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666,262,453B
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635M
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listlengths 1
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⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-14 02:38:35
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A385611 | Numbers that can be written as s^w + t^x + u^y + v^z with 1 < s < t < u and {s,t,u,v} = {w,x,y,z} (the sequence of exponents can be any permutation of s,t,u,v). | [
"202",
"245",
"254",
"322",
"340",
"348",
"377",
"383",
"400",
"422",
"460",
"465",
"468",
"532",
"545",
"548",
"568",
"603",
"628",
"688",
"700",
"730",
"736",
"738",
"739",
"845",
"865",
"876",
"892",
"922",
"936",
"961",
"977",
"1002",
"1029",
"1033",
"1036",
"1092",
"1122",
"1138",
"1174",
"1205",
"1234",
"1236",
"1265",
"1269",
"1338",
"1403",
"1407",
"1433"
]
| [
"nonn",
"new"
]
| 18 | 1 | 1 | [
"A001597",
"A385232",
"A385233",
"A385611"
]
| null | Jean-Marc Rebert, Jul 04 2025 | 2025-07-08T22:11:20 | oeisdata/seq/A385/A385611.seq | 2bbf5281d82089b4e65246ba5d594667 |
A385612 | Decimal expansion zeta''''(0) (negated). | [
"2",
"3",
"9",
"9",
"7",
"1",
"0",
"3",
"1",
"8",
"8",
"0",
"1",
"3",
"7",
"0",
"7",
"9",
"5",
"8",
"9",
"8",
"7",
"2",
"1",
"9",
"5",
"2",
"7",
"7",
"4",
"1",
"0",
"0",
"5",
"6",
"6",
"1",
"8",
"9",
"1",
"1",
"3",
"9",
"9",
"3",
"4",
"9",
"2",
"1",
"7",
"0",
"3",
"4",
"2",
"4",
"9",
"7",
"6",
"0",
"0",
"9",
"3",
"3",
"3",
"0",
"4",
"6",
"3",
"8",
"2",
"9",
"3",
"8",
"6",
"3",
"3",
"4",
"4",
"9",
"9",
"1",
"3",
"8",
"2",
"8",
"6",
"1",
"8",
"2",
"2",
"7",
"5",
"7",
"8",
"1",
"3",
"3",
"4",
"6",
"9",
"4",
"9",
"0",
"3"
]
| [
"nonn",
"cons",
"new"
]
| 26 | 2 | 1 | [
"A001620",
"A061444",
"A075700",
"A082633",
"A086279",
"A086280",
"A257549",
"A261508",
"A385612"
]
| null | Artur Jasinski, Jul 04 2025 | 2025-07-05T09:59:11 | oeisdata/seq/A385/A385612.seq | 66be226d45c3506e3dfc4435e8e9beb2 |
A385614 | Numbers of the form x^x + y^y, 1 < x < y. | [
"31",
"260",
"283",
"3129",
"3152",
"3381",
"46660",
"46683",
"46912",
"49781",
"823547",
"823570",
"823799",
"826668",
"870199",
"16777220",
"16777243",
"16777472",
"16780341",
"16823872",
"17600759",
"387420493",
"387420516",
"387420745",
"387423614",
"387467145",
"388244032",
"404197705",
"10000000004"
]
| [
"nonn",
"easy",
"new"
]
| 26 | 1 | 1 | [
"A000312",
"A173054",
"A385232",
"A385614"
]
| null | Sean A. Irvine, Jul 04 2025 | 2025-07-06T06:38:22 | oeisdata/seq/A385/A385614.seq | d006b686ec0a1c339966fcadd36b8bf2 |
A385615 | Star numbers corresponding to the point numbers in A385330. | [
"1",
"2",
"2",
"3",
"2",
"3",
"3",
"4",
"2",
"4",
"3",
"4",
"2",
"3",
"4",
"5",
"3",
"4",
"2",
"5",
"4",
"5",
"3",
"5",
"4",
"2",
"3",
"5",
"6",
"4",
"5",
"6",
"3",
"4",
"6",
"2",
"5",
"6",
"4",
"5",
"3",
"6",
"5",
"4",
"6",
"7",
"2",
"3",
"5",
"7",
"6",
"4",
"7",
"5",
"6",
"3",
"7",
"4",
"6",
"2",
"5",
"7",
"6",
"4",
"7",
"5",
"3",
"6",
"7",
"8",
"5",
"4",
"6",
"7",
"2",
"8",
"3",
"5",
"8",
"7",
"6",
"4",
"8",
"7",
"5",
"6",
"8"
]
| [
"nonn",
"tabf",
"new"
]
| 6 | 1 | 2 | [
"A385330",
"A385615"
]
| null | Sean A. Irvine and Tamas Sandor Nagy, Jul 08 2025 | 2025-07-09T05:32:05 | oeisdata/seq/A385/A385615.seq | 50bd2dcee185476b7016a0e8a69a31b7 |
A385617 | G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(x) + A(2*x)) ). | [
"1",
"2",
"10",
"82",
"1062",
"22646",
"846570",
"58644858",
"7808479582",
"2038568219422",
"1054007965984050",
"1084591195956246130",
"2226674324358059364150",
"9131600163886719149539590",
"74851744440590132840318820090",
"1226745312860243142951267683147178",
"40204124737879503807503331117931168974"
]
| [
"nonn",
"new"
]
| 14 | 0 | 2 | [
"A000051",
"A015083",
"A047749",
"A385617",
"A385618",
"A385622"
]
| null | Seiichi Manyama, Jul 05 2025 | 2025-07-05T09:16:52 | oeisdata/seq/A385/A385617.seq | ca0f0e4b1c29f5b0762be568d1d6da82 |
A385618 | G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(2*x) + A(3*x)) ). | [
"1",
"2",
"14",
"230",
"9014",
"913334",
"254986934",
"203241812630",
"471322195238102",
"3214892041613961206",
"64937611960188470964662",
"3901256965326759127330935830",
"699101347969640933511109922382422",
"374397435055450676411068538643233721206",
"599979003238812649083869782544110463986119734"
]
| [
"nonn",
"new"
]
| 13 | 0 | 2 | [
"A007689",
"A015083",
"A015084",
"A047749",
"A385617",
"A385618"
]
| null | Seiichi Manyama, Jul 05 2025 | 2025-07-05T09:58:48 | oeisdata/seq/A385/A385618.seq | 405a594a3927b31d71af76475379902c |
A385619 | E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(2*x)) ). | [
"1",
"2",
"16",
"320",
"14176",
"1363872",
"288285760",
"135499302976",
"142083696478720",
"331241746024775168",
"1705949708332396248064",
"19272264281263882812337152",
"474329882865823082358501265408",
"25275628582523724268037232839274496",
"2899873213836728319564120809900380069888"
]
| [
"nonn",
"new"
]
| 11 | 0 | 2 | [
"A385617",
"A385619"
]
| null | Seiichi Manyama, Jul 05 2025 | 2025-07-05T09:29:23 | oeisdata/seq/A385/A385619.seq | d9b00521ef16d9f6339e4555c6d24861 |
A385620 | E.g.f. A(x) satisfies A(x) = exp( x*(A(2*x) + A(3*x)) ). | [
"1",
"2",
"24",
"1064",
"158144",
"78427712",
"130391102464",
"725657074158592",
"13450842239318679552",
"825492067428121929359360",
"166724642619378284453845213184",
"110175812687250637947409895640473600",
"236918101449618886434191300434062010777600",
"1649425480856495624442166311045759714226010423296"
]
| [
"nonn",
"new"
]
| 13 | 0 | 2 | [
"A058014",
"A096538",
"A385526",
"A385620"
]
| null | Seiichi Manyama, Jul 05 2025 | 2025-07-05T09:59:02 | oeisdata/seq/A385/A385620.seq | 875563473c842a7445ffbbeea7f38f18 |
A385621 | E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(3*x))/2 ). | [
"1",
"1",
"5",
"88",
"5301",
"1115376",
"823422553",
"2109689685664",
"18480955532693321",
"545890697425512822016",
"53732023859661557312932461",
"17451409191554766719804179944960",
"18549102840350232594174973144785505021",
"64075761168350693656591055399719635872352256",
"715103564008507527975398262955305194708318040264449"
]
| [
"nonn",
"new"
]
| 12 | 0 | 3 | [
"A007051",
"A385621",
"A385622"
]
| null | Seiichi Manyama, Jul 05 2025 | 2025-07-05T09:58:53 | oeisdata/seq/A385/A385621.seq | ed794ed33ea8c3d57431288846c25e51 |
A385622 | G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(x) + A(3*x))/2 ). | [
"1",
"1",
"3",
"20",
"321",
"13847",
"1718124",
"630600310",
"691143519765",
"2269026118814651",
"22336295204505116859",
"659523795328845920952570",
"58417979762116119140729740620",
"15523000838307934869469597031994180",
"12374377440444177691000805646758968904928",
"29593162781962095695448333383964939013238970030"
]
| [
"nonn",
"new"
]
| 13 | 0 | 3 | [
"A007051",
"A385617",
"A385621",
"A385622"
]
| null | Seiichi Manyama, Jul 05 2025 | 2025-07-05T09:58:49 | oeisdata/seq/A385/A385622.seq | 8aeb0bc94aeca559594e46f37a97e887 |
A385623 | Array read by ascending antidiagonals: A(n,k) is the number obtained by concatenation of n with k in that order, with k >= 0. | [
"0",
"10",
"1",
"20",
"11",
"2",
"30",
"21",
"12",
"3",
"40",
"31",
"22",
"13",
"4",
"50",
"41",
"32",
"23",
"14",
"5",
"60",
"51",
"42",
"33",
"24",
"15",
"6",
"70",
"61",
"52",
"43",
"34",
"25",
"16",
"7",
"80",
"71",
"62",
"53",
"44",
"35",
"26",
"17",
"8",
"90",
"81",
"72",
"63",
"54",
"45",
"36",
"27",
"18",
"9",
"100",
"91",
"82",
"73",
"64",
"55",
"46",
"37",
"28",
"19",
"10",
"110",
"101",
"92",
"83",
"74",
"65",
"56",
"47",
"38",
"29",
"110",
"11"
]
| [
"nonn",
"base",
"easy",
"look",
"tabl",
"new"
]
| 17 | 0 | 2 | [
"A001477",
"A008592",
"A017281",
"A017293",
"A017305",
"A017317",
"A017329",
"A017341",
"A017353",
"A017365",
"A017377",
"A020338",
"A055642",
"A385623",
"A385624"
]
| null | Stefano Spezia, Jul 05 2025 | 2025-07-11T15:37:30 | oeisdata/seq/A385/A385623.seq | 4c97d4c1674f4cbeb4a7b3a40e4a2d0d |
A385624 | Antidiagonal sums of the array defined in A385623. | [
"0",
"11",
"33",
"66",
"110",
"165",
"231",
"308",
"396",
"495",
"605",
"816",
"1128",
"1541",
"2055",
"2670",
"3386",
"4203",
"5121",
"6140",
"7260",
"8481",
"9803",
"11226",
"12750",
"14375",
"16101",
"17928",
"19856",
"21885",
"24015",
"26246",
"28578",
"31011",
"33545",
"36180",
"38916",
"41753",
"44691",
"47730",
"50870",
"54111",
"57453",
"60896"
]
| [
"nonn",
"base",
"new"
]
| 12 | 0 | 2 | [
"A385623",
"A385624"
]
| null | Stefano Spezia, Jul 05 2025 | 2025-07-09T23:50:50 | oeisdata/seq/A385/A385624.seq | 040709216e6fdab4424fa15c2a697a73 |
A385625 | Sum of the divisors d of n with an odd number of primes not exceeding d. | [
"0",
"2",
"0",
"2",
"5",
"8",
"0",
"2",
"0",
"7",
"11",
"20",
"0",
"2",
"5",
"2",
"17",
"26",
"0",
"7",
"0",
"13",
"23",
"44",
"30",
"28",
"27",
"30",
"0",
"13",
"31",
"34",
"44",
"53",
"40",
"74",
"0",
"2",
"0",
"7",
"41",
"50",
"0",
"13",
"5",
"25",
"47",
"92",
"49",
"82",
"68",
"80",
"0",
"53",
"16",
"30",
"0",
"2",
"59",
"85",
"0",
"33",
"0",
"34",
"5",
"52",
"67",
"121",
"92",
"112",
"0",
"98",
"73",
"76",
"105",
"78",
"88",
"112",
"0",
"7",
"27",
"43",
"83",
"174",
"107",
"88",
"87",
"101",
"0",
"31",
"0",
"25",
"31",
"49",
"5",
"124",
"97",
"149"
]
| [
"nonn",
"easy",
"new"
]
| 11 | 1 | 2 | [
"A000203",
"A000720",
"A071986",
"A345219",
"A385625",
"A385628"
]
| null | Wesley Ivan Hurt, Jul 05 2025 | 2025-07-05T09:36:13 | oeisdata/seq/A385/A385625.seq | c91cae111acf4ccb26ecafd7548b65dc |
A385626 | Table read by rows: T(n, k) = binomial(n, k) * fibonomial(n, k). | [
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"6",
"6",
"1",
"1",
"12",
"36",
"12",
"1",
"1",
"25",
"150",
"150",
"25",
"1",
"1",
"48",
"600",
"1200",
"600",
"48",
"1",
"1",
"91",
"2184",
"9100",
"9100",
"2184",
"91",
"1",
"1",
"168",
"7644",
"61152",
"127400",
"61152",
"7644",
"168",
"1",
"1",
"306",
"25704",
"389844",
"1559376",
"1559376",
"389844",
"25704",
"306",
"1"
]
| [
"nonn",
"tabl",
"new"
]
| 9 | 0 | 5 | [
"A003266",
"A007318",
"A010048",
"A385626",
"A385630"
]
| null | Peter Luschny, Jul 05 2025 | 2025-07-05T09:58:36 | oeisdata/seq/A385/A385626.seq | e1dc6f5621bfd58fb6863b44d8048180 |
A385627 | Table read by rows: T(n, k) = (binomial(n, k) * fibonomial(n, k)) mod 2. | [
"1",
"1",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"1",
"0",
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"1",
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"1",
"1",
"1",
"1",
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1"
]
| [
"nonn",
"tabl",
"new"
]
| 10 | 0 | null | [
"A007318",
"A010048",
"A047999",
"A385395",
"A385456",
"A385626",
"A385627",
"A385630"
]
| null | Peter Luschny, Jul 06 2025 | 2025-07-07T03:18:42 | oeisdata/seq/A385/A385627.seq | ba8eb06436dd1e25b17e9ccb43a072db |
A385628 | Sum of the divisors d of n with an even number of primes not exceeding d. | [
"1",
"1",
"4",
"5",
"1",
"4",
"8",
"13",
"13",
"11",
"1",
"8",
"14",
"22",
"19",
"29",
"1",
"13",
"20",
"35",
"32",
"23",
"1",
"16",
"1",
"14",
"13",
"26",
"30",
"59",
"1",
"29",
"4",
"1",
"8",
"17",
"38",
"58",
"56",
"83",
"1",
"46",
"44",
"71",
"73",
"47",
"1",
"32",
"8",
"11",
"4",
"18",
"54",
"67",
"56",
"90",
"80",
"88",
"1",
"83",
"62",
"63",
"104",
"93",
"79",
"92",
"1",
"5",
"4",
"32",
"72",
"97",
"1",
"38",
"19",
"62",
"8",
"56",
"80",
"179",
"94",
"83",
"1",
"50",
"1",
"44",
"33",
"79",
"90",
"203",
"112",
"143",
"97",
"95",
"115"
]
| [
"nonn",
"easy",
"new"
]
| 8 | 1 | 3 | [
"A000203",
"A000720",
"A131377",
"A345220",
"A385625",
"A385628"
]
| null | Wesley Ivan Hurt, Jul 05 2025 | 2025-07-05T09:36:40 | oeisdata/seq/A385/A385628.seq | 49781a2f895854050018b7ba3a008414 |
A385630 | a(n) = n! * Prod_{k=1..n} Fibonacci(k). | [
"1",
"1",
"2",
"12",
"144",
"3600",
"172800",
"15724800",
"2641766400",
"808380518400",
"444609285120000",
"435272490132480000",
"752150862948925440000",
"2278264963872295157760000",
"12024682479317973842657280000",
"110025844685759460660314112000000",
"1737528139277513402747680456704000000"
]
| [
"nonn",
"new"
]
| 8 | 0 | 3 | [
"A000045",
"A000142",
"A003266",
"A385630"
]
| null | Peter Luschny, Jul 05 2025 | 2025-07-05T09:58:42 | oeisdata/seq/A385/A385630.seq | 4b12d372cdcb4a26dd9fea3a63880ed3 |
A385631 | Products of five consecutive integers whose prime divisors are consecutive primes starting at 2. | [
"120",
"720",
"2520",
"6720",
"15120",
"30240",
"55440",
"240240",
"360360"
]
| [
"nonn",
"fini",
"full",
"new"
]
| 8 | 1 | 1 | [
"A052787",
"A055932",
"A217056",
"A385189",
"A385415",
"A385631"
]
| null | Ken Clements, Jul 05 2025 | 2025-07-09T16:36:07 | oeisdata/seq/A385/A385631.seq | b4e82280c59a8450d6ad4f23d087af61 |
A385633 | a(n) = a(n-1) + a(n-3), with a(0) = 1, a(1) = 4, a(2) = 8. | [
"1",
"4",
"8",
"9",
"13",
"21",
"30",
"43",
"64",
"94",
"137",
"201",
"295",
"432",
"633",
"928",
"1360",
"1993",
"2921",
"4281",
"6274",
"9195",
"13476",
"19750",
"28945",
"42421",
"62171",
"91116",
"133537",
"195708",
"286824",
"420361",
"616069",
"902893",
"1323254",
"1939323",
"2842216",
"4165470",
"6104793",
"8947009",
"13112479",
"19217272"
]
| [
"nonn",
"easy",
"new"
]
| 15 | 0 | 2 | [
"A000930",
"A179070",
"A385633"
]
| null | Greg Dresden and Saim Usmani, Jul 05 2025 | 2025-07-09T22:14:59 | oeisdata/seq/A385/A385633.seq | 5eaed7082e3759d2fb9a282b5d78c515 |
A385634 | Period 8: repeat [1, 3, 7, 2, 6, 5, 4, 8]. | [
"1",
"3",
"7",
"2",
"6",
"5",
"4",
"8",
"1",
"3",
"7",
"2",
"6",
"5",
"4",
"8",
"1",
"3",
"7",
"2",
"6",
"5",
"4",
"8",
"1",
"3",
"7",
"2",
"6",
"5",
"4",
"8",
"1",
"3",
"7",
"2",
"6",
"5",
"4",
"8",
"1",
"3",
"7",
"2",
"6",
"5",
"4",
"8",
"1",
"3",
"7",
"2",
"6",
"5",
"4",
"8",
"1",
"3",
"7",
"2",
"6",
"5",
"4",
"8",
"1",
"3",
"7",
"2",
"6",
"5",
"4",
"8",
"1",
"3",
"7",
"2",
"6",
"5",
"4",
"8",
"1",
"3",
"7",
"2",
"6",
"5",
"4",
"8"
]
| [
"nonn",
"easy",
"new"
]
| 27 | 0 | 2 | [
"A385491",
"A385634"
]
| null | Christopher W Moriarty, Jul 05 2025 | 2025-07-13T11:08:59 | oeisdata/seq/A385/A385634.seq | cb5f7379f9daf70565cf47ae0e1baccb |
A385635 | G.f. satisfies A(x) = x + Product_{n>=2} A(x^n) with A(0) = 1. | [
"1",
"1",
"1",
"1",
"2",
"2",
"4",
"4",
"8",
"8",
"13",
"15",
"26",
"26",
"41",
"48",
"73",
"80",
"119",
"136",
"198",
"225",
"313",
"367",
"518",
"585",
"797",
"941",
"1264",
"1466",
"1953",
"2285",
"3022",
"3524",
"4571",
"5391",
"6993",
"8152",
"10440",
"12316",
"15684",
"18370",
"23236",
"27327",
"34389",
"40364",
"50370",
"59292",
"73880",
"86547",
"107080",
"125976",
"155266",
"182058"
]
| [
"nonn",
"new"
]
| 9 | 0 | 5 | [
"A129374",
"A129375",
"A385635"
]
| null | Paul D. Hanna, Jul 05 2025 | 2025-07-06T05:08:02 | oeisdata/seq/A385/A385635.seq | acada605003d3e9103f9a1cd45accbcf |
A385636 | Numbers k where sin(sqrt(k)) reaches successive record high values. | [
"0",
"1",
"2",
"60",
"61",
"62",
"200",
"417",
"2687",
"1536009",
"57157270",
"81436635",
"143005063"
]
| [
"nonn",
"more",
"new"
]
| 15 | 1 | 3 | [
"A046959",
"A046964",
"A046965",
"A385636"
]
| null | Artur Jasinski, Jul 05 2025 | 2025-07-13T00:53:24 | oeisdata/seq/A385/A385636.seq | e39833834a6a310529d08280296a25de |
A385640 | Numbers k such that the sum of the digits of k divides k and the sum of the digits of k^2 divides k^2. | [
"1",
"2",
"3",
"6",
"9",
"10",
"12",
"18",
"20",
"21",
"24",
"30",
"36",
"42",
"45",
"48",
"54",
"60",
"63",
"72",
"80",
"84",
"90",
"100",
"102",
"108",
"110",
"111",
"112",
"117",
"120",
"126",
"132",
"140",
"144",
"150",
"156",
"162",
"180",
"190",
"198",
"200",
"201",
"204",
"207",
"210",
"216",
"220",
"234",
"240",
"243",
"252",
"264",
"270",
"288",
"300",
"306",
"315"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 21 | 1 | 2 | [
"A005349",
"A007953",
"A385640",
"A385656"
]
| null | Vighnesh Patil, Jul 05 2025 | 2025-07-09T10:13:31 | oeisdata/seq/A385/A385640.seq | e87d35ab3952cac6f00e7f2f06e8d4de |
A385642 | G.f. A(x) satisfies 2*(1-x) = Sum_{n=-oo..+oo} (x - A(x)^n)^(n+1) * (A(x) - x^n)^(n+1). | [
"1",
"1",
"1",
"2",
"4",
"8",
"13",
"35",
"86",
"191",
"447",
"1103",
"2810",
"6974",
"17471",
"44795",
"115279",
"296474",
"763834",
"1981967",
"5164628",
"13473784",
"35236723",
"92443470",
"243157407",
"640688394",
"1691077318",
"4472493065",
"11849608512",
"31441695581",
"83545685025",
"222309673546",
"592337513731",
"1580160709355",
"4220133780310"
]
| [
"nonn",
"new"
]
| 9 | 1 | 4 | null | null | Paul D. Hanna, Jul 05 2025 | 2025-07-06T05:18:24 | oeisdata/seq/A385/A385642.seq | b2231157e36c8829acdaa6fdc2d542df |
A385643 | Galileo sequence with ratio k = 5: a(1) = 1, a(2) = k, a(2*n-1) = floor(((k + 1)*a(n) -1)/2), and a(2*n) = floor((k + 1)*a(n)/2) + 1 for n > 2. | [
"1",
"5",
"14",
"16",
"41",
"43",
"47",
"49",
"122",
"124",
"128",
"130",
"140",
"142",
"146",
"148",
"365",
"367",
"371",
"373",
"383",
"385",
"389",
"391",
"419",
"421",
"425",
"427",
"437",
"439",
"443",
"445",
"1094",
"1096",
"1100",
"1102",
"1112",
"1114",
"1118",
"1120",
"1148",
"1150",
"1154",
"1156",
"1166",
"1168",
"1172",
"1174",
"1256",
"1258",
"1262"
]
| [
"nonn",
"easy",
"look",
"new"
]
| 8 | 1 | 2 | [
"A005408",
"A037861",
"A385587",
"A385610",
"A385643"
]
| null | Stefano Spezia, Jul 06 2025 | 2025-07-09T18:57:56 | oeisdata/seq/A385/A385643.seq | d86f7ea728434d8ded4ff9351804244e |
A385644 | Swap multiplication and exponentiation in the canonical prime factorization of n. | [
"2",
"3",
"4",
"5",
"8",
"7",
"6",
"6",
"32",
"11",
"64",
"13",
"128",
"243",
"8",
"17",
"64",
"19",
"1024",
"2187",
"2048",
"23",
"216",
"10",
"8192",
"9",
"16384",
"29",
"14134776518227074636666380005943348126619871175004951664972849610340958208",
"31",
"10",
"177147",
"131072",
"78125",
"4096",
"37",
"524288",
"1594323",
"7776",
"41"
]
| [
"nonn",
"new"
]
| 32 | 2 | 1 | [
"A000026",
"A001414",
"A005361",
"A008474",
"A385644"
]
| null | Jens Ahlström, Jul 06 2025 | 2025-07-12T08:37:06 | oeisdata/seq/A385/A385644.seq | 6568c07944b031a7394a04f31d27a0c9 |
A385647 | Decimal expansion of 1 - log(2)/2. | [
"6",
"5",
"3",
"4",
"2",
"6",
"4",
"0",
"9",
"7",
"2",
"0",
"0",
"2",
"7",
"3",
"4",
"5",
"2",
"9",
"1",
"3",
"8",
"3",
"9",
"3",
"9",
"2",
"7",
"0",
"9",
"1",
"1",
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"1",
"5",
"9",
"6",
"2",
"2",
"4",
"9",
"9",
"3",
"2",
"8",
"1",
"9",
"8",
"7",
"2",
"3",
"7",
"2",
"9",
"3",
"9",
"6",
"5",
"9",
"9",
"9",
"5",
"2",
"5",
"3",
"3",
"0",
"3",
"1",
"8",
"9",
"0",
"1",
"5",
"1",
"5",
"2",
"6",
"4",
"2",
"1",
"9",
"7",
"0",
"6",
"8",
"3",
"3",
"6"
]
| [
"nonn",
"cons",
"easy",
"new"
]
| 19 | 0 | 1 | [
"A002162",
"A091651",
"A382854",
"A385647"
]
| null | Paolo Xausa, Jul 06 2025 | 2025-07-07T11:53:53 | oeisdata/seq/A385/A385647.seq | 35f9254dbaec743068f83e810a2847ee |
A385648 | G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(x) + A(2*x))^2 ). | [
"1",
"4",
"64",
"1872",
"91328",
"7563648",
"1115422976",
"306988895488",
"162926170881024",
"169827391985854464",
"350891899856754294784",
"1443597302250006622052352",
"11851990053153536620868173824",
"194396568906445310993071164686336",
"6373487768490075927307409156798611456"
]
| [
"nonn",
"new"
]
| 10 | 0 | 2 | [
"A171192",
"A385617",
"A385648",
"A385649",
"A385650"
]
| null | Seiichi Manyama, Jul 06 2025 | 2025-07-06T10:39:39 | oeisdata/seq/A385/A385648.seq | 31f0a8a4d887e25f2380bdd167fcb2fe |
A385649 | G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(x) + A(2*x))^3 ). | [
"1",
"8",
"352",
"29696",
"4263424",
"1049470976",
"462206058496",
"380751228633088",
"605491779706159104",
"1892234112450731442176",
"11725274627114715154743296",
"144692808471111027067403108352",
"3563512028948515548768609167736832",
"175339259291213196115801459160952864768"
]
| [
"nonn",
"new"
]
| 10 | 0 | 2 | [
"A171193",
"A385617",
"A385648",
"A385649",
"A385651"
]
| null | Seiichi Manyama, Jul 06 2025 | 2025-07-06T10:39:35 | oeisdata/seq/A385/A385649.seq | 57f9068876ff30d7ceaef84cd9e96acb |
A385650 | E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(2*x))^2 ). | [
"1",
"4",
"112",
"8800",
"1586944",
"624664064",
"536747751424",
"1018102925488128",
"4288756843049058304",
"40076190507961751044096",
"826422665125748814526283776",
"37363126329930414708850363990016",
"3679235193626553722088195031035805696",
"784317990902751658071943156321585144528896"
]
| [
"nonn",
"new"
]
| 10 | 0 | 2 | [
"A168600",
"A385619",
"A385648",
"A385650",
"A385651"
]
| null | Seiichi Manyama, Jul 06 2025 | 2025-07-06T10:39:49 | oeisdata/seq/A385/A385650.seq | ba52d74dec2ef9b3458565e0686b068a |
A385651 | E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(2*x))^3 ). | [
"1",
"8",
"640",
"150272",
"81879040",
"97446821888",
"252536538529792",
"1441194498488532992",
"18238881125752291459072",
"511646632486244583515095040",
"31662959021226253504069431721984",
"4295217009165735294411016058313900032",
"1268984197722535033624735101886101792489472"
]
| [
"nonn",
"new"
]
| 11 | 0 | 2 | [
"A168601",
"A385619",
"A385649",
"A385650",
"A385651"
]
| null | Seiichi Manyama, Jul 06 2025 | 2025-07-06T10:39:42 | oeisdata/seq/A385/A385651.seq | 59985c2540ad240e55d6c28d75147f71 |
A385652 | Maximum frequency of gpf(k) for 2 <= k <= n, where gpf(k) = A006530(k) is the greatest prime factor of k. | [
"1",
"1",
"2",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"4",
"4",
"4",
"4",
"4",
"4",
"5",
"5",
"5",
"5",
"5",
"5",
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"7",
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"7",
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"10",
"10",
"10",
"10",
"10",
"10",
"10",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"12"
]
| [
"nonn",
"new"
]
| 12 | 2 | 3 | [
"A006530",
"A078899",
"A385503",
"A385652",
"A385653",
"A385654"
]
| null | Pontus von Brömssen, Jul 06 2025 | 2025-07-13T19:21:22 | oeisdata/seq/A385/A385652.seq | 16c07f61897685f7bb754c9f275ac056 |
A385653 | Least k such that A385652(k) = n. | [
"2",
"4",
"8",
"12",
"18",
"24",
"27",
"36",
"48",
"54",
"72",
"80",
"90",
"100",
"120",
"125",
"135",
"150",
"160",
"180",
"196",
"210",
"224",
"245",
"252",
"280",
"294",
"315",
"336",
"343",
"350",
"378",
"392",
"420",
"441",
"448",
"490",
"504",
"525",
"560",
"567",
"588",
"630",
"672",
"686",
"700",
"735",
"756",
"784",
"840",
"875",
"882",
"896",
"945",
"980"
]
| [
"nonn",
"new"
]
| 11 | 1 | 1 | [
"A006530",
"A078899",
"A289662",
"A385503",
"A385652",
"A385653",
"A385654"
]
| null | Pontus von Brömssen, Jul 06 2025 | 2025-07-13T19:21:52 | oeisdata/seq/A385/A385653.seq | 853a5d27ddd1b3940833a2ba2c26b69f |
A385654 | Greatest prime factor of A385653(n). | [
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"7",
"7",
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"7",
"7",
"7",
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"7",
"7",
"7",
"7",
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"7",
"7",
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"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"13",
"13",
"13",
"13",
"13",
"7",
"13",
"13",
"13",
"13",
"13",
"13"
]
| [
"nonn",
"new"
]
| 9 | 1 | 1 | [
"A006530",
"A289662",
"A385503",
"A385652",
"A385653",
"A385654"
]
| null | Pontus von Brömssen, Jul 06 2025 | 2025-07-13T19:22:01 | oeisdata/seq/A385/A385654.seq | b4c0e91d073c810d39ccb7fa60c7279d |
A385656 | Numbers k such that the sum of the decimal digits of k^2 divides k^2. | [
"1",
"2",
"3",
"6",
"9",
"10",
"12",
"15",
"18",
"20",
"21",
"24",
"30",
"36",
"39",
"42",
"45",
"48",
"49",
"51",
"52",
"54",
"60",
"63",
"65",
"66",
"68",
"72",
"78",
"80",
"84",
"88",
"90",
"96",
"100",
"102",
"104",
"105",
"108",
"110",
"111",
"112",
"117",
"120",
"126",
"132",
"138",
"140",
"144",
"148",
"150",
"156",
"162",
"168",
"174",
"180",
"182",
"190",
"198",
"200",
"201",
"204",
"207"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 25 | 1 | 2 | [
"A005349",
"A007953",
"A034706",
"A118547",
"A385640",
"A385656"
]
| null | Vighnesh Patil, Jul 06 2025 | 2025-07-09T16:50:05 | oeisdata/seq/A385/A385656.seq | 18ea89033f039855f4cbc9f577aca515 |
A385659 | Decimal expansion of log_10(1 + 1/3). | [
"1",
"2",
"4",
"9",
"3",
"8",
"7",
"3",
"6",
"6",
"0",
"8",
"2",
"9",
"9",
"9",
"5",
"3",
"1",
"3",
"2",
"4",
"4",
"9",
"8",
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"6",
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"5",
"2",
"1",
"2",
"1",
"7",
"7",
"9",
"0",
"9",
"8",
"9",
"2",
"8",
"1",
"9",
"4",
"8",
"9",
"8",
"7",
"2",
"2",
"5",
"7",
"6",
"5",
"1",
"8",
"7",
"8",
"9",
"5",
"9",
"3",
"0",
"8",
"8",
"6"
]
| [
"nonn",
"cons",
"easy",
"new"
]
| 24 | 0 | 2 | [
"A007524",
"A104140",
"A154203",
"A154580",
"A385659"
]
| null | Marco Ripà, Jul 06 2025 | 2025-07-13T11:08:48 | oeisdata/seq/A385/A385659.seq | 7b115d9961d1bcbe6023367dfc8e00c6 |
A385684 | Numbers k such that (38^k - 3^k)/35 is prime. | [
"2",
"3",
"19",
"101",
"229",
"1031",
"2393",
"3121",
"4021"
]
| [
"nonn",
"hard",
"more",
"new"
]
| 4 | 1 | 1 | [
"A062587",
"A062589",
"A127996",
"A127997",
"A128344",
"A204940",
"A217320",
"A225807",
"A229542",
"A375161",
"A375236",
"A377031",
"A385684"
]
| null | Robert Price, Jul 06 2025 | 2025-07-10T23:18:23 | oeisdata/seq/A385/A385684.seq | f7b9d12bd082008f165127c280cf93fd |
A385685 | Sequence where k is appended after every k! occurrences of 1, with multiple values following a 1 listed in order. | [
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"2",
"3",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"2",
"3",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"2",
"3",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"2",
"3",
"4",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"2",
"3",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"2",
"3",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"2",
"3",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"2",
"3",
"4",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"2",
"3"
]
| [
"nonn",
"new"
]
| 17 | 0 | 3 | [
"A000142",
"A382093",
"A385685",
"A385686"
]
| null | Jwalin Bhatt, Jul 06 2025 | 2025-07-12T08:34:13 | oeisdata/seq/A385/A385685.seq | 05c134d700c21ecbb62534705ba3b949 |
A385686 | Decimal expansion of exp((Sum_{k>=2} log(k)/k!)/(e-1)). | [
"1",
"4",
"2",
"1",
"0",
"3",
"7",
"9",
"5",
"9",
"7",
"3",
"1",
"9",
"6",
"0",
"7",
"1",
"5",
"3",
"3",
"7",
"8",
"1",
"4",
"4",
"8",
"9",
"0",
"5",
"9",
"2",
"8",
"5",
"6",
"9",
"5",
"3",
"9",
"8",
"2",
"5",
"7",
"1",
"7",
"4",
"2",
"9",
"3",
"2",
"0",
"0",
"7",
"8",
"6",
"8",
"1",
"0",
"2",
"8",
"0",
"5",
"1",
"8",
"1",
"5",
"8",
"2",
"2",
"1",
"6",
"1",
"7",
"5",
"8",
"0",
"8",
"3",
"0",
"7",
"1",
"7",
"9",
"7",
"5"
]
| [
"nonn",
"cons",
"new"
]
| 18 | 1 | 2 | [
"A296301",
"A306243",
"A382095",
"A385685",
"A385686"
]
| null | Jwalin Bhatt, Jul 06 2025 | 2025-07-13T16:29:14 | oeisdata/seq/A385/A385686.seq | a33ca42e494ff1d47d968be44f03d670 |
A385687 | E.g.f. A(x) satisfies A(x) = exp( x*((A(x) + A(-x))/2)^2 ). | [
"1",
"1",
"1",
"7",
"25",
"341",
"2161",
"44115",
"404209",
"11010025",
"132273601",
"4508793983",
"67085545033",
"2747071330173",
"48765277295281",
"2331905267846731",
"48106649137922017",
"2631174441142423505",
"61862217319644572161",
"3809106344377237185399",
"100542158725584301036921"
]
| [
"nonn",
"new"
]
| 18 | 0 | 4 | [
"A058014",
"A143546",
"A360987",
"A385687",
"A385688",
"A385690"
]
| null | Seiichi Manyama, Jul 06 2025 | 2025-07-07T10:46:56 | oeisdata/seq/A385/A385687.seq | a243f01414097ecc7d49c7eb71fdd2df |
A385688 | E.g.f. A(x) satisfies A(x) = exp( x*((A(x) + A(-x))/2)^3 ). | [
"1",
"1",
"1",
"10",
"37",
"736",
"4861",
"145552",
"1392553",
"55772416",
"700205401",
"35139710464",
"546584937229",
"32977620613120",
"612127803448981",
"43150087404292096",
"930914421449463505",
"75083676142358560768",
"1846230024226716759601",
"167681514857730519728128",
"4629062510444281987051381"
]
| [
"nonn",
"new"
]
| 16 | 0 | 4 | [
"A058014",
"A143547",
"A360988",
"A385687",
"A385688"
]
| null | Seiichi Manyama, Jul 06 2025 | 2025-07-07T10:46:46 | oeisdata/seq/A385/A385688.seq | 0cba3582f5e3a4715803822b5651cb83 |
A385689 | a(n) = 6*binomial(n,4) + 6*binomial(n,3) + 4*binomial(n,2) + 2*n + 1. | [
"1",
"3",
"9",
"25",
"63",
"141",
"283",
"519",
"885",
"1423",
"2181",
"3213",
"4579",
"6345",
"8583",
"11371",
"14793",
"18939",
"23905",
"29793",
"36711",
"44773",
"54099",
"64815",
"77053",
"90951",
"106653",
"124309",
"144075",
"166113",
"190591",
"217683",
"247569",
"280435",
"316473",
"355881",
"398863",
"445629",
"496395",
"551383",
"610821",
"674943"
]
| [
"nonn",
"easy",
"new"
]
| 11 | 0 | 2 | [
"A127873",
"A385689"
]
| null | Enrique Navarrete, Jul 07 2025 | 2025-07-12T22:41:55 | oeisdata/seq/A385/A385689.seq | a98f05f48785395baf9276c6dfff767f |
A385690 | E.g.f. A(x) satisfies A(x) = exp( x*A(x)*(A(x) + A(-x))/2 ). | [
"1",
"1",
"3",
"25",
"233",
"3901",
"62707",
"1591493",
"36539953",
"1246111705",
"37259797091",
"1597211237425",
"58891746904729",
"3041999861503253",
"133421178853319827",
"8066042741507516701",
"410229480337750129889",
"28415048957473232282161",
"1644249408980809155863491"
]
| [
"nonn",
"new"
]
| 11 | 0 | 3 | [
"A217138",
"A385687",
"A385690",
"A385692"
]
| null | Seiichi Manyama, Jul 07 2025 | 2025-07-07T10:46:40 | oeisdata/seq/A385/A385690.seq | 39087e4c7c55cb2e4f87c56dc3943d43 |
A385691 | E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(w*x) + A(w^2*x))/3 ), where w = exp(2*Pi*i/3). | [
"1",
"1",
"1",
"1",
"5",
"21",
"61",
"568",
"4257",
"20917",
"286451",
"3099141",
"21555865",
"390273898",
"5524889553",
"49790422501",
"1121734897937",
"19631020478229",
"217441607213557",
"5862333450708460",
"122222268766006641",
"1606671304363320805",
"50443794604147639487",
"1220712011020970521461"
]
| [
"nonn",
"new"
]
| 14 | 0 | 5 | [
"A058014",
"A124753",
"A385691"
]
| null | Seiichi Manyama, Jul 07 2025 | 2025-07-07T10:21:30 | oeisdata/seq/A385/A385691.seq | 7f1c77df41ea676b11b4c3a3253c658f |
A385692 | E.g.f. A(x) satisfies A(x) = exp( x*A(x)*(A(x) + A(w*x) + A(w^2*x))/3 ), where w = exp(2*Pi*i/3). | [
"1",
"1",
"3",
"16",
"189",
"2256",
"32167",
"767313",
"16423185",
"385872832",
"13923826371",
"431494792224",
"14162204393053",
"685135173015801",
"27831222972658029",
"1174037911440510736",
"71264909409165117009",
"3582888868151242791360",
"184756481500401258020443",
"13494513883839138274687425"
]
| [
"nonn",
"new"
]
| 8 | 0 | 3 | [
"A385690",
"A385692"
]
| null | Seiichi Manyama, Jul 07 2025 | 2025-07-07T10:21:06 | oeisdata/seq/A385/A385692.seq | c185ba6dae1dd376cf90deda457532c4 |
A385694 | Decimal expansion of the volume of a triaugmented hexagonal prism with unit edge. | [
"3",
"3",
"0",
"5",
"1",
"8",
"2",
"9",
"9",
"2",
"5",
"3",
"9",
"8",
"6",
"3",
"4",
"6",
"4",
"6",
"9",
"2",
"0",
"1",
"3",
"8",
"7",
"4",
"3",
"6",
"3",
"6",
"5",
"7",
"5",
"8",
"9",
"6",
"9",
"9",
"0",
"4",
"3",
"8",
"1",
"8",
"4",
"0",
"4",
"0",
"4",
"4",
"9",
"7",
"8",
"6",
"7",
"2",
"0",
"5",
"0",
"3",
"3",
"8",
"1",
"7",
"3",
"2",
"6",
"5",
"7",
"6",
"4",
"5",
"9",
"4",
"2",
"5",
"3",
"5",
"7",
"5",
"0",
"4",
"6",
"9",
"1",
"3",
"0",
"4"
]
| [
"nonn",
"cons",
"easy",
"new"
]
| 8 | 1 | 1 | [
"A010503",
"A104956",
"A385259",
"A385569",
"A385578",
"A385694"
]
| null | Paolo Xausa, Jul 07 2025 | 2025-07-11T22:32:37 | oeisdata/seq/A385/A385694.seq | 7f8e9ef4e67085484131865e57ae37d0 |
A385695 | Decimal expansion of the volume of an augmented dodecahedron with unit edge. | [
"7",
"9",
"6",
"4",
"6",
"2",
"1",
"7",
"9",
"3",
"0",
"2",
"0",
"4",
"5",
"6",
"5",
"3",
"9",
"3",
"9",
"9",
"7",
"6",
"9",
"4",
"8",
"9",
"8",
"1",
"0",
"2",
"0",
"3",
"2",
"5",
"5",
"1",
"6",
"4",
"4",
"4",
"1",
"2",
"2",
"7",
"6",
"3",
"7",
"3",
"1",
"6",
"9",
"2",
"2",
"6",
"5",
"2",
"0",
"2",
"4",
"2",
"3",
"1",
"3",
"6",
"0",
"5",
"1",
"6",
"6",
"5",
"8",
"4",
"3",
"4",
"4",
"0",
"0",
"4",
"4",
"4",
"7",
"8",
"4",
"1",
"5",
"9",
"1",
"4"
]
| [
"nonn",
"cons",
"easy",
"new"
]
| 11 | 1 | 1 | [
"A002163",
"A102769",
"A179552",
"A385695",
"A385696",
"A385802",
"A385804"
]
| null | Paolo Xausa, Jul 08 2025 | 2025-07-13T07:07:07 | oeisdata/seq/A385/A385695.seq | 52abe9307809cc06150a2bb6a9594a96 |
A385696 | Decimal expansion of the surface area of an augmented dodecahedron with unit edge. | [
"2",
"1",
"0",
"9",
"0",
"3",
"1",
"4",
"9",
"1",
"5",
"9",
"3",
"9",
"7",
"3",
"2",
"7",
"6",
"7",
"2",
"5",
"8",
"4",
"3",
"9",
"6",
"7",
"8",
"1",
"5",
"7",
"0",
"4",
"6",
"0",
"5",
"2",
"1",
"5",
"9",
"6",
"2",
"2",
"4",
"3",
"7",
"3",
"7",
"5",
"1",
"5",
"7",
"4",
"0",
"6",
"3",
"4",
"7",
"8",
"0",
"0",
"5",
"0",
"1",
"5",
"7",
"7",
"4",
"7",
"5",
"1",
"8",
"5",
"4",
"3",
"4",
"6",
"2",
"8",
"5",
"9",
"1",
"0",
"0",
"8",
"2",
"8",
"6",
"3"
]
| [
"nonn",
"cons",
"easy",
"new"
]
| 10 | 2 | 1 | [
"A002194",
"A010476",
"A385695",
"A385696",
"A385803",
"A385805"
]
| null | Paolo Xausa, Jul 08 2025 | 2025-07-13T07:07:36 | oeisdata/seq/A385/A385696.seq | 1b2cd5e9ef6bbca92cb17096235f9944 |
A385698 | E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(-x))*(A(x) + A(w*x) + A(w^2*x))/6 ), where w = exp(2*Pi*i/3). | [
"1",
"1",
"1",
"4",
"29",
"256",
"1501",
"28715",
"266001",
"4590064",
"99387041",
"2223185152",
"30919119661",
"1183047504809",
"21297988134879",
"656259407452756",
"23786602263322385",
"856920025214144512",
"18903506095173283273",
"1086514755640058121323",
"29116796997476903252841"
]
| [
"nonn",
"new"
]
| 7 | 0 | 4 | [
"A385698",
"A385699"
]
| null | Seiichi Manyama, Jul 07 2025 | 2025-07-07T10:21:01 | oeisdata/seq/A385/A385698.seq | 3ec5c0638afacee0599739f2399c239a |
A385699 | G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(x) + A(-x))*(A(x) + A(w*x) + A(w^2*x))/6 ), where w = exp(2*Pi*i/3). | [
"1",
"1",
"1",
"2",
"5",
"13",
"24",
"88",
"181",
"523",
"1616",
"4891",
"10540",
"42009",
"94953",
"294102",
"957259",
"3028320",
"6864540",
"28208447",
"66180997",
"211105506",
"703497178",
"2273009790",
"5283518340",
"22058432677",
"52795736539",
"171169636087",
"578132050147",
"1891182035377",
"4462525373212"
]
| [
"nonn",
"new"
]
| 14 | 0 | 4 | [
"A047749",
"A124753",
"A217138",
"A385698",
"A385699"
]
| null | Seiichi Manyama, Jul 07 2025 | 2025-07-07T10:46:36 | oeisdata/seq/A385/A385699.seq | 8de601a66cbaa01c4a415a46ffc5d8ac |
A385700 | Numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 4. | [
"0",
"4",
"8",
"21",
"23",
"25",
"27",
"29",
"40",
"42",
"44",
"46",
"48",
"61",
"63",
"65",
"67",
"69",
"80",
"82",
"84",
"86",
"88",
"201",
"203",
"205",
"207",
"209",
"211",
"213",
"215",
"217",
"219",
"221",
"223",
"225",
"227",
"229",
"231",
"233",
"235",
"237",
"239",
"241",
"243",
"245",
"247",
"249",
"251",
"253",
"255",
"257",
"259",
"261",
"263",
"265",
"267",
"269"
]
| [
"nonn",
"base",
"easy",
"look",
"new"
]
| 19 | 1 | 2 | [
"A001477",
"A008585",
"A008591",
"A217398",
"A273892",
"A385700",
"A385701",
"A385702",
"A385703"
]
| null | Stefano Spezia, Jul 07 2025 | 2025-07-08T14:15:30 | oeisdata/seq/A385/A385700.seq | 410f33d6577885ea1815973713989307 |
A385701 | Numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 6. | [
"0",
"6",
"21",
"24",
"27",
"42",
"45",
"48",
"60",
"63",
"66",
"69",
"81",
"84",
"87",
"201",
"204",
"207",
"210",
"213",
"216",
"219",
"222",
"225",
"228",
"231",
"234",
"237",
"240",
"243",
"246",
"249",
"252",
"255",
"258",
"261",
"264",
"267",
"270",
"273",
"276",
"279",
"282",
"285",
"288",
"291",
"294",
"297",
"402",
"405",
"408",
"411",
"414",
"417",
"420",
"423",
"426",
"429"
]
| [
"nonn",
"base",
"easy",
"look",
"new"
]
| 16 | 1 | 2 | [
"A001477",
"A008585",
"A008591",
"A217398",
"A273892",
"A385700",
"A385701",
"A385702",
"A385703"
]
| null | Stefano Spezia, Jul 07 2025 | 2025-07-08T14:15:16 | oeisdata/seq/A385/A385701.seq | 4f8a0c767b91af95edb73a69a5fb037c |
A385702 | Numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 7. | [
"0",
"7",
"12",
"19",
"24",
"36",
"41",
"48",
"53",
"65",
"70",
"77",
"82",
"89",
"94",
"102",
"109",
"116",
"123",
"130",
"137",
"144",
"151",
"158",
"165",
"172",
"179",
"186",
"193",
"204",
"211",
"218",
"225",
"232",
"239",
"246",
"253",
"260",
"267",
"274",
"281",
"288",
"295",
"306",
"313",
"320",
"327",
"334",
"341",
"348",
"355",
"362",
"369",
"376",
"383",
"390",
"397"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 16 | 1 | 2 | [
"A001477",
"A008585",
"A008591",
"A217398",
"A273892",
"A385700",
"A385701",
"A385702",
"A385703"
]
| null | Stefano Spezia, Jul 07 2025 | 2025-07-08T14:15:07 | oeisdata/seq/A385/A385702.seq | 5fde8799efdea0f1977f4f7c20e06af9 |
A385703 | Numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 8. | [
"0",
"8",
"23",
"27",
"42",
"46",
"61",
"65",
"69",
"80",
"84",
"88",
"203",
"207",
"211",
"215",
"219",
"223",
"227",
"231",
"235",
"239",
"243",
"247",
"251",
"255",
"259",
"263",
"267",
"271",
"275",
"279",
"283",
"287",
"291",
"295",
"299",
"402",
"406",
"410",
"414",
"418",
"422",
"426",
"430",
"434",
"438",
"442",
"446",
"450",
"454",
"458",
"462",
"466",
"470",
"474"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 15 | 1 | 2 | [
"A001477",
"A008585",
"A008591",
"A217398",
"A273892",
"A385700",
"A385701",
"A385702",
"A385703"
]
| null | Stefano Spezia, Jul 07 2025 | 2025-07-08T14:14:57 | oeisdata/seq/A385/A385703.seq | 6188d9337a58e318c876db9699c81897 |
A385705 | Primes p such that there exists prime q < p such that sigma(p+1)=sigma(q+1). | [
"37",
"61",
"109",
"139",
"157",
"181",
"193",
"233",
"269",
"283",
"347",
"349",
"353",
"367",
"373",
"379",
"487",
"521",
"541",
"563",
"571",
"593",
"613",
"617",
"619",
"641",
"643",
"709",
"727",
"739",
"797",
"811",
"823",
"829",
"853",
"857",
"877",
"907",
"983",
"991",
"1033",
"1051",
"1097",
"1103",
"1117",
"1193",
"1217",
"1229",
"1231",
"1237"
]
| [
"nonn",
"easy",
"new"
]
| 13 | 1 | 1 | [
"A000040",
"A000203",
"A008333",
"A385586",
"A385705"
]
| null | S. I. Dimitrov, Jul 07 2025 | 2025-07-08T10:42:57 | oeisdata/seq/A385/A385705.seq | c6f1f4771330358aaee14ca420e92fc7 |
A385715 | Square array read by descending antidiagonals: A(n,k) is the number of fixed n-dimensional (n,2)-polyominoids, n >= 2, of size k >= 1. | [
"1",
"2",
"3",
"6",
"18",
"6",
"19",
"158",
"60",
"10",
"63",
"1611",
"916",
"140",
"15",
"216",
"17811",
"16698",
"3060",
"270",
"21",
"760",
"207395",
"336210",
"81090",
"7690",
"462",
"28",
"2725",
"2505858",
"7218768",
"2396434",
"268005",
"16226",
"728",
"36",
"9910",
"31125711",
"162185112",
"76020890",
"10477161",
"701589",
"30408",
"1080",
"45"
]
| [
"nonn",
"tabl",
"new"
]
| 16 | 2 | 2 | [
"A000217",
"A001168",
"A075678",
"A213820",
"A366335",
"A385291",
"A385581",
"A385715"
]
| null | John Mason, Jul 07 2025 | 2025-07-13T12:51:11 | oeisdata/seq/A385/A385715.seq | e86b5431bf97884297c23cd282b9261c |
A385717 | a(n) = a(n-1) + a(n-2) + a(n-3), with a(1) = 4, a(2) = 13, a(3) = 42. | [
"4",
"13",
"42",
"59",
"114",
"215",
"388",
"717",
"1320",
"2425",
"4462",
"8207",
"15094",
"27763",
"51064",
"93921",
"172748",
"317733",
"584402",
"1074883",
"1977018",
"3636303",
"6688204",
"12301525",
"22626032",
"41615761",
"76543318",
"140785111",
"258944190",
"476272619"
]
| [
"nonn",
"easy",
"new"
]
| 9 | 1 | 1 | [
"A100683",
"A354080",
"A385717"
]
| null | Greg Dresden and Jiarui Zhou, Jul 07 2025 | 2025-07-13T17:32:04 | oeisdata/seq/A385/A385717.seq | a19df8bb3b3be8fbc145bca11082def4 |
A385718 | Primes p such that there exists prime q < p such that sigma(q+1) = sigma(p+2) = p + q. | [
"367",
"457",
"691",
"341647",
"909091",
"1803421",
"2640571",
"3076903",
"3413191",
"5228611",
"6152383",
"6541477",
"6545197",
"6695503",
"10161133",
"10770313",
"15319693",
"31128511",
"31687069",
"39946483",
"52764031",
"58886803",
"104494483",
"207855001",
"283882153",
"307912921",
"309201751",
"529570609",
"574061053"
]
| [
"nonn",
"new"
]
| 11 | 1 | 1 | [
"A000040",
"A000203",
"A008333",
"A063990",
"A259180",
"A385586",
"A385718"
]
| null | S. I. Dimitrov, Jul 07 2025 | 2025-07-08T09:13:46 | oeisdata/seq/A385/A385718.seq | 3a11448fb76b18a915b801085b7405ce |
A385720 | Numbers k >= 1 such that k/A000005(k) + (k+1)/A000005(k+1) is an integer. | [
"1",
"5",
"6",
"8",
"10",
"13",
"22",
"37",
"45",
"46",
"58",
"61",
"62",
"69",
"73",
"74",
"77",
"82",
"89",
"106",
"114",
"117",
"126",
"146",
"149",
"150",
"154",
"157",
"166",
"167",
"178",
"186",
"193",
"197",
"198",
"206",
"221",
"226",
"233",
"237",
"258",
"261",
"262",
"263",
"266",
"277",
"278",
"279",
"280",
"290",
"293",
"306",
"309",
"311",
"312",
"313"
]
| [
"nonn",
"new"
]
| 16 | 1 | 2 | [
"A000005",
"A005384",
"A005385",
"A077065",
"A256072",
"A385720"
]
| null | Ctibor O. Zizka, Jul 07 2025 | 2025-07-13T16:44:05 | oeisdata/seq/A385/A385720.seq | aeb0a185c5efbd2135f93bf1e3c2ab49 |
A385724 | The least integer of n consecutive numbers where each has its sum of prime factors, with multiplicity, being a prime. | [
"17",
"2",
"5",
"10",
"1547",
"8837",
"1293224",
"52445796",
"3267037",
"896531141",
"183208285259"
]
| [
"nonn",
"more",
"new"
]
| 10 | 1 | 1 | [
"A100118",
"A337310",
"A385724"
]
| null | Zhining Yang, Jul 08 2025 | 2025-07-13T15:36:15 | oeisdata/seq/A385/A385724.seq | e0db780d7a5b2339041182e4e5b5f43b |
A385725 | E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(i*x) + A(-x) + A(-i*x))/4 ), where i is the imaginary unit. | [
"1",
"1",
"1",
"1",
"1",
"6",
"31",
"106",
"281",
"3160",
"29701",
"176056",
"768241",
"12702704",
"173361371",
"1466276176",
"8937060081",
"195180709248",
"3494232292681",
"38426220716416",
"301057954180801",
"8174141246647552",
"181144607099402871",
"2452803139819922176",
"23494461553739152201",
"762800754226165963776"
]
| [
"nonn",
"new"
]
| 10 | 0 | 6 | [
"A000272",
"A058014",
"A118968",
"A385691",
"A385725"
]
| null | Seiichi Manyama, Jul 08 2025 | 2025-07-08T07:47:22 | oeisdata/seq/A385/A385725.seq | 37ada687b3e500ba1f36b88c2ede8bfa |
A385726 | a(n) = 3^n - 6*binomial(n,4) - 6*binomial(n,3) - 4*binomial(n,2) - 2*n - 1. | [
"0",
"0",
"0",
"2",
"18",
"102",
"446",
"1668",
"5676",
"18260",
"59049",
"177147",
"531441",
"1594323",
"4782969",
"14348907",
"43046721",
"129140163",
"387420489",
"1162261467",
"3486784401",
"10460353203",
"31381059609",
"94143178827",
"282429536481",
"847288609443",
"2541865828329",
"7625597484987",
"22876792454961",
"68630377364883"
]
| [
"nonn",
"easy",
"new"
]
| 7 | 0 | 4 | [
"A383343",
"A385689",
"A385726"
]
| null | Enrique Navarrete, Jul 08 2025 | 2025-07-12T18:46:32 | oeisdata/seq/A385/A385726.seq | 7920c6d747e3b1b80d593ad3f8713c44 |
A385732 | Triangle read by rows: the numerators of the Lucas triangle. | [
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"4",
"4",
"1",
"1",
"7",
"28",
"7",
"1",
"1",
"11",
"77",
"77",
"11",
"1",
"1",
"18",
"66",
"231",
"66",
"18",
"1",
"1",
"29",
"174",
"957",
"957",
"174",
"29",
"1",
"1",
"47",
"1363",
"4089",
"44979",
"4089",
"1363",
"47",
"1",
"1",
"76",
"3572",
"25897",
"155382",
"155382",
"25897",
"3572",
"76",
"1",
"1",
"123",
"3116",
"36613",
"1061777",
"19111986",
"1061777",
"36613",
"3116",
"123",
"1"
]
| [
"nonn",
"tabl",
"frac",
"new"
]
| 15 | 0 | 5 | [
"A003266",
"A010048",
"A070825",
"A385732",
"A385733"
]
| null | Peter Luschny, Jul 08 2025 | 2025-07-08T22:27:13 | oeisdata/seq/A385/A385732.seq | e798acdc21b89d2d9b5938bc4a8a10a7 |
A385733 | Triangle read by rows: the denominators of the Lucas triangle. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"1",
"3",
"3",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"3",
"2",
"14",
"2",
"3",
"1",
"1",
"1",
"1",
"3",
"3",
"7",
"7",
"3",
"3",
"1",
"1",
"1",
"1",
"1",
"1",
"7",
"77",
"7",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"7",
"77",
"77",
"7",
"1",
"1",
"1",
"1",
"1",
"1",
"3",
"2",
"1",
"11",
"99",
"11",
"1",
"2",
"3",
"1",
"1"
]
| [
"nonn",
"tabl",
"frac",
"new"
]
| 8 | 0 | 13 | [
"A003266",
"A010048",
"A070825",
"A385732",
"A385733"
]
| null | Peter Luschny, Jul 08 2025 | 2025-07-08T22:27:43 | oeisdata/seq/A385/A385733.seq | b0f9273b03201a4a3ab91e12e9c3b6cb |
A385734 | Lucas triangle A385732/A385733 mod 2. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"0",
"0",
"-1",
"0",
"0",
"1",
"1",
"1",
"0",
"-1",
"-1",
"0",
"1",
"1",
"1",
"1",
"1",
"-1",
"-1",
"-1",
"1",
"1",
"1",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"0",
"0",
"-1",
"0",
"0",
"1",
"0",
"0",
"-1",
"0",
"0",
"1"
]
| [
"sign",
"tabl",
"new"
]
| 6 | 0 | null | [
"A385456",
"A385732",
"A385733",
"A385734"
]
| null | Peter Luschny, Jul 08 2025 | 2025-07-08T22:26:46 | oeisdata/seq/A385/A385734.seq | 53653b3fd16b7c927cc0fb4ef9cd41ca |
A385738 | For n >= 1, a(n) is the least k such that the Sum_{i=0..(n-1)} (k+i)/A000005(k+i) is an integer or a(n) = -1 if no such k exists. | [
"1",
"1",
"6",
"6",
"8",
"5",
"6",
"23",
"5",
"22",
"50",
"26",
"28",
"65",
"119",
"145",
"26",
"349",
"282",
"375",
"280",
"404",
"278",
"369",
"279",
"370",
"277",
"276",
"369",
"378",
"389",
"378",
"389",
"15",
"389",
"13",
"12",
"210",
"10",
"9",
"8",
"210",
"6",
"212",
"421",
"209",
"419",
"3",
"2",
"1",
"378",
"419",
"421",
"418",
"418",
"1026",
"373",
"105",
"104"
]
| [
"nonn",
"new"
]
| 12 | 1 | 3 | [
"A000005",
"A385738"
]
| null | Ctibor O. Zizka, Jul 08 2025 | 2025-07-13T16:44:33 | oeisdata/seq/A385/A385738.seq | 3d5975036b5bc5ddd946f28c28a15cba |
A385739 | Primes p such that there exists a prime q < p such that sigma(q-1) = sigma(p+1) = p + q. | [
"5563",
"203431",
"389923",
"901423",
"5495263",
"7418863",
"28128367",
"188953969",
"210627577",
"392753209",
"402877087",
"505757683",
"619418689"
]
| [
"nonn",
"hard",
"more",
"new"
]
| 9 | 1 | 1 | [
"A000040",
"A000203",
"A008333",
"A063990",
"A259180",
"A385586",
"A385718",
"A385739"
]
| null | S. I. Dimitrov, Jul 08 2025 | 2025-07-13T16:53:58 | oeisdata/seq/A385/A385739.seq | a0bc9ae06365ef1a5a4ed8e966fdda54 |
A385740 | Primes p such that there exists a prime q < p such that sigma(p-1) = sigma(q-1) = p + q. | [
"1163",
"7583",
"17099",
"48857",
"65963",
"172859",
"5408423",
"6804047",
"19247087",
"73162367",
"77695043",
"109775657",
"109871933",
"116464757",
"160454717",
"175031957",
"175288493",
"218543393",
"268382183",
"303220769",
"379299989",
"705800723",
"823155779",
"889218389",
"967371143"
]
| [
"nonn",
"hard",
"more",
"new"
]
| 10 | 1 | 1 | [
"A000040",
"A000203",
"A008333",
"A063990",
"A259180",
"A385586",
"A385718",
"A385739",
"A385740"
]
| null | S. I. Dimitrov, Jul 08 2025 | 2025-07-13T16:53:25 | oeisdata/seq/A385/A385740.seq | b0e2e6209c6b206bb4a1d78541a01850 |
A385741 | a(n) = Sum_{k=0..n} (binomial(n, k) mod 9). | [
"1",
"2",
"4",
"8",
"16",
"14",
"28",
"38",
"31",
"8",
"16",
"32",
"28",
"56",
"49",
"62",
"52",
"68",
"28",
"56",
"76",
"62",
"79",
"122",
"91",
"92",
"112",
"8",
"16",
"32",
"28",
"56",
"76",
"80",
"124",
"140",
"28",
"56",
"103",
"80",
"142",
"158",
"145",
"146",
"184",
"62",
"124",
"158",
"100",
"146",
"184",
"188",
"232",
"230",
"28",
"56",
"76",
"80",
"151",
"158",
"136",
"236"
]
| [
"nonn",
"new"
]
| 29 | 0 | 2 | [
"A001316",
"A051638",
"A384715",
"A385285",
"A385741"
]
| null | Chai Wah Wu, Jul 09 2025 | 2025-07-12T02:15:55 | oeisdata/seq/A385/A385741.seq | 439f17d0eda5e5751da09faf18f775e5 |
A385743 | Numbers k such that A384247(k) = A384247(k+1). | [
"1",
"20",
"27",
"35",
"63",
"64",
"104",
"143",
"194",
"208",
"740",
"836",
"1220",
"1299",
"1419",
"1803",
"1892",
"2625",
"3255",
"3705",
"3716",
"3843",
"4096",
"5184",
"5186",
"5635",
"5695",
"7868",
"10659",
"13365",
"16904",
"17948",
"18507",
"18914",
"21007",
"22935",
"25388",
"25545",
"27675",
"30380",
"31599",
"32304",
"32864",
"34595"
]
| [
"nonn",
"new"
]
| 8 | 1 | 2 | [
"A001274",
"A287055",
"A293184",
"A301866",
"A326403",
"A349307",
"A384247",
"A385743"
]
| null | Amiram Eldar, Jul 08 2025 | 2025-07-12T18:50:15 | oeisdata/seq/A385/A385743.seq | c375c72a01f94a6a49a00350c110bd04 |
A385744 | The number of iterations of the infinitary analog of the totient function A384247 that are required to reach from n to 1. | [
"0",
"1",
"2",
"3",
"4",
"2",
"3",
"4",
"5",
"4",
"5",
"3",
"4",
"3",
"5",
"6",
"7",
"5",
"6",
"4",
"4",
"5",
"6",
"5",
"6",
"4",
"6",
"6",
"7",
"5",
"6",
"7",
"5",
"7",
"6",
"6",
"7",
"6",
"6",
"7",
"8",
"4",
"5",
"6",
"8",
"6",
"7",
"6",
"7",
"6",
"8",
"7",
"8",
"6",
"8",
"6",
"7",
"7",
"8",
"6",
"7",
"6",
"7",
"7",
"7",
"5",
"6",
"7",
"7",
"6",
"7",
"8",
"9",
"7",
"7",
"7",
"7",
"6",
"7",
"7",
"8",
"8",
"9",
"7",
"8",
"5",
"7"
]
| [
"nonn",
"easy",
"new"
]
| 7 | 1 | 3 | [
"A003434",
"A049865",
"A225320",
"A333609",
"A384247",
"A385744",
"A385745",
"A385746",
"A385747"
]
| null | Amiram Eldar, Jul 08 2025 | 2025-07-11T01:27:35 | oeisdata/seq/A385/A385744.seq | ec8e94a3c5a908b50be01ffdfceb57d1 |
A385745 | The sum of the iterated infinitary analog of the totient function A384247 when started at n. | [
"0",
"1",
"3",
"6",
"10",
"3",
"9",
"10",
"18",
"10",
"20",
"9",
"21",
"9",
"18",
"33",
"49",
"18",
"36",
"21",
"21",
"20",
"42",
"18",
"42",
"21",
"36",
"36",
"64",
"18",
"48",
"49",
"41",
"49",
"42",
"42",
"78",
"36",
"42",
"49",
"89",
"21",
"63",
"48",
"81",
"42",
"88",
"48",
"96",
"42",
"81",
"78",
"130",
"36",
"89",
"42",
"78",
"64",
"122",
"42",
"102",
"48",
"96",
"96",
"96",
"41",
"107"
]
| [
"nonn",
"easy",
"new"
]
| 7 | 1 | 3 | [
"A092693",
"A329153",
"A333611",
"A384247",
"A385744",
"A385745",
"A385746",
"A385747"
]
| null | Amiram Eldar, Jul 08 2025 | 2025-07-11T01:27:45 | oeisdata/seq/A385/A385745.seq | c14e89836d06d92c032da6d81dec4ce3 |
A385746 | Numbers that are equal to the sum of their iterated infinitary analog of the totient function A384247. | [
"3",
"10",
"18",
"21",
"48",
"160",
"288",
"3252",
"9304",
"13965",
"68526",
"719631",
"1531101",
"1954782",
"28900572",
"39189195",
"14708055957"
]
| [
"nonn",
"more",
"new"
]
| 4 | 1 | 1 | [
"A082897",
"A286067",
"A330273",
"A384247",
"A385744",
"A385745",
"A385746",
"A385747"
]
| null | Amiram Eldar, Jul 08 2025 | 2025-07-11T01:27:40 | oeisdata/seq/A385/A385746.seq | 8e060ea4cc94c364e5289cdfa1644077 |
A385747 | Least number that reaches 1 after exactly n iterations of the infinitary analog of the totient function A384247. | [
"1",
"2",
"3",
"4",
"5",
"9",
"16",
"17",
"41",
"73",
"101",
"197",
"467",
"829",
"1109",
"2761",
"4849",
"7831",
"12401",
"26189",
"52379",
"85853",
"139589",
"237007",
"395533",
"947043",
"1967027",
"3446033",
"5396427",
"9510437",
"17502533",
"35005067",
"71202449",
"90187609",
"164664701",
"395199461",
"705113873",
"1265735729",
"1803553457"
]
| [
"nonn",
"new"
]
| 5 | 0 | 2 | [
"A003271",
"A005424",
"A007755",
"A333610",
"A384247",
"A385744",
"A385745",
"A385746",
"A385747"
]
| null | Amiram Eldar, Jul 08 2025 | 2025-07-12T18:50:09 | oeisdata/seq/A385/A385747.seq | 1d1a086c3497930a750a3f9e7c0159d6 |
A385748 | Numbers k such that A384247(k) divides k. | [
"1",
"2",
"6",
"8",
"12",
"24",
"32",
"54",
"96",
"108",
"128",
"192",
"216",
"240",
"384",
"486",
"512",
"864",
"972",
"1536",
"1728",
"1944",
"2048",
"2160",
"3072",
"3456",
"4374",
"6000",
"6144",
"7776",
"8192",
"8748",
"13824",
"15552",
"17496",
"19440",
"24576",
"27648",
"31104",
"32768",
"39366",
"49152",
"54000",
"55296",
"61440",
"65280",
"69984"
]
| [
"nonn",
"new"
]
| 11 | 1 | 2 | [
"A007694",
"A019434",
"A092506",
"A298759",
"A319481",
"A335327",
"A373057",
"A384247",
"A385748"
]
| null | Amiram Eldar, Jul 08 2025 | 2025-07-12T18:50:26 | oeisdata/seq/A385/A385748.seq | a66c4466f3179271adc203280fa2fcf1 |
A385750 | a(n) = Sum_{k=0..n} Stirling2(n,k) * (n!/k!)^2. | [
"1",
"1",
"5",
"64",
"1681",
"78651",
"5891041",
"653545390",
"101785047169",
"21431911982437",
"5927319770834701",
"2101574777340578156",
"935265924020629176625",
"512945332353359967175999",
"341342159773993944429746793",
"272012935493149854994361194426",
"256689188247205271953044107166721",
"284051735653584424779666013789038985"
]
| [
"nonn",
"new"
]
| 5 | 0 | 3 | [
"A000110",
"A064618",
"A119392",
"A119400",
"A385750",
"A385751",
"A385752"
]
| null | Ilya Gutkovskiy, Jul 08 2025 | 2025-07-11T14:52:13 | oeisdata/seq/A385/A385750.seq | dca96138290ac42799698d6c21de05e4 |
A385751 | a(n) = Sum_{k=0..n} |Stirling1(n,k)| * (n!/k!)^2. | [
"1",
"1",
"5",
"100",
"5137",
"539851",
"101035441",
"30669875230",
"14117057058945",
"9364637252286181",
"8603755430968248301",
"10603853731438585516856",
"17077610933602804111318705",
"35160631271792580418277658415",
"90839446923946068488317221868825",
"289828370988497912073923950177143826",
"1126236403418687405801564385561640043521"
]
| [
"nonn",
"new"
]
| 7 | 0 | 3 | [
"A119390",
"A320502",
"A385750",
"A385751",
"A385752"
]
| null | Ilya Gutkovskiy, Jul 08 2025 | 2025-07-11T14:51:53 | oeisdata/seq/A385/A385751.seq | c695beea67afc1c94a7f88e321946b75 |
A385752 | a(n) = Sum_{k=0..n} Stirling1(n,k) * (n!/k!)^2. | [
"1",
"1",
"-3",
"46",
"-1967",
"179351",
"-29861639",
"8200834972",
"-3456505906559",
"2118756407303197",
"-1811589861406160699",
"2089746219541021377546",
"-3164800617505630505525903",
"6151223064132377579849537011",
"-15052264342298428131766095419839",
"45616620088948927404807879986431576",
"-168785206495071742797011703980958673919"
]
| [
"sign",
"new"
]
| 5 | 0 | 3 | [
"A119391",
"A192554",
"A385750",
"A385751",
"A385752"
]
| null | Ilya Gutkovskiy, Jul 08 2025 | 2025-07-11T14:52:24 | oeisdata/seq/A385/A385752.seq | 6810a393d034aa3dd000273d68dade46 |
A385754 | Positive numbers not occurring in A384797. | [
"1",
"6",
"16",
"20",
"25",
"30",
"33",
"41",
"48",
"53",
"57",
"59",
"62",
"67",
"74",
"75",
"78",
"86",
"90",
"93",
"98",
"100",
"107",
"110",
"113",
"114",
"123",
"128",
"130",
"135",
"138",
"142",
"145",
"151",
"153",
"157",
"159",
"162",
"165",
"168",
"178",
"183",
"191",
"202",
"204",
"211",
"212",
"220",
"223",
"229",
"232",
"245",
"254",
"255",
"283",
"286",
"291",
"301"
]
| [
"nonn",
"new"
]
| 6 | 1 | 2 | [
"A047800",
"A077773",
"A363762",
"A384797",
"A385754"
]
| null | Hugo Pfoertner, Jul 08 2025 | 2025-07-08T14:19:58 | oeisdata/seq/A385/A385754.seq | 9d11452b1ca0363c3073dea61b67e3fe |
A385755 | Numbers k with a unique combination of bigomega(k) and sopfr(k). | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"16",
"17",
"18",
"19",
"22",
"23",
"24",
"26",
"29",
"30",
"31",
"32",
"34",
"35",
"36",
"37",
"38",
"41",
"43",
"46",
"47",
"48",
"53",
"58",
"59",
"61",
"62",
"64",
"67",
"70",
"71",
"72",
"73",
"74",
"79",
"82",
"83",
"86",
"89",
"94",
"96",
"97",
"101",
"103",
"106",
"107",
"109",
"113",
"118",
"122",
"127",
"128",
"131"
]
| [
"nonn",
"new"
]
| 31 | 1 | 2 | [
"A000040",
"A000079",
"A001222",
"A001414",
"A100484",
"A385755",
"A385756",
"A385811"
]
| null | Hugo Pfoertner, Jul 09 2025 | 2025-07-13T12:38:58 | oeisdata/seq/A385/A385755.seq | 5b00393d09e42e0ebb02b58836745037 |
A385756 | Complement of A385755. | [
"20",
"21",
"25",
"27",
"28",
"33",
"39",
"40",
"42",
"44",
"45",
"49",
"50",
"51",
"52",
"54",
"55",
"56",
"57",
"60",
"63",
"65",
"66",
"68",
"69",
"75",
"76",
"77",
"78",
"80",
"81",
"84",
"85",
"87",
"88",
"90",
"91",
"92",
"93",
"95",
"98",
"99",
"100",
"102",
"104",
"105",
"108",
"110",
"111",
"112",
"114",
"115",
"116",
"117",
"119",
"120",
"121",
"123",
"124",
"125",
"126",
"129"
]
| [
"nonn",
"new"
]
| 12 | 1 | 1 | [
"A001222",
"A001414",
"A385755",
"A385756",
"A385811"
]
| null | Hugo Pfoertner, Jul 09 2025 | 2025-07-11T16:40:23 | oeisdata/seq/A385/A385756.seq | 6296751793414ee7c1c004dad1c077cd |
A385757 | a(n) is the smallest number having n smaller numbers with the same number of prime factors (counted with multiplicity). | [
"3",
"5",
"7",
"11",
"13",
"17",
"19",
"23",
"26",
"31",
"34",
"35",
"38",
"39",
"46",
"49",
"51",
"55",
"57",
"58",
"62",
"65",
"69",
"74",
"77",
"82",
"85",
"86",
"87",
"91",
"93",
"94",
"95",
"106",
"111",
"115",
"118",
"119",
"121",
"122",
"123",
"129",
"133",
"134",
"141",
"142",
"143",
"145",
"146",
"155",
"158",
"159",
"161",
"166",
"169",
"177",
"178",
"183",
"185",
"187",
"194",
"201",
"202",
"203",
"205"
]
| [
"nonn",
"new"
]
| 6 | 1 | 1 | [
"A001222",
"A081376",
"A335097",
"A338483",
"A385757"
]
| null | Ilya Gutkovskiy, Jul 08 2025 | 2025-07-13T19:56:01 | oeisdata/seq/A385/A385757.seq | 294111880863a98aa16fc13881f34023 |
A385758 | G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^3*A''(x))). | [
"1",
"2",
"5",
"25",
"241",
"3850",
"92699",
"3159424",
"145529893",
"8737971990",
"664337673319",
"62461188300465",
"7121505696653881",
"968606284138975286",
"154985833403909522361",
"28828521246104115576631",
"6169483384435711859804021",
"1505386674395483103372685258",
"415493606617772745031305469471"
]
| [
"nonn",
"new"
]
| 13 | 0 | 2 | [
"A321087",
"A385758",
"A385759",
"A385760",
"A385761",
"A385762"
]
| null | Seiichi Manyama, Jul 09 2025 | 2025-07-10T22:40:46 | oeisdata/seq/A385/A385758.seq | 03b1913fae80327c0ae5790505e39653 |
A385759 | G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^4*A'''(x))). | [
"1",
"2",
"5",
"15",
"141",
"3932",
"251717",
"31216948",
"6680698525",
"2271470142438",
"1153913665217481",
"835435792656039975",
"830424340158140342961",
"1099482665756962845820704",
"1891111018270919721409143729",
"4137752010118540256190073466415",
"11312615890237585633045672755792789"
]
| [
"nonn",
"new"
]
| 12 | 0 | 2 | [
"A321087",
"A385758",
"A385759",
"A385760",
"A385761"
]
| null | Seiichi Manyama, Jul 09 2025 | 2025-07-10T22:40:41 | oeisdata/seq/A385/A385759.seq | dee26366673b245b99192b7b6baa8815 |
A385760 | G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^5*A''''(x))). | [
"1",
"2",
"5",
"15",
"51",
"1412",
"175067",
"63725638",
"53784616915",
"90573359145678",
"274256185472187231",
"1383348290257488337035",
"10961652126528967555229301",
"130268275255842369871718355444",
"2235924687457083597476492688851325",
"53724798520519979444347750309693062183"
]
| [
"nonn",
"new"
]
| 12 | 0 | 2 | [
"A321087",
"A385758",
"A385759",
"A385760",
"A385761"
]
| null | Seiichi Manyama, Jul 09 2025 | 2025-07-10T22:40:35 | oeisdata/seq/A385/A385760.seq | 574e0dac74209667b2786405ea1db373 |
A385761 | G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^6*A'''''(x))). | [
"1",
"2",
"5",
"15",
"51",
"188",
"23291",
"16862710",
"42561503035",
"286183563337662",
"4328240254531111671",
"130903298544350358627387",
"7257802488822060515691899445",
"689810579878520205782663179307100",
"106537105206016369903910237449838232525",
"25594900303804029125790200935921438169789415"
]
| [
"nonn",
"new"
]
| 11 | 0 | 2 | [
"A321087",
"A385758",
"A385759",
"A385760",
"A385761"
]
| null | Seiichi Manyama, Jul 09 2025 | 2025-07-10T22:40:15 | oeisdata/seq/A385/A385761.seq | 6ce07eee92571de51735aa61d3d1f408 |
A385762 | G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^3*A''(x)). | [
"1",
"1",
"2",
"9",
"80",
"1204",
"27788",
"918831",
"41389972",
"2443323132",
"183303840972",
"17050267807478",
"1926895029660880",
"260150110806399232",
"41365993162914888760",
"7652990621445212758255",
"1630131235132495370561820",
"396129991240222795968202788",
"108937459572870420021782788268"
]
| [
"nonn",
"new"
]
| 11 | 0 | 3 | [
"A000108",
"A088716",
"A385762",
"A385763",
"A385764",
"A385765"
]
| null | Seiichi Manyama, Jul 09 2025 | 2025-07-09T10:14:28 | oeisdata/seq/A385/A385762.seq | 98eec609073fb661864e72e3e8c02b2b |
A385763 | G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^4*A'''(x)). | [
"1",
"1",
"2",
"5",
"44",
"1188",
"74880",
"9211479",
"1962123260",
"665169218468",
"337242780292376",
"243827199998597254",
"242120748323922920272",
"320325994582940359050400",
"550640627320172764415124000",
"1204251372776149567847238889047",
"3291219553094816112273747054673476"
]
| [
"nonn",
"new"
]
| 12 | 0 | 3 | [
"A000108",
"A088716",
"A385762",
"A385763",
"A385764",
"A385765"
]
| null | Seiichi Manyama, Jul 09 2025 | 2025-07-09T10:14:32 | oeisdata/seq/A385/A385763.seq | 1f85f73e9f36cb257a2e118014b4fb01 |
A385764 | G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^5*A''''(x)). | [
"1",
"1",
"2",
"5",
"14",
"378",
"46500",
"16879869",
"14229776750",
"23948731244678",
"72492823741526156",
"365581334105823084634",
"2896500982661242290253612",
"34419121542689992919239814260",
"590735385934420874267059790772360",
"14193599152271246770955912922939691797",
"465024889616667096875210999651863472880846"
]
| [
"nonn",
"new"
]
| 12 | 0 | 3 | [
"A000108",
"A088716",
"A385762",
"A385763",
"A385764",
"A385765"
]
| null | Seiichi Manyama, Jul 09 2025 | 2025-07-09T10:14:21 | oeisdata/seq/A385/A385764.seq | 2d4a62560176ddba38c8d6484343fdcd |
A385765 | G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^6*A'''''(x)). | [
"1",
"1",
"2",
"5",
"14",
"42",
"5172",
"3739389",
"9434483630",
"63428037194102",
"959222215928392076",
"29009757539769286481866",
"1608387988236777669667251772",
"152866019594999736359695792369300",
"23609086665918990295149462904374925800",
"5671917808033245221993631555503554148332485"
]
| [
"nonn",
"new"
]
| 12 | 0 | 3 | [
"A000108",
"A088716",
"A385761",
"A385762",
"A385763",
"A385764",
"A385765"
]
| null | Seiichi Manyama, Jul 09 2025 | 2025-07-09T10:14:11 | oeisdata/seq/A385/A385765.seq | 39125a879218ba5e1ed8bd7bcc7f469f |
A385766 | G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x)^2 - x^2*A(x)*A'(x))). | [
"1",
"2",
"9",
"66",
"629",
"7071",
"89609",
"1248355",
"18820831",
"303879698",
"5215803877",
"94656100969",
"1808853399445",
"36282216181916",
"761902799960049",
"16714472406574829",
"382369378451581045",
"9107117241193913850",
"225512045313741357841",
"5798133159909683869788"
]
| [
"nonn",
"new"
]
| 17 | 0 | 2 | [
"A321087",
"A385766",
"A385767"
]
| null | Seiichi Manyama, Jul 09 2025 | 2025-07-10T10:58:56 | oeisdata/seq/A385/A385766.seq | 7e3aad3088946186bbf998bdcaf69c23 |
A385767 | G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x)^3 - x^2*A(x)^2*A'(x))). | [
"1",
"2",
"11",
"103",
"1240",
"17405",
"272647",
"4652676",
"85204285",
"1657791964",
"34030090459",
"733238701637",
"16520229963511",
"388058679087053",
"9481616930642904",
"240524381652918706",
"6324953229391777117",
"172191111285984106951",
"4847629590517906310392",
"140987258808372483601766"
]
| [
"nonn",
"new"
]
| 12 | 0 | 2 | [
"A321087",
"A349289",
"A385766",
"A385767"
]
| null | Seiichi Manyama, Jul 09 2025 | 2025-07-10T22:40:12 | oeisdata/seq/A385/A385767.seq | 0a744e86f20ce985f0b993c52f5ab0a1 |
A385768 | Primes having only {0, 4, 9} as digits. | [
"409",
"449",
"499",
"4049",
"4099",
"4409",
"4909",
"4999",
"9049",
"9949",
"40009",
"40099",
"40499",
"40949",
"44449",
"44909",
"49009",
"49409",
"49499",
"49999",
"90499",
"94009",
"94049",
"94099",
"94949",
"94999",
"99409",
"400009",
"400409",
"400949",
"404009",
"404099",
"404449",
"409099",
"409499",
"409909",
"409999"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 16 | 1 | 1 | [
"A000040",
"A020466",
"A385768",
"A385776"
]
| null | Jason Bard, Jul 09 2025 | 2025-07-12T21:20:38 | oeisdata/seq/A385/A385768.seq | 507f564f46ba8068032d91ce544378a3 |
A385769 | Primes having only {0, 5, 9} as digits. | [
"5",
"59",
"509",
"599",
"5009",
"5059",
"5099",
"9059",
"50599",
"50909",
"55009",
"59009",
"59509",
"59999",
"90059",
"90599",
"95009",
"95959",
"99559",
"500009",
"500509",
"500909",
"505559",
"509909",
"509959",
"550009",
"550909",
"559099",
"590099",
"590599",
"590959",
"599009",
"599959",
"599999",
"900959"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 18 | 1 | 1 | [
"A000040",
"A020468",
"A030433",
"A385769",
"A385776"
]
| null | Jason Bard, Jul 09 2025 | 2025-07-12T21:20:42 | oeisdata/seq/A385/A385769.seq | f89245f7cdf5c1c6ec83957dd88e525d |
A385770 | Primes having only {0, 6, 7} as digits. | [
"7",
"67",
"607",
"677",
"6007",
"6067",
"6607",
"7607",
"60077",
"60607",
"66067",
"67607",
"67777",
"70067",
"70607",
"70667",
"76607",
"76667",
"76777",
"606077",
"606607",
"607007",
"607067",
"607667",
"660067",
"660607",
"666067",
"666607",
"666667",
"666707",
"670777",
"676007",
"677077",
"677767",
"700067"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 13 | 1 | 1 | [
"A000040",
"A020469",
"A030432",
"A385770",
"A385776"
]
| null | Jason Bard, Jul 09 2025 | 2025-07-12T21:20:46 | oeisdata/seq/A385/A385770.seq | 5b3cdb439b36b6f16804b33354765bdd |
A385771 | Primes having only {0, 7, 8} as digits. | [
"7",
"787",
"877",
"887",
"7877",
"8087",
"8707",
"8807",
"8887",
"70877",
"78007",
"78707",
"78787",
"78877",
"78887",
"80077",
"80777",
"87877",
"87887",
"88007",
"88807",
"700087",
"700877",
"707887",
"708007",
"777787",
"777877",
"778777",
"780707",
"780877",
"780887",
"787777",
"787807",
"788077",
"788087",
"800077"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 14 | 1 | 1 | [
"A000040",
"A020470",
"A030432",
"A385771",
"A385776"
]
| null | Jason Bard, Jul 09 2025 | 2025-07-12T21:20:54 | oeisdata/seq/A385/A385771.seq | c0dc1e6f397fa4724bc7f5700d0e6f9c |
A385772 | Primes having only {0, 8, 9} as digits. | [
"89",
"809",
"8009",
"8089",
"8999",
"80809",
"80909",
"80989",
"89009",
"89809",
"89899",
"89909",
"89989",
"90089",
"90989",
"98009",
"98809",
"98899",
"98909",
"98999",
"99089",
"99809",
"99989",
"800089",
"800909",
"800999",
"809909",
"880909",
"888809",
"888989",
"889909",
"890809",
"890999",
"898889",
"899009",
"900089"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 13 | 1 | 1 | [
"A000040",
"A020472",
"A030433",
"A385772",
"A385776"
]
| null | Jason Bard, Jul 09 2025 | 2025-07-12T21:20:58 | oeisdata/seq/A385/A385772.seq | 651b0d283ed089741edafb0f9ae6c0db |
A385773 | Primes having only {1, 2, 5} as digits. | [
"2",
"5",
"11",
"151",
"211",
"251",
"521",
"1151",
"1511",
"2111",
"2221",
"2251",
"2521",
"2551",
"5521",
"11251",
"11551",
"12211",
"12251",
"12511",
"15121",
"15511",
"15551",
"21121",
"21211",
"21221",
"21521",
"22111",
"22511",
"25111",
"25121",
"51151",
"51511",
"51521",
"51551",
"52121",
"52511",
"55511",
"111121",
"111211"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 14 | 1 | 1 | [
"A000040",
"A020453",
"A024050",
"A385773",
"A385776"
]
| null | Jason Bard, Jul 09 2025 | 2025-07-12T21:21:02 | oeisdata/seq/A385/A385773.seq | 9a36cfaec13a242e198302f4831abda7 |
A385774 | Primes having only {1, 2, 6} as digits. | [
"2",
"11",
"61",
"211",
"661",
"1621",
"2111",
"2161",
"2221",
"2621",
"6121",
"6211",
"6221",
"6661",
"11161",
"11261",
"11621",
"12161",
"12211",
"12611",
"16111",
"16661",
"21121",
"21211",
"21221",
"21611",
"21661",
"22111",
"22621",
"26111",
"26161",
"26261",
"61121",
"61211",
"61261",
"66161",
"66221",
"111121",
"111211"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 13 | 1 | 1 | [
"A000040",
"A020450",
"A020454",
"A385774",
"A385776"
]
| null | Jason Bard, Jul 09 2025 | 2025-07-12T21:21:06 | oeisdata/seq/A385/A385774.seq | bd4371fee5481ca1712a2e1ecf7b5357 |
A385775 | Primes having only {1, 2, 8} as digits. | [
"2",
"11",
"181",
"211",
"281",
"811",
"821",
"881",
"1181",
"1811",
"2111",
"2221",
"2281",
"8111",
"8221",
"8821",
"11821",
"12211",
"12281",
"12821",
"18121",
"18181",
"18211",
"21121",
"21211",
"21221",
"21821",
"21881",
"22111",
"22811",
"28111",
"28181",
"28211",
"81181",
"81281",
"82811",
"88211",
"88811",
"111121"
]
| [
"nonn",
"base",
"easy",
"new"
]
| 13 | 1 | 1 | [
"A000040",
"A020450",
"A020456",
"A385775",
"A385776"
]
| null | Jason Bard, Jul 09 2025 | 2025-07-12T21:20:15 | oeisdata/seq/A385/A385775.seq | 434c277ff0a2b4c6f800d81d9bba8c14 |
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