
|
A013980
|
Number of commutative elements in Coxeter group F_n.
|
[
"24",
"106",
"464",
"2003",
"8560",
"36333",
"153584",
"647775",
"2729365",
"11496788",
"48433965",
"204115805",
"860593940",
"3630164290",
"15319869152",
"64680076487",
"273183844396",
"1154223866418",
"4878180558021",
"20622538937234",
"87202351145432",
"368810395465291"
] |
[
"nonn"
] | 14 | 3 | 1 |
[
"A000045",
"A000108",
"A013980"
] | null |
Ken Fan
| 2024-08-06T07:13:46 |
oeisdata/seq/A013/A013980.seq
|
28cccfd859b6e005720e4763b744b2bf
|
A013981
|
Number of commutative elements in Coxeter group H_n.
|
[
"1",
"2",
"9",
"44",
"195",
"804",
"3185",
"12368",
"47607",
"182720",
"701349",
"2695978",
"10384231",
"40083848",
"155052001",
"600949336",
"2333344095",
"9074611032",
"35344215245",
"137844431690",
"538253680159",
"2104090575136",
"8233413950409"
] |
[
"nonn",
"easy"
] | 10 | 0 | 2 | null | null |
Ken Fan
| 2020-01-21T04:37:20 |
oeisdata/seq/A013/A013981.seq
|
25fb295f23fb4b9ff02ba42eb311b734
|
A013982
|
Expansion of 1/(1-x^2-x^3-x^4-x^5).
|
[
"1",
"0",
"1",
"1",
"2",
"3",
"4",
"7",
"10",
"16",
"24",
"37",
"57",
"87",
"134",
"205",
"315",
"483",
"741",
"1137",
"1744",
"2676",
"4105",
"6298",
"9662",
"14823",
"22741",
"34888",
"53524",
"82114",
"125976",
"193267",
"296502",
"454881",
"697859",
"1070626",
"1642509"
] |
[
"nonn",
"easy",
"changed"
] | 35 | 0 | 5 | null | null |
N. J. A. Sloane
| 2025-07-08T02:51:36 |
oeisdata/seq/A013/A013982.seq
|
6266b996998892e4a4b44232512161ed
|
A013983
|
Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6).
|
[
"1",
"0",
"1",
"1",
"2",
"3",
"5",
"7",
"12",
"18",
"29",
"45",
"71",
"111",
"175",
"274",
"431",
"676",
"1062",
"1667",
"2618",
"4110",
"6454",
"10133",
"15911",
"24982",
"39226",
"61590",
"96706",
"151842",
"238415",
"374346",
"587779",
"922899",
"1449088",
"2275281",
"3572527"
] |
[
"nonn",
"easy",
"changed"
] | 36 | 0 | 5 |
[
"A013983",
"A023437"
] | null |
N. J. A. Sloane
| 2025-07-08T02:51:43 |
oeisdata/seq/A013/A013983.seq
|
471255fb07332b40c1c5b8b1bf4dfe30
|
A013984
|
Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6-x^7).
|
[
"1",
"0",
"1",
"1",
"2",
"3",
"5",
"8",
"12",
"20",
"31",
"50",
"79",
"126",
"200",
"318",
"506",
"804",
"1279",
"2033",
"3233",
"5140",
"8173",
"12995",
"20662",
"32853",
"52236",
"83056",
"132059",
"209975",
"333861",
"530841",
"844040",
"1342028",
"2133832",
"3392804",
"5394577"
] |
[
"nonn",
"easy",
"changed"
] | 27 | 0 | 5 | null | null |
N. J. A. Sloane
| 2025-07-08T02:51:49 |
oeisdata/seq/A013/A013984.seq
|
8ee1ef90b40f08e1383a568ce5f34c0c
|
A013985
|
Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8).
|
[
"1",
"0",
"1",
"1",
"2",
"3",
"5",
"8",
"13",
"20",
"33",
"52",
"84",
"134",
"215",
"344",
"551",
"882",
"1413",
"2262",
"3623",
"5801",
"9290",
"14876",
"23822",
"38147",
"61087",
"97821",
"156646",
"250844",
"401689",
"643243",
"1030056",
"1649477",
"2641386",
"4229776",
"6773341"
] |
[
"nonn",
"easy",
"changed"
] | 14 | 0 | 5 |
[
"A000045",
"A013985"
] | null |
N. J. A. Sloane
| 2025-07-08T02:51:55 |
oeisdata/seq/A013/A013985.seq
|
bbf73089b415e586200d718d2c55e470
|
A013986
|
Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9).
|
[
"1",
"0",
"1",
"1",
"2",
"3",
"5",
"8",
"13",
"21",
"33",
"54",
"86",
"139",
"223",
"359",
"577",
"928",
"1492",
"2399",
"3858",
"6203",
"9975",
"16039",
"25791",
"41471",
"66685",
"107228",
"172421",
"277250",
"445813",
"716860",
"1152698",
"1853519",
"2980426",
"4792474",
"7706215"
] |
[
"nonn",
"easy",
"changed"
] | 23 | 0 | 5 |
[
"A000045",
"A013986"
] | null |
N. J. A. Sloane
| 2025-07-08T02:52:01 |
oeisdata/seq/A013/A013986.seq
|
c523df8fd9c32c14e2aff5c2280abf30
|
A013987
|
Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10).
|
[
"1",
"0",
"1",
"1",
"2",
"3",
"5",
"8",
"13",
"21",
"34",
"54",
"88",
"141",
"228",
"367",
"592",
"954",
"1538",
"2479",
"3996",
"6441",
"10383",
"16736",
"26978",
"43486",
"70097",
"112991",
"182134",
"293587",
"473242",
"762833",
"1229634",
"1982084",
"3194982",
"5150088",
"8301584",
"13381575",
"21570168",
"34769609",
"56046190"
] |
[
"nonn",
"easy",
"changed"
] | 21 | 0 | 5 |
[
"A000045",
"A013987"
] | null |
N. J. A. Sloane
| 2025-07-08T02:52:08 |
oeisdata/seq/A013/A013987.seq
|
2dc7e82ac18d430811a78d109af841fe
|
A013988
|
Triangle read by rows, the inverse Bell transform of n!*binomial(5,n) (without column 0).
|
[
"1",
"5",
"1",
"55",
"15",
"1",
"935",
"295",
"30",
"1",
"21505",
"7425",
"925",
"50",
"1",
"623645",
"229405",
"32400",
"2225",
"75",
"1",
"21827575",
"8423415",
"1298605",
"103600",
"4550",
"105",
"1",
"894930575",
"358764175",
"59069010",
"5235405",
"271950",
"8330",
"140",
"1",
"42061737025",
"17398082625",
"3016869625",
"289426830",
"16929255",
"621810",
"14070",
"180",
"1"
] |
[
"easy",
"nonn",
"tabl"
] | 43 | 1 | 2 |
[
"A000369",
"A001497",
"A004747",
"A008277",
"A008543",
"A010054",
"A011801",
"A013988",
"A028844",
"A049224",
"A264428"
] | null |
Wolfdieter Lang
| 2023-10-03T13:14:33 |
oeisdata/seq/A013/A013988.seq
|
1797302400345f872260d3a2fa175a56
|
A013989
|
a(n) = (n+1)*(a(n-1)/n + a(n-2)), with a(0)=1, a(1)=2.
|
[
"1",
"2",
"6",
"16",
"50",
"156",
"532",
"1856",
"6876",
"26200",
"104456",
"428352",
"1821976",
"7959056",
"35857200",
"165592576",
"785514512",
"3812387616",
"18948962656",
"96194028800",
"498931946016",
"2638959243712",
"14234346694976"
] |
[
"nonn",
"easy"
] | 43 | 0 | 2 |
[
"A000085",
"A013989"
] | null |
N. J. A. Sloane, Dan Hoey, 1996
| 2023-07-06T07:02:01 |
oeisdata/seq/A013/A013989.seq
|
ae5fe556d4b555c640c48b9e23eaa9d5
|
A013990
|
Number of edge-disjoint paths between opposite corners of n X n grid.
|
[
"1",
"1",
"2",
"16",
"800",
"323632",
"1086297184",
"30766606427588",
"7466577706821521924",
"15681997226277809235573754",
"286995508313697459220070082104780",
"45988915870193885369543805313062149050276"
] |
[
"nonn",
"hard"
] | 9 | 0 | 3 |
[
"A013990",
"A013991",
"A013992",
"A013993",
"A013994",
"A013995",
"A013996",
"A013997"
] | null |
Dan Hoey
| 2018-09-24T02:02:30 |
oeisdata/seq/A013/A013990.seq
|
a44b389b1aaeac901f3209cbf2a34699
|
A013991
|
Number of edge-disjoint paths between opposite corners of a 2 X n grid.
|
[
"1",
"1",
"4",
"16",
"72",
"335",
"1562",
"7273",
"33850",
"157534",
"733148",
"3412005",
"15879172",
"73900265",
"343925312",
"1600598044",
"7449042040",
"34667184251",
"161338016046",
"750852888177",
"3494403076902",
"16262643529850",
"75684907767980",
"352230881365025",
"1639251436594792",
"7628931517771089"
] |
[
"nonn",
"easy"
] | 21 | 0 | 3 |
[
"A013990",
"A013991",
"A013992",
"A013993",
"A013994",
"A013995",
"A013996",
"A013997"
] | null |
Dan Hoey
| 2022-09-08T08:44:39 |
oeisdata/seq/A013/A013991.seq
|
d5cd2e03691a17f21c775dd130bba721
|
A013992
|
Number of edge-disjoint paths between opposite corners of 3 X n grid.
|
[
"1",
"1",
"8",
"72",
"800",
"9754",
"121130",
"1508919",
"18787340",
"233941432",
"2912502538",
"36262251784",
"451462592746",
"5620827261214",
"69979671635586",
"871259379376415",
"10847277968319460",
"135050246142276024",
"1681392997487494568",
"20933580943579610208",
"260625895660539796224"
] |
[
"nonn"
] | 12 | 0 | 3 |
[
"A013990",
"A013991",
"A013992",
"A013993",
"A013994",
"A013995",
"A013996",
"A013997"
] | null |
Dan Hoey
| 2018-09-18T04:46:31 |
oeisdata/seq/A013/A013992.seq
|
64d0f190f1dfe74dc71a3ceb2f89f93a
|
A013993
|
Number of edge-disjoint paths between opposite corners of 4 X n grid.
|
[
"1",
"1",
"16",
"335",
"9754",
"323632",
"11171466",
"389866263",
"13662905466",
"479251547011",
"16821606120516",
"590415835527858",
"20726430358013659",
"727543012137899046",
"25540208938124629118",
"896540705406585866451"
] |
[
"nonn"
] | 11 | 0 | 3 |
[
"A013990",
"A013991",
"A013992",
"A013993",
"A013994",
"A013995",
"A013996",
"A013997"
] | null |
Dan Hoey
| 2018-09-19T04:05:31 |
oeisdata/seq/A013/A013993.seq
|
2e70e4718fac1caef59af94f6efc8147
|
A013994
|
Number of edge-disjoint paths between opposite corners of 5xn grid.
|
[
"1",
"1",
"32",
"1562",
"121130",
"11171466",
"1086297184",
"107939069941",
"10816244385930",
"1088622220193884",
"109714281030331408",
"11069298856395333635",
"1116902915717574810660",
"112738159254434557027160"
] |
[
"nonn"
] | 11 | 0 | 3 |
[
"A013990",
"A013991",
"A013992",
"A013993",
"A013994",
"A013995",
"A013996",
"A013997"
] | null |
Dan Hoey
| 2018-09-19T04:05:22 |
oeisdata/seq/A013/A013994.seq
|
446eee7dcd5e732f95d5dd1ac2b1642c
|
A013995
|
Number of edge-disjoint paths between opposite corners of 6 X n grid.
|
[
"1",
"1",
"64",
"7273",
"1508919",
"389866263",
"107939069941",
"30766606427588",
"8900924886661736",
"2592366455926147562",
"758069487021252428263",
"222005624352493942917379",
"65098736121811226967665264"
] |
[
"nonn"
] | 11 | 0 | 3 |
[
"A013990",
"A013991",
"A013992",
"A013993",
"A013994",
"A013995",
"A013996",
"A013997"
] | null |
Dan Hoey
| 2018-09-20T15:14:10 |
oeisdata/seq/A013/A013995.seq
|
26b41addfecaaf72b086e859eb43918b
|
A013996
|
Number of edge-disjoint paths between opposite corners of 7 X n grid.
|
[
"1",
"1",
"128",
"33850",
"18787340",
"13662905466",
"10816244385930",
"8900924886661736",
"7466577706821521924",
"6332745788043635410871",
"5399881205287667310503858",
"4621213692709052543074522862"
] |
[
"nonn"
] | 9 | 0 | 3 | null | null |
Dan Hoey
| 2018-09-20T15:13:45 |
oeisdata/seq/A013/A013996.seq
|
5be88a7ee5fc4d80ba14502d5e488a2d
|
A013997
|
Number of edge-disjoint paths between opposite corners of 8 X n grid.
|
[
"1",
"1",
"256",
"157534",
"233941432",
"479251547011",
"1088622220193884",
"2592366455926147562",
"6332745788043635410871",
"15681997226277809235573754",
"39167604588475049043393511660"
] |
[
"nonn"
] | 9 | 0 | 3 | null | null |
Dan Hoey
| 2018-09-20T17:48:54 |
oeisdata/seq/A013/A013997.seq
|
2283106344315099ed4c04a9f455d4f4
|
A013998
|
Unrestricted Perrin pseudoprimes.
|
[
"271441",
"904631",
"16532714",
"24658561",
"27422714",
"27664033",
"46672291",
"102690901",
"130944133",
"196075949",
"214038533",
"517697641",
"545670533",
"801123451",
"855073301",
"903136901",
"970355431",
"1091327579",
"1133818561",
"1235188597",
"1389675541",
"1502682721",
"2059739221",
"2304156469",
"2976407809",
"3273820903"
] |
[
"nonn"
] | 127 | 1 | 1 |
[
"A000010",
"A001608",
"A013998",
"A018187",
"A173656"
] | null |
R. K. Guy
| 2025-02-16T08:32:32 |
oeisdata/seq/A013/A013998.seq
|
38802beae628bc6ee90c9d822eb55196
|
A013999
|
From applying the "rational mean" to the number e.
|
[
"1",
"1",
"2",
"8",
"42",
"258",
"1824",
"14664",
"132360",
"1326120",
"14606640",
"175448160",
"2282469840",
"31972303440",
"479793807360",
"7679384173440",
"130586660507520",
"2351111258805120",
"44679858911251200",
"893744703503769600",
"18771276190401504000",
"413017883356110278400"
] |
[
"nonn"
] | 43 | 0 | 3 |
[
"A000271",
"A013999"
] | null |
Domingo Gomez Morin (Dgomezm(AT)etheron.net)
| 2023-11-11T14:23:12 |
oeisdata/seq/A013/A013999.seq
|
d66b8d779042ee14d855bbd1fe6aa852
|
A014000
|
First coordinate of fundamental unit of real quadratic field with discriminant A003658(n), n >= 2.
|
[
"0",
"1",
"2",
"1",
"3",
"2",
"5",
"8",
"2",
"19",
"5",
"3",
"27",
"10",
"3",
"15",
"131",
"4",
"17",
"7",
"11",
"943",
"170",
"4",
"4",
"197",
"447",
"24",
"13",
"5035",
"9",
"5",
"37",
"118",
"703",
"11",
"1520",
"15371",
"79",
"35",
"1595",
"6",
"87",
"11",
"28",
"37",
"25",
"98",
"10847",
"6",
"13",
"3482",
"6",
"57731",
"604",
"24335",
"63",
"48",
"1637147",
"13",
"478763"
] |
[
"nonn"
] | 42 | 2 | 3 |
[
"A003652",
"A003658",
"A014000",
"A014046",
"A014077"
] | null |
Eric Rains (rains(AT)caltech.edu)
| 2019-12-14T01:46:42 |
oeisdata/seq/A014/A014000.seq
|
12d8ee42e743b37f7e6701dacbd7699c
|
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