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666,262,453B
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635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
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⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
| filename
stringlengths 29
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| hash
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A383626 | Expansion of 1/( Product_{k=0..15} (1 + (-1)^k * (2*k+1) * x) )^(1/16). | [
"1",
"1",
"171",
"511",
"67219",
"332691",
"35484101",
"243740561",
"21888901107",
"191172628003",
"14869055610001",
"156592613526141",
"10782221986043741",
"132098336706362573",
"8194613483517245067",
"113784873403069510831",
"6451310743087387098451",
"99520550430366438297171"
]
| [
"nonn"
]
| 8 | 0 | 3 | [
"A002426",
"A383624",
"A383625",
"A383626"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-12T03:37:52 | oeisdata/seq/A383/A383626.seq | 0663bad801270691d33de50bc7634a41 |
A383627 | Expansion of 1/( Product_{k=0..2} (1 - (3*k+1) * x) )^(1/3). | [
"1",
"4",
"19",
"100",
"562",
"3304",
"20062",
"124744",
"789553",
"5065444",
"32840347",
"214681636",
"1412786872",
"9348241504",
"62138211112",
"414627600736",
"2775808278058",
"18636412183336",
"125436195473662",
"846145250012776",
"5719044971926972",
"38723124875350960",
"262609593669266404"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A016223",
"A370781",
"A383627",
"A383628",
"A383629",
"A383630",
"A383631",
"A383632",
"A383633"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-12T03:18:11 | oeisdata/seq/A383/A383627.seq | 044c486fc2f177af9eae7bd9739b8a90 |
A383628 | Expansion of 1/( Product_{k=0..3} (1 - (4*k+1) * x) )^(1/4). | [
"1",
"7",
"59",
"553",
"5555",
"58597",
"640789",
"7201383",
"82659891",
"964698805",
"11408855809",
"136374495803",
"1644405320701",
"19971195162107",
"244004256374395",
"2996243293813273",
"36950056359522771",
"457349452121086917",
"5678884294812093329",
"70710759962448700955",
"882616583068179751945"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A383627",
"A383628",
"A383629",
"A383630",
"A383631",
"A383632",
"A383633",
"A383634"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-03T09:38:09 | oeisdata/seq/A383/A383628.seq | 0c4b76cd9a4b435b21b35eb8637d39ca |
A383629 | Expansion of 1/( Product_{k=0..4} (1 - (5*k+1) * x) )^(1/5). | [
"1",
"11",
"146",
"2156",
"34166",
"569426",
"9854436",
"175552696",
"3199485331",
"59384374841",
"1118636310726",
"21329345218236",
"410804181673996",
"7978922735099756",
"156074211110053016",
"3071360731347145776",
"60752572593061028911",
"1207041376109801598421",
"24073933939936470329806"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A383627",
"A383628",
"A383629",
"A383630",
"A383631",
"A383632",
"A383633",
"A383635"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-03T09:38:02 | oeisdata/seq/A383/A383629.seq | e9e56e2776fbf0d06cce2c43b096a80e |
A383630 | Expansion of 1/( Product_{k=0..6} (1 - (7*k+1) * x) )^(1/7). | [
"1",
"22",
"582",
"17116",
"540457",
"17965662",
"620869768",
"22116614080",
"807128297844",
"30040462521784",
"1136357972482216",
"43571763517455888",
"1689879290748884068",
"66179996449115623096",
"2613460738278752421648",
"103950807765143954047840",
"4160551692685459730727454"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A383627",
"A383628",
"A383629",
"A383630",
"A383631",
"A383632",
"A383633"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-05T07:29:22 | oeisdata/seq/A383/A383630.seq | 1475db774204960bbbae5f63763083ff |
A383631 | Expansion of 1/( Product_{k=0..7} (1 - (8*k+1) * x) )^(1/8). | [
"1",
"29",
"1009",
"39005",
"1618849",
"70741469",
"3214527633",
"150606953757",
"7231305564225",
"354221417305757",
"17641204276036657",
"890872808134921949",
"45521466404971069921",
"2349568589682742349405",
"122328082368695017498321",
"6416984703345086646305181",
"338833672698752842286404737"
]
| [
"nonn"
]
| 6 | 0 | 2 | [
"A383627",
"A383628",
"A383629",
"A383630",
"A383631",
"A383632",
"A383633"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-03T09:38:05 | oeisdata/seq/A383/A383631.seq | 76f873170a93e88c9ad0c67b48b97def |
A383632 | Expansion of 1/( Product_{k=0..8} (1 - (9*k+1) * x) )^(1/9). | [
"1",
"37",
"1639",
"80623",
"4257424",
"236721412",
"13688641144",
"816291120808",
"49895692924132",
"3112177949225236",
"197407027057353724",
"12699858803178669148",
"826900665838817386456",
"54398158759680212197576",
"3610650035912536155468808",
"241521616482786052388206408",
"16265890564063100473094045146"
]
| [
"nonn"
]
| 6 | 0 | 2 | [
"A383627",
"A383628",
"A383629",
"A383630",
"A383631",
"A383632",
"A383633"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-03T09:40:58 | oeisdata/seq/A383/A383632.seq | 446dcc9863d6b19f622390bc1c2f6c06 |
A383633 | Expansion of 1/( Product_{k=0..10} (1 - (11*k+1) * x) )^(1/11). | [
"1",
"56",
"3741",
"277256",
"22052713",
"1846878936",
"160878051401",
"14454374710216",
"1331486959280259",
"125190717874655720",
"11973642784650273211",
"1161838196321182959096",
"114133506709827074843495",
"11331528323810252967417064",
"1135444330405820622163425351",
"114694796036872449398436891896"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A383627",
"A383628",
"A383629",
"A383630",
"A383631",
"A383632",
"A383633"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-12T03:26:21 | oeisdata/seq/A383/A383633.seq | e504fe49de2cb26b0e40becbb295e6ca |
A383634 | Expansion of 1/( Product_{k=0..3} (1 - (4*k+1) * x) ). | [
"1",
"28",
"530",
"8540",
"126651",
"1791048",
"24604420",
"331842280",
"4422301301",
"58467523268",
"768888466710",
"10074907080420",
"131688310339951",
"1718380224948688",
"22396840268491400",
"291680037734786960",
"3796530709486682601",
"49397112147411259308",
"642542379001477422490",
"8356470240627243865900"
]
| [
"nonn",
"easy"
]
| 20 | 0 | 2 | [
"A383628",
"A383634"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-04T14:44:01 | oeisdata/seq/A383/A383634.seq | 7ddad9518266fcb6d5d9d398c6702c31 |
A383635 | Expansion of 1/( Product_{k=0..4} (1 - (5*k+1) * x) ). | [
"1",
"55",
"1940",
"56210",
"1461495",
"35567301",
"829147810",
"18774611680",
"416583297845",
"9111004217315",
"197197849460976",
"4235712944853390",
"90470493402792595",
"1924292232588575905",
"40801645704191871710",
"863108809168841357276",
"18225784176922532902545"
]
| [
"nonn",
"easy"
]
| 21 | 0 | 2 | [
"A383629",
"A383635"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-04T14:44:19 | oeisdata/seq/A383/A383635.seq | eb423c16d59b9eae97ee568ba50548c1 |
A383636 | Integers k such that there is no prime of the form x*y+1 with x+y=k. | [
"1",
"6",
"30",
"54"
]
| [
"nonn",
"hard"
]
| 15 | 1 | 2 | [
"A026728",
"A109905",
"A383636"
]
| null | Michel Marcus, May 03 2025 | 2025-05-07T11:24:53 | oeisdata/seq/A383/A383636.seq | f27d3023ab2ecad3f5005098a376154a |
A383637 | Expansion of 1/((1-x) * (1+3*x) * (1-5*x)). | [
"1",
"3",
"22",
"90",
"511",
"2373",
"12412",
"60420",
"307021",
"1520343",
"7646002",
"38097150",
"190884331",
"953225913",
"4769716792",
"23837822280",
"119221396441",
"596010127083",
"2980341200782",
"14900834307810",
"74506786627351",
"372526087871853",
"1862653975153972",
"9313199268385740",
"46566208164081061"
]
| [
"nonn",
"easy"
]
| 26 | 0 | 2 | [
"A079773",
"A120612",
"A383637"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-04T13:59:02 | oeisdata/seq/A383/A383637.seq | c6a5a32a8854f40074b61931a56990ad |
A383638 | Right-truncatable happy numbers: every prefix is a happy number and no digits are zero. | [
"1",
"7",
"13",
"19",
"79",
"133",
"139",
"192",
"193",
"793",
"1332",
"1333",
"1335",
"1337",
"1339",
"1393",
"1929",
"1933",
"7937",
"7938",
"13323",
"13332",
"13334",
"13339",
"13393",
"13933",
"19293",
"19295",
"19296",
"19333",
"79372",
"79384",
"79386",
"133236",
"133326",
"133399",
"133939",
"139339",
"192934",
"192951",
"192954"
]
| [
"nonn",
"base",
"fini",
"full"
]
| 9 | 1 | 2 | [
"A007770",
"A383638"
]
| null | Shyam Sunder Gupta, May 03 2025 | 2025-05-08T22:44:26 | oeisdata/seq/A383/A383638.seq | 29ea9ebcb33052ff5f3a86345c1b14e3 |
A383639 | Left-truncatable happy numbers: every suffix is a happy number and no digits are zero. | [
"1",
"7",
"31",
"91",
"97",
"291",
"331",
"391",
"397",
"931",
"2331",
"3331",
"3391",
"3931",
"5331",
"7331",
"7397",
"8397",
"9291",
"9331",
"23331",
"27397",
"32331",
"33391",
"33931",
"39291",
"39331",
"43331",
"48397",
"59291",
"68397",
"69291",
"93331",
"127397",
"159291",
"427397",
"439291",
"459291",
"469291",
"623331",
"632331"
]
| [
"nonn",
"base",
"fini",
"full"
]
| 6 | 1 | 2 | [
"A007770",
"A383639"
]
| null | Shyam Sunder Gupta, May 03 2025 | 2025-05-08T22:41:49 | oeisdata/seq/A383/A383639.seq | 1bf2e70b072c50de4871d3a81b242a38 |
A383640 | Internal digits of k^3 include digits of k as substring, k does not end in 0. | [
"56",
"782",
"5111",
"8089",
"8216",
"9553",
"11768",
"14357",
"18229",
"53257",
"64164",
"65137",
"72556",
"98442",
"213405",
"271516",
"830686",
"941976",
"1969394",
"2420681",
"2751442",
"4150015",
"5354867",
"7045156",
"9590417",
"9699457",
"10333214",
"13427757",
"21955652",
"31213974",
"32743132",
"35272742"
]
| [
"nonn",
"base"
]
| 10 | 1 | 1 | [
"A046837",
"A052210",
"A383640"
]
| null | Shyam Sunder Gupta, May 03 2025 | 2025-05-09T10:29:53 | oeisdata/seq/A383/A383640.seq | 83a5b52cebf8ba7710068d44bc1fa624 |
A383641 | a(n) is the difference between the sum of even composites and the sum of the odd composites in the first n positive integers. | [
"0",
"0",
"0",
"4",
"4",
"10",
"10",
"18",
"9",
"19",
"19",
"31",
"31",
"45",
"30",
"46",
"46",
"64",
"64",
"84",
"63",
"85",
"85",
"109",
"84",
"110",
"83",
"111",
"111",
"141",
"141",
"173",
"140",
"174",
"139",
"175",
"175",
"213",
"174",
"214",
"214",
"256",
"256",
"300",
"255",
"301",
"301",
"349",
"300",
"350",
"299",
"351",
"351",
"405",
"350",
"406",
"349",
"407",
"407"
]
| [
"nonn"
]
| 18 | 1 | 4 | [
"A000720",
"A002808",
"A004526",
"A010701",
"A028552",
"A034387",
"A066247",
"A071904",
"A101256",
"A193356",
"A262044",
"A383259",
"A383641"
]
| null | Felix Huber, May 08 2025 | 2025-05-14T21:44:46 | oeisdata/seq/A383/A383641.seq | 8bddfcfa55c9d4634cb952ba620f398e |
A383642 | Numbers k = x + y with x and y positive integers such that x*y is a cube. | [
"2",
"6",
"9",
"12",
"16",
"20",
"28",
"30",
"33",
"34",
"35",
"42",
"48",
"54",
"56",
"58",
"65",
"70",
"72",
"75",
"84",
"86",
"90",
"91",
"96",
"105",
"110",
"114",
"120",
"124",
"126",
"128",
"132",
"133",
"152",
"153",
"156",
"160",
"162",
"180",
"182",
"189",
"198",
"201",
"205",
"209",
"210",
"217",
"224",
"236",
"238",
"240",
"243",
"246",
"250",
"254",
"258",
"264",
"267"
]
| [
"nonn"
]
| 39 | 1 | 1 | [
"A000578",
"A003325",
"A337140",
"A383642"
]
| null | Huaineng He, May 03 2025 | 2025-05-14T18:02:20 | oeisdata/seq/A383/A383642.seq | ed1cca894d6f5078335f514137c8b6c1 |
A383643 | Number of n-dimensional additively indecomposable positive definite integral lattices (or quadratic forms). | [
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"2"
]
| [
"nonn",
"hard",
"more"
]
| 15 | 1 | 9 | [
"A380746",
"A383643"
]
| null | Robin Visser, May 09 2025 | 2025-05-15T21:28:07 | oeisdata/seq/A383/A383643.seq | b7d4d7d25814973c32b57d5e12afc094 |
A383644 | a(n) is the number of zeros in the left half-plane of the Maclaurin polynomial of degree n for exp(z). | [
"1",
"2",
"3",
"4",
"3",
"4",
"5",
"6",
"7",
"6",
"7",
"8",
"9",
"10",
"11",
"10",
"11",
"12",
"13",
"14",
"13",
"14",
"15",
"16",
"17",
"16",
"17",
"18",
"19",
"20",
"19",
"20",
"21",
"22",
"23",
"24",
"23",
"24",
"25",
"26",
"27",
"26",
"27",
"28",
"29",
"30",
"29",
"30",
"31",
"32",
"33",
"32",
"33",
"34",
"35",
"36",
"37",
"36",
"37",
"38",
"39",
"40",
"39",
"40",
"41",
"42",
"43",
"42",
"43",
"44"
]
| [
"nonn"
]
| 13 | 1 | 2 | [
"A330187",
"A332324",
"A332420",
"A383644"
]
| null | Michel Lagneau, May 03 2025 | 2025-05-20T16:53:24 | oeisdata/seq/A383/A383644.seq | 0674e9347075300d0dca8486d9c73776 |
A383645 | Consecutive internal states of the linear congruential pseudo-random number generator (17405*s+10395331) mod 2^24 when started at s=1. | [
"1",
"10412736",
"16578179",
"2262842",
"2257173",
"4251524",
"3870775",
"3934750",
"10123369",
"13310344",
"356907",
"14791746",
"14354941",
"11842764",
"8826975",
"14928294",
"8608209",
"15734096",
"7839443",
"6803018",
"3333093",
"7266068",
"9654663",
"9209390",
"10306617",
"15070744",
"4922491",
"5109074"
]
| [
"nonn",
"easy"
]
| 53 | 1 | 2 | [
"A096550",
"A096561",
"A383645"
]
| null | Sean A. Irvine, May 23 2025 | 2025-05-26T09:54:16 | oeisdata/seq/A383/A383645.seq | 922267e4405b97533d229fc95996df6c |
A383646 | Smallest number that takes n steps to reach 1 under iteration of sum-of-cubes-of-digits map. | [
"1",
"10",
"112",
"1189",
"778",
"13477",
"2388889999999999999999"
]
| [
"nonn",
"base"
]
| 29 | 0 | 2 | [
"A001273",
"A007770",
"A035504",
"A383646"
]
| null | Shyam Sunder Gupta, May 11 2025 | 2025-05-15T00:59:42 | oeisdata/seq/A383/A383646.seq | 14ff3b293014dca93d84278693b1a5df |
A383647 | Decimal expansion of 15/(2*Pi^4). | [
"0",
"7",
"6",
"9",
"9",
"4",
"8",
"6",
"6",
"9",
"1",
"0",
"1",
"3",
"2",
"5",
"1",
"3",
"9",
"1",
"8",
"6",
"4",
"5",
"8",
"7",
"4",
"5",
"0",
"3",
"3",
"9",
"0",
"2",
"0",
"6",
"0",
"6",
"3",
"7",
"0",
"8",
"5",
"1",
"3",
"9",
"0",
"2",
"2",
"8",
"6",
"9",
"7",
"0",
"3",
"8",
"6",
"2",
"6",
"0",
"2",
"6",
"6",
"0",
"3",
"9",
"8",
"0",
"2",
"4",
"7",
"0",
"0",
"6",
"6",
"6",
"3",
"9",
"4",
"0",
"1",
"8",
"6",
"8",
"0",
"4",
"2",
"8",
"6",
"4",
"4",
"7",
"1",
"4",
"6",
"7",
"8",
"6",
"7",
"9",
"2"
]
| [
"nonn",
"cons"
]
| 12 | 0 | 2 | [
"A030059",
"A082020",
"A088245",
"A088246",
"A092425",
"A151927",
"A383647"
]
| null | Stefano Spezia, May 03 2025 | 2025-05-06T16:20:49 | oeisdata/seq/A383/A383647.seq | 8610c1c67f9387d6754d81a7ae99bf96 |
A383648 | Expansion of 1/((1-x) * (1+3*x) * (1-5*x) * (1+7*x) * (1-9*x)). | [
"1",
"5",
"95",
"595",
"7686",
"55230",
"607090",
"4754090",
"48061871",
"397151755",
"3829847385",
"32718352485",
"306907974556",
"2676025381580",
"24692022876980",
"217997482615780",
"1991711627877741",
"17717860670676705",
"160916534238851875",
"1438073191564643975",
"13013962546963583426"
]
| [
"nonn",
"easy"
]
| 22 | 0 | 2 | [
"A381853",
"A383648"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-04T14:43:38 | oeisdata/seq/A383/A383648.seq | 641c017093b7685fedadea577c8fbf21 |
A383649 | Numbers k such that A206369(k) is prime. | [
"3",
"4",
"6",
"8",
"9",
"16",
"18",
"49",
"64",
"81",
"98",
"162",
"169",
"338",
"625",
"729",
"1024",
"1250",
"1458",
"4096",
"4489",
"6241",
"8978",
"12482",
"14641",
"19321",
"22801",
"26569",
"29282",
"37249",
"38642",
"45602",
"53138",
"65536",
"74498",
"113569",
"121801",
"143641",
"208849",
"227138",
"243602",
"262144",
"287282",
"292681",
"375769",
"413449",
"417698"
]
| [
"nonn"
]
| 22 | 1 | 1 | [
"A127727",
"A206369",
"A383649"
]
| null | Shreyansh Jaiswal, May 04 2025 | 2025-05-09T22:25:14 | oeisdata/seq/A383/A383649.seq | b0825cbb49fb1b8455424b16c6cd2487 |
A383650 | Averages k of a twin prime pair such that 3*k*2^d is also the average of a twin prime pair for some divisor d of 3*k. | [
"4",
"6",
"12",
"18",
"30",
"60",
"72",
"108",
"138",
"192",
"240",
"270",
"312",
"348",
"420",
"432",
"570",
"642",
"810",
"822",
"828",
"1020",
"1050",
"1092",
"1302",
"1320",
"1452",
"1620",
"1668",
"1698",
"1722",
"1950",
"1998",
"2310",
"2550",
"2688",
"2712",
"2730",
"2970",
"3000",
"3168",
"3258",
"3330",
"3372",
"3462",
"3468",
"3540",
"3582",
"4092"
]
| [
"nonn"
]
| 19 | 1 | 1 | [
"A000040",
"A005101",
"A014574",
"A173490",
"A383475",
"A383650"
]
| null | Juri-Stepan Gerasimov, May 04 2025 | 2025-05-06T11:51:17 | oeisdata/seq/A383/A383650.seq | 95673516c402ba91e17b426a420a34b3 |
A383651 | Expansion of 1/((1-x) * (1+4*x) * (1-6*x)). | [
"1",
"3",
"31",
"135",
"1015",
"5271",
"34903",
"196311",
"1230295",
"7172055",
"43871191",
"259871703",
"1572651991",
"9382224855",
"56508097495",
"338189591511",
"2032573522903",
"12181697242071",
"73145159033815",
"438651051877335",
"2632785920566231",
"15793197086188503",
"94773256265966551"
]
| [
"nonn",
"easy"
]
| 22 | 0 | 2 | [
"A051958",
"A083578",
"A383651"
]
| null | Seiichi Manyama, May 04 2025 | 2025-05-04T14:43:33 | oeisdata/seq/A383/A383651.seq | 4a19c8c6b9a290225023ae9161e4d470 |
A383652 | Primes p preceded and followed by gaps whose product is less than (log(p))^2. | [
"17",
"19",
"41",
"43",
"59",
"61",
"71",
"73",
"101",
"103",
"107",
"109",
"137",
"139",
"149",
"151",
"163",
"167",
"179",
"181",
"191",
"193",
"197",
"199",
"227",
"229",
"233",
"239",
"241",
"269",
"271",
"277",
"281",
"283",
"311",
"313",
"347",
"349",
"353",
"379",
"383",
"397",
"401",
"419",
"421",
"431",
"433",
"439",
"443",
"457",
"461",
"463",
"487",
"491",
"499",
"503",
"521",
"523",
"563",
"569",
"571",
"593",
"599"
]
| [
"nonn"
]
| 22 | 1 | 1 | [
"A083550",
"A288907",
"A381850",
"A383652"
]
| null | Alain Rocchelli, May 04 2025 | 2025-05-13T15:09:23 | oeisdata/seq/A383/A383652.seq | b194a7738a86fba85b124eace7461647 |
A383653 | Integers m such that m^4 is the sum of squares of two or more consecutive integers, positive or negative. | [
"1",
"13",
"26",
"33",
"295",
"330",
"364",
"1085",
"5005",
"5546",
"5682",
"6305",
"6538",
"15516",
"415151",
"1990368",
"3538366",
"34011252",
"42016497",
"79565281",
"139107722",
"175761059",
"254801664",
"418093065",
"667378972",
"1214995500",
"3609736702",
"4353556896"
]
| [
"nonn",
"more"
]
| 29 | 1 | 2 | [
"A000330",
"A097812",
"A189173",
"A383359",
"A383367",
"A383653",
"A383654"
]
| null | Xianwen Wang, May 04 2025 | 2025-05-13T22:44:50 | oeisdata/seq/A383/A383653.seq | e32ca398ba50cf42e81132bedba9172f |
A383654 | a(n) is the number k such that A383653(n)^4 is the sum of squares of k consecutive integers. | [
"2",
"2",
"169",
"242",
"177",
"352",
"1536",
"2401",
"40898",
"163607",
"230121",
"60625",
"218089",
"185761",
"19512097",
"47761921",
"1170329056",
"1224370081",
"7957888849",
"10842382346",
"11474926944",
"208152552417",
"12230369281",
"190412616875",
"497818686976",
"72899460001",
"1384334025217",
"313455536641"
]
| [
"nonn",
"more"
]
| 33 | 1 | 1 | [
"A000330",
"A097812",
"A189173",
"A383359",
"A383367",
"A383653",
"A383654"
]
| null | Xianwen Wang, May 04 2025 | 2025-05-14T15:44:57 | oeisdata/seq/A383/A383654.seq | e54b80998271787888a758493931f83d |
A383655 | Triangle read by rows: T(n,k) is the number of n-node Stanley graphs containing exactly k isolated points, n>=0, 0<=k<=n. | [
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"3",
"0",
"1",
"11",
"8",
"6",
"0",
"1",
"72",
"55",
"20",
"10",
"0",
"1",
"677",
"432",
"165",
"40",
"15",
"0",
"1",
"8686",
"4739",
"1512",
"385",
"70",
"21",
"0",
"1",
"152191",
"69488",
"18956",
"4032",
"770",
"112",
"28",
"0",
"1",
"3632916",
"1369719",
"312696",
"56868",
"9072",
"1386",
"168",
"36",
"0",
"1",
"118317913",
"36329160",
"6848595",
"1042320",
"142170",
"18144",
"2310",
"240",
"45",
"0",
"1"
]
| [
"nonn",
"tabl"
]
| 15 | 0 | 7 | [
"A135922",
"A323842",
"A383655"
]
| null | Geoffrey Critzer, May 04 2025 | 2025-05-07T11:35:22 | oeisdata/seq/A383/A383655.seq | 7b6a4add33bdab18fec7138b6e7f81cf |
A383656 | Triangular array read by rows: T(n,k) is the number of n-node Stanley graphs containing exactly k connected components, n>=0, 0<=k<=n. | [
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"2",
"3",
"1",
"0",
"8",
"11",
"6",
"1",
"0",
"52",
"60",
"35",
"10",
"1",
"0",
"502",
"472",
"255",
"85",
"15",
"1",
"0",
"6824",
"5166",
"2422",
"805",
"175",
"21",
"1",
"0",
"127166",
"76712",
"30072",
"9177",
"2100",
"322",
"28",
"1",
"0",
"3205924",
"1526910",
"486800",
"129360",
"28497",
"4788",
"546",
"36",
"1",
"0",
"108975934",
"40603534",
"10292970",
"2285240",
"455805",
"76629",
"9870",
"870",
"45",
"1"
]
| [
"nonn",
"tabl"
]
| 18 | 0 | 8 | [
"A135922",
"A323843",
"A383656"
]
| null | Geoffrey Critzer, May 04 2025 | 2025-05-08T02:21:19 | oeisdata/seq/A383/A383656.seq | 7202112d09d0160a0a05ae388c43b10e |
A383657 | Numerator of Dirichlet g.f.: Sum_{n>=1} a(n)/n^s = zeta(s)^(3/2). | [
"1",
"3",
"3",
"15",
"3",
"9",
"3",
"35",
"15",
"9",
"3",
"45",
"3",
"9",
"9",
"315",
"3",
"45",
"3",
"45",
"9",
"9",
"3",
"105",
"15",
"9",
"35",
"45",
"3",
"27",
"3",
"693",
"9",
"9",
"9",
"225",
"3",
"9",
"9",
"105",
"3",
"27",
"3",
"45",
"45",
"9",
"3",
"945",
"15",
"45",
"9",
"45",
"3",
"105",
"9",
"105",
"9",
"9",
"3",
"135",
"3",
"9",
"45",
"3003",
"9",
"27",
"3",
"45",
"9",
"27",
"3",
"525",
"3"
]
| [
"nonn",
"frac",
"mult"
]
| 16 | 1 | 2 | [
"A000005",
"A007425",
"A007426",
"A034695",
"A046643",
"A046644",
"A061200",
"A256688",
"A256689",
"A256690",
"A256691",
"A256692",
"A256693",
"A383657",
"A383658"
]
| null | Vaclav Kotesovec, May 04 2025 | 2025-05-04T23:44:22 | oeisdata/seq/A383/A383657.seq | 158c1c8b3bc02712f1b6d7d07fa09d69 |
A383658 | Denominator of Dirichlet g.f.: Sum_{n>=1} a(n)/n^s = zeta(s)^(3/2). | [
"1",
"2",
"2",
"8",
"2",
"4",
"2",
"16",
"8",
"4",
"2",
"16",
"2",
"4",
"4",
"128",
"2",
"16",
"2",
"16",
"4",
"4",
"2",
"32",
"8",
"4",
"16",
"16",
"2",
"8",
"2",
"256",
"4",
"4",
"4",
"64",
"2",
"4",
"4",
"32",
"2",
"8",
"2",
"16",
"16",
"4",
"2",
"256",
"8",
"16",
"4",
"16",
"2",
"32",
"4",
"32",
"4",
"4",
"2",
"32",
"2",
"4",
"16",
"1024",
"4",
"8",
"2",
"16",
"4",
"8",
"2",
"128",
"2",
"4",
"16",
"16",
"4"
]
| [
"nonn",
"frac",
"mult"
]
| 17 | 1 | 2 | [
"A000005",
"A007425",
"A007426",
"A034695",
"A046643",
"A046644",
"A061200",
"A256688",
"A256689",
"A256690",
"A256691",
"A256692",
"A256693",
"A383657",
"A383658"
]
| null | Vaclav Kotesovec, May 04 2025 | 2025-05-07T11:32:53 | oeisdata/seq/A383/A383658.seq | 64fe1fa3788cbed551b6bf00a6fa59ce |
A383659 | Decimal expansion of phi + 2*log(phi), where phi is the golden ratio. | [
"2",
"5",
"8",
"0",
"4",
"5",
"7",
"6",
"3",
"8",
"8",
"6",
"9",
"1",
"0",
"1",
"7",
"4",
"3",
"2",
"0",
"0",
"1",
"0",
"4",
"6",
"6",
"1",
"2",
"1",
"4",
"3",
"7",
"4",
"9",
"6",
"3",
"9",
"9",
"0",
"6",
"7",
"7",
"8",
"4",
"8",
"5",
"7",
"7",
"0",
"8",
"3",
"9",
"0",
"1",
"4",
"5",
"7",
"4",
"8",
"4",
"9",
"6",
"0",
"3",
"8",
"5",
"5",
"8",
"8",
"1",
"9",
"8",
"0",
"3",
"5",
"3",
"4",
"5",
"9",
"9",
"8",
"5",
"3",
"1",
"2",
"2"
]
| [
"nonn",
"cons"
]
| 18 | 1 | 1 | [
"A001622",
"A002390",
"A202543",
"A383659",
"A384238",
"A384682"
]
| null | Kritsada Moomuang, Jun 11 2025 | 2025-06-17T22:24:35 | oeisdata/seq/A383/A383659.seq | 8f6019e8c9c93620a45d81925ee0b275 |
A383660 | Number of closed knight's tours in the first 2n cells of a 3 X ceiling(2n/3) board. | [
"4",
"0",
"4",
"24",
"16",
"56",
"306",
"176",
"456",
"2632",
"1536",
"4828",
"26788",
"15424",
"44952",
"254288",
"147728",
"448032",
"2502568",
"1448416",
"4310048",
"24228704",
"14060048",
"42195584",
"236335248",
"136947616",
"409403328",
"2297294496",
"1332257856",
"3989883552",
"22366625344",
"12965578752",
"38798663104",
"217604833360",
"126169362176"
]
| [
"nonn"
]
| 15 | 11 | 1 | [
"A070030",
"A383660",
"A383661",
"A383662",
"A383663",
"A383664"
]
| null | Don Knuth, May 04 2025 | 2025-06-23T14:41:01 | oeisdata/seq/A383/A383660.seq | c3f7fbd04ed8dbfd17ee4c08921e3003 |
A383661 | Number of closed knight's tours in the first 2n cells of a 5 X ceiling(2n/5) board. | [
"1",
"0",
"1",
"30",
"0",
"148",
"8",
"78",
"9309",
"612",
"62749",
"44202",
"42049",
"2916485",
"147192",
"18284136",
"13311268",
"13008389",
"973107552",
"51147756",
"6190192748",
"4557702762",
"4311375354",
"316985255470",
"16552301184",
"2015267424300",
"1495135512514",
"1417634375316",
"104324890543686",
"5459334927260",
"663068761241948"
]
| [
"nonn"
]
| 17 | 9 | 4 | [
"A175855",
"A383660",
"A383661",
"A383662",
"A383663",
"A383664"
]
| null | Don Knuth, May 04 2025 | 2025-06-23T14:41:06 | oeisdata/seq/A383/A383661.seq | 3d4e54d7c06b7d67dc3af3894661b67c |
A383662 | Number of closed knight's tours in the first 2n cells of a 6 X ceiling(2n/6) board. | [
"6",
"0",
"2",
"302",
"8",
"151",
"19072",
"9862",
"18202",
"1603948",
"1067638",
"1310791",
"107096187",
"55488142",
"66608924",
"6149236417",
"3374967940",
"4259963914",
"402706752421",
"239187240144",
"292999006211",
"26470682075988",
"15360134570696",
"18595568012716",
"1685811256230132",
"964730606632516",
"1173328484648288"
]
| [
"nonn"
]
| 16 | 11 | 1 | [
"A175881",
"A383660",
"A383661",
"A383662",
"A383663",
"A383664"
]
| null | Don Knuth, May 04 2025 | 2025-06-23T14:41:10 | oeisdata/seq/A383/A383662.seq | 787440b71bb517dca3c80f491fdfd486 |
A383663 | Number of closed knight's tours in the first 2n cells of a 7 X ceiling(2n/7) board. | [
"2",
"11",
"58",
"0",
"21",
"1020",
"9309",
"1481",
"34162",
"1295034",
"1067638",
"2213327",
"50139185",
"682189688",
"144994543",
"2607067351",
"53099426601",
"34524432316",
"57716933870",
"1388556345255",
"16330667126220",
"3697750041989",
"70341043737487",
"1662805965511580",
"1250063279938854",
"2122662114673944"
]
| [
"nonn"
]
| 16 | 11 | 1 | [
"A193054",
"A383660",
"A383661",
"A383662",
"A383663",
"A383664"
]
| null | Don Knuth, May 04 2025 | 2025-06-23T14:41:19 | oeisdata/seq/A383/A383663.seq | 2041862889fd8df9d1c56f71eca34979 |
A383664 | Number of closed knight's tours in the first 2n cells of an 8 X ceiling(2n/8) board. | [
"4",
"12",
"212",
"0",
"50",
"4525",
"101730",
"44202",
"66034",
"2408624",
"69362264",
"55488142",
"101343548",
"2398536889",
"43391615822",
"34524432316",
"52661182514",
"1231713564493",
"20780788492646",
"13267364410532",
"21515340977481",
"552407941427835",
"10211663162678661",
"7112881119092574",
"11873618786859165"
]
| [
"nonn"
]
| 14 | 13 | 1 | [
"A193055",
"A383660",
"A383661",
"A383662",
"A383663",
"A383664"
]
| null | Don Knuth, May 04 2025 | 2025-05-05T15:18:53 | oeisdata/seq/A383/A383664.seq | 4b2e30975155bcdd7e5bd643c4e356d2 |
A383665 | a(n) is the least number k such that k, k - s and k + s all have n prime divisors, counted with multiplicity, where s is the sum of the decimal digits of k. | [
"15",
"102",
"204",
"408",
"3078",
"14496",
"88448",
"128768",
"6857312",
"111411968",
"844844000",
"6059394048",
"13384999936",
"948305874880",
"6373064359936",
"186505184249928"
]
| [
"nonn",
"base",
"hard",
"more"
]
| 17 | 2 | 1 | [
"A001222",
"A007953",
"A062028",
"A066568",
"A381851",
"A382996",
"A383665"
]
| null | Zak Seidov and Robert Israel, May 04 2025 | 2025-05-29T00:54:04 | oeisdata/seq/A383/A383665.seq | 45647b8b119547d8ebfc93efe97db95d |
A383666 | Numbers in whose binary representation no bit (0 or 1) occurs exactly once. | [
"3",
"7",
"9",
"10",
"12",
"15",
"17",
"18",
"19",
"20",
"21",
"22",
"24",
"25",
"26",
"28",
"31",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"40",
"41",
"42",
"43",
"44",
"45",
"46",
"48",
"49",
"50",
"51",
"52",
"53",
"54",
"56",
"57",
"58",
"60",
"63",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"72",
"73",
"74",
"75",
"76",
"77",
"78",
"79",
"80",
"81",
"82",
"83",
"84",
"85",
"86"
]
| [
"nonn",
"base",
"easy"
]
| 34 | 1 | 1 | [
"A030130",
"A158581",
"A383666",
"A383667"
]
| null | Clark Kimberling, May 07 2025 | 2025-05-21T12:40:18 | oeisdata/seq/A383/A383666.seq | cde811a1d739e979320f892eba81daa1 |
A383667 | Binary words beginning with 1 in which no binary digit occurs only once. | [
"11",
"111",
"1001",
"1010",
"1100",
"1111",
"10001",
"10010",
"10011",
"10100",
"10101",
"10110",
"11000",
"11001",
"11010",
"11100",
"11111",
"100001",
"100010",
"100011",
"100100",
"100101",
"100110",
"100111",
"101000",
"101001",
"101010",
"101011",
"101100",
"101101",
"101110",
"110000",
"110001",
"110010",
"110011"
]
| [
"nonn",
"base"
]
| 14 | 1 | 1 | [
"A158581",
"A383666",
"A383667"
]
| null | Clark Kimberling, May 07 2025 | 2025-05-21T12:39:44 | oeisdata/seq/A383/A383667.seq | c03685034a153a126af8d653c87920b1 |
A383668 | Numbers whose binary representation has a positive number of 0s, all with even runlength. | [
"4",
"9",
"12",
"16",
"19",
"25",
"28",
"33",
"36",
"39",
"48",
"51",
"57",
"60",
"64",
"67",
"73",
"76",
"79",
"97",
"100",
"103",
"112",
"115",
"121",
"124",
"129",
"132",
"135",
"144",
"147",
"153",
"156",
"159",
"192",
"195",
"201",
"204",
"207",
"225",
"228",
"231",
"240",
"243",
"249",
"252",
"256",
"259",
"265",
"268",
"271",
"289",
"292",
"295",
"304",
"307"
]
| [
"nonn",
"look",
"base"
]
| 16 | 1 | 1 | [
"A060142",
"A383668",
"A383669"
]
| null | Clark Kimberling, May 15 2025 | 2025-06-18T01:00:49 | oeisdata/seq/A383/A383668.seq | 625ac551082f9dc1dcc2ba3e68c31e12 |
A383669 | Numbers whose binary representation has a positive number of 0s, all with odd runlength. | [
"2",
"5",
"6",
"8",
"10",
"11",
"13",
"14",
"17",
"21",
"22",
"23",
"24",
"26",
"27",
"29",
"30",
"32",
"34",
"35",
"40",
"42",
"43",
"45",
"46",
"47",
"49",
"53",
"54",
"55",
"56",
"58",
"59",
"61",
"62",
"65",
"69",
"70",
"71",
"81",
"85",
"86",
"87",
"88",
"90",
"91",
"93",
"94",
"95",
"96",
"98",
"99",
"104",
"106",
"107",
"109",
"110",
"111",
"113",
"117",
"118",
"119",
"120"
]
| [
"nonn",
"look",
"base"
]
| 14 | 1 | 1 | [
"A060142",
"A383668",
"A383669"
]
| null | Clark Kimberling, May 15 2025 | 2025-06-18T01:00:44 | oeisdata/seq/A383/A383669.seq | dec44ced1200b0f9603d022cc15a1eeb |
A383670 | Limiting word, as a sequence, obtained by prefixing with 0 the limiting sequence of s(n) defined by s(0) = 0, s(1) = 12, s(n) = the concatenation of s(n - 1) and s(n - 2). | [
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1"
]
| [
"nonn"
]
| 22 | 1 | 3 | [
"A000045",
"A001950",
"A003849",
"A026352",
"A276885",
"A383670",
"A383671"
]
| null | Clark Kimberling, May 15 2025 | 2025-05-21T20:30:53 | oeisdata/seq/A383/A383670.seq | 20f97b3078fef23538aadd4b0efec927 |
A383671 | The limiting word that starts with 0, as a sequence, generated by s(0) = 0, s(1) = 12, s(n) = concatenation of s(n - 2) and s(n - 1). | [
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"1",
"2",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"2"
]
| [
"nonn"
]
| 18 | 0 | 3 | [
"A000045",
"A003849",
"A022413",
"A026356",
"A047924",
"A383670",
"A383671"
]
| null | Clark Kimberling, May 15 2025 | 2025-05-21T23:36:34 | oeisdata/seq/A383/A383671.seq | 56587d5e508b223e30a03815e4f2aa78 |
A383672 | Squarefree numbers k such that k^2+1 is not squarefree. | [
"7",
"38",
"41",
"43",
"57",
"70",
"82",
"93",
"107",
"118",
"143",
"157",
"182",
"193",
"218",
"239",
"251",
"257",
"282",
"293",
"307",
"318",
"327",
"357",
"382",
"393",
"407",
"418",
"437",
"443",
"457",
"482",
"493",
"515",
"518",
"543",
"557",
"577",
"582",
"593",
"606",
"607",
"618",
"643",
"682",
"707",
"718",
"743",
"746",
"757",
"782",
"793",
"807",
"818",
"829",
"843",
"857",
"893"
]
| [
"nonn"
]
| 17 | 1 | 1 | [
"A005117",
"A049532",
"A080666",
"A141932",
"A141941",
"A224718",
"A383672"
]
| null | Alexandre Herrera, May 04 2025 | 2025-05-09T19:59:59 | oeisdata/seq/A383/A383672.seq | 76e221bb6631901c457e47271c6fda0f |
A383673 | a(n) is the number of n X n Latin squares obeying a certain self-referential property defined in the comments. | [
"1",
"2",
"0",
"1",
"2",
"0",
"0",
"2",
"2",
"0",
"4",
"0",
"4",
"0",
"0",
"2"
]
| [
"nonn",
"more",
"hard"
]
| 22 | 1 | 2 | null | null | Luis Novoa, May 04 2025 | 2025-05-15T15:55:01 | oeisdata/seq/A383/A383673.seq | cc62f2929968764ce9a1420eb58a8bf4 |
A383674 | Decimal expansion of Integral_{0..1} 1 / ((1+x^4) * sqrt(1-x^4)) dx. | [
"1",
"0",
"4",
"8",
"2",
"1",
"3",
"4",
"7",
"0",
"2",
"7",
"1",
"7",
"5",
"4",
"1",
"0",
"7",
"4",
"2",
"4",
"0",
"4",
"0",
"3",
"2",
"0",
"3",
"8",
"2",
"7",
"1",
"7",
"7",
"1",
"3",
"9",
"4",
"5",
"3",
"3",
"4",
"9",
"1",
"2",
"7",
"7",
"9",
"7",
"9",
"4",
"0",
"1",
"8",
"3",
"2",
"6",
"0",
"7",
"3",
"4",
"9",
"9",
"9",
"8",
"8",
"6",
"7",
"4",
"6",
"9",
"7",
"5",
"5",
"3",
"3",
"7",
"9",
"6",
"8",
"7",
"3",
"8",
"6",
"0",
"7"
]
| [
"nonn",
"cons"
]
| 8 | 1 | 3 | [
"A019675",
"A383674",
"A383676"
]
| null | Sean A. Irvine, May 04 2025 | 2025-05-04T23:44:06 | oeisdata/seq/A383/A383674.seq | 6e6c89f6248ef46e16372d013b76df5d |
A383675 | Number of n-digit terms in A157711. | [
"0",
"0",
"0",
"0",
"1",
"0",
"2",
"2",
"1",
"4",
"9",
"5",
"8",
"3",
"9",
"9",
"12",
"6",
"14",
"4",
"5",
"9",
"8",
"10",
"13",
"10",
"8",
"19",
"17",
"15",
"20",
"16",
"27",
"16",
"26",
"14",
"23",
"18",
"26",
"22",
"40",
"23",
"21",
"18",
"32",
"24",
"29",
"15",
"33",
"21",
"25",
"33",
"34",
"25",
"25",
"22",
"47",
"30",
"40",
"25",
"37",
"29",
"38",
"33",
"47",
"30",
"41",
"37",
"45",
"41",
"46",
"33",
"42",
"36",
"52",
"39",
"48",
"28",
"49",
"37"
]
| [
"nonn",
"base"
]
| 51 | 1 | 7 | [
"A157711",
"A383675"
]
| null | Hans Havermann, May 29 2025 | 2025-06-16T15:17:37 | oeisdata/seq/A383/A383675.seq | baf948d7d6d61abe072bc81cb614edbc |
A383676 | Decimal expansion of Integral_{0..1} x^4 / ((1+x^4) * sqrt(1-x^4)) dx. | [
"2",
"6",
"2",
"8",
"1",
"5",
"3",
"0",
"6",
"8",
"7",
"4",
"3",
"0",
"5",
"7",
"9",
"7",
"8",
"0",
"8",
"3",
"7",
"9",
"4",
"7",
"4",
"5",
"6",
"2",
"8",
"4",
"1",
"9",
"9",
"2",
"8",
"9",
"6",
"0",
"4",
"2",
"5",
"6",
"2",
"9",
"3",
"6",
"0",
"1",
"7",
"5",
"6",
"3",
"0",
"8",
"2",
"3",
"3",
"7",
"3",
"5",
"1",
"9",
"1",
"1",
"7",
"2",
"0",
"5",
"9",
"5",
"9",
"8",
"1",
"8",
"2",
"7",
"4",
"3",
"7",
"7",
"2",
"9",
"0",
"6",
"9"
]
| [
"nonn",
"cons"
]
| 6 | 0 | 1 | [
"A019675",
"A383674",
"A383676"
]
| null | Sean A. Irvine, May 04 2025 | 2025-05-04T23:44:10 | oeisdata/seq/A383/A383676.seq | 8c1bf08ef25eb72b68800038d17feedc |
A383677 | Irregular triangle read by rows: T(n,k), 2 <= n , 3 <= k <= largest k such that A067175(k) <= n , is the smallest n-digit number m such that omega(m) = A001221(m) = k, and its largest prime factor equals the sum of its remaining prime factors. or -1 if no such number exists. | [
"30",
"120",
"-1",
"1080",
"3135",
"3570",
"10336",
"10695",
"10626",
"-1",
"100672",
"102695",
"103730",
"844305",
"-1",
"1003520",
"1005039",
"1003450",
"1218945",
"1231230",
"-1",
"10017286",
"10000295",
"10003390",
"10064145",
"10314150",
"-1",
"100216924",
"100019275",
"100017216",
"100367745",
"100327920",
"463798335",
"-1"
]
| [
"sign",
"tabf",
"base"
]
| 108 | 2 | 1 | [
"A001221",
"A002110",
"A067175",
"A365795",
"A382469",
"A383677",
"A383725",
"A383726",
"A383728",
"A383729"
]
| null | Jean-Marc Rebert, May 11 2025 | 2025-06-18T21:41:15 | oeisdata/seq/A383/A383677.seq | 592db35d98fcd4ba236e4b628fdf3958 |
A383678 | a(n) = [x^n] Product_{k=0..n} (1 + (2*n+k)*x). | [
"1",
"5",
"74",
"1650",
"48504",
"1763100",
"76223664",
"3817038960",
"217177416576",
"13834411290720",
"975244141065600",
"75366122480858880",
"6335159176892851200",
"575442172080117538560",
"56165570794932257433600",
"5862137958472255891200000",
"651508569509254106827161600",
"76814449419352043102473728000"
]
| [
"nonn"
]
| 44 | 0 | 2 | [
"A000142",
"A165675",
"A382347",
"A383678",
"A384024"
]
| null | Seiichi Manyama, May 18 2025 | 2025-05-23T03:02:51 | oeisdata/seq/A383/A383678.seq | 5d350936ebdafeb3dad9ddaf4e116a5d |
A383679 | The lesser of two consecutive primes whose gap equals the difference between their digital sums. | [
"2",
"3",
"5",
"11",
"13",
"17",
"23",
"31",
"41",
"43",
"53",
"61",
"71",
"73",
"83",
"101",
"103",
"107",
"131",
"137",
"151",
"163",
"173",
"191",
"193",
"197",
"223",
"227",
"233",
"251",
"263",
"271",
"281",
"311",
"313",
"331",
"347",
"353",
"373",
"383",
"401",
"431",
"433",
"443",
"461",
"463",
"491",
"503",
"521",
"541",
"563",
"571",
"593",
"601",
"613",
"617"
]
| [
"nonn",
"base",
"easy"
]
| 11 | 1 | 1 | [
"A000040",
"A001223",
"A007953",
"A383679",
"A383680",
"A383681",
"A383685"
]
| null | Stefano Spezia, May 05 2025 | 2025-05-07T11:25:54 | oeisdata/seq/A383/A383679.seq | 3dcfb4b953994921ed910038cf9d7747 |
A383680 | The greater of two consecutive primes whose gap equals the difference between their digital sums. | [
"3",
"5",
"7",
"13",
"17",
"19",
"29",
"37",
"43",
"47",
"59",
"67",
"73",
"79",
"89",
"103",
"107",
"109",
"137",
"139",
"157",
"167",
"179",
"193",
"197",
"199",
"227",
"229",
"239",
"257",
"269",
"277",
"283",
"313",
"317",
"337",
"349",
"359",
"379",
"389",
"409",
"433",
"439",
"449",
"463",
"467",
"499",
"509",
"523",
"547",
"569",
"577",
"599",
"607",
"617",
"619"
]
| [
"nonn",
"base",
"easy"
]
| 9 | 1 | 1 | [
"A000040",
"A001223",
"A007953",
"A383679",
"A383680",
"A383681",
"A383686"
]
| null | Stefano Spezia, May 05 2025 | 2025-05-07T11:26:00 | oeisdata/seq/A383/A383680.seq | 06d96f6cdd9e82f4d47c5fa361db3a5b |
A383681 | Disjunctive union of A383679 and A383680. | [
"2",
"7",
"11",
"19",
"23",
"29",
"31",
"37",
"41",
"47",
"53",
"59",
"61",
"67",
"71",
"79",
"83",
"89",
"101",
"109",
"131",
"139",
"151",
"157",
"163",
"167",
"173",
"179",
"191",
"199",
"223",
"229",
"233",
"239",
"251",
"257",
"263",
"269",
"271",
"277",
"281",
"283",
"311",
"317",
"331",
"337",
"347",
"349",
"353",
"359",
"373",
"379",
"383",
"389",
"401",
"409",
"431"
]
| [
"nonn",
"base",
"easy"
]
| 8 | 1 | 1 | [
"A000040",
"A001223",
"A007953",
"A383679",
"A383680",
"A383681",
"A383687"
]
| null | Stefano Spezia, May 05 2025 | 2025-05-07T11:26:13 | oeisdata/seq/A383/A383681.seq | 2e0918fa064ddae39578a6e4a46b2952 |
A383682 | The largest nonnegative integer value of j for which each integer n, n+2, ..., j-4, j-2, j can be written as the sum of the squares of the elements of a partition of n. | [
"1",
"4",
"5",
"10",
"13",
"14",
"21",
"34",
"35",
"46",
"61",
"62",
"77",
"78",
"95",
"114",
"121",
"142",
"165",
"190",
"225",
"246",
"277",
"290",
"345",
"358",
"359",
"396",
"435",
"446",
"487",
"530",
"575",
"622",
"679",
"722",
"783",
"790",
"791",
"846",
"903",
"1022",
"1085",
"1086",
"1151",
"1230",
"1287",
"1358",
"1373",
"1374",
"1521",
"1522",
"1599"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A381811",
"A383682"
]
| null | Noah A Rosenberg, May 05 2025 | 2025-05-10T19:31:33 | oeisdata/seq/A383/A383682.seq | 6e58e26e318bd0a39abda140cd456b04 |
A383683 | The number of possible values that can be obtained for the Shannon diversity index across all partitions of n. | [
"1",
"1",
"2",
"3",
"5",
"7",
"11",
"15",
"21",
"29",
"39",
"52",
"68",
"89",
"117",
"150",
"192",
"244",
"309",
"387",
"485",
"603",
"749",
"922",
"1130",
"1384",
"1680",
"2035",
"2440",
"2922",
"3478",
"4118",
"4867",
"5728",
"6740",
"7879",
"9206",
"10741",
"12502",
"14516",
"16846",
"19533",
"22620",
"26164",
"30252",
"34967",
"40450",
"46786"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A000041",
"A000607",
"A383683"
]
| null | Noah A Rosenberg, May 05 2025 | 2025-05-06T15:20:40 | oeisdata/seq/A383/A383683.seq | 8768550385a80db1e7eb83f2a4063809 |
A383684 | Minimum number of transversals in an extended self-orthogonal diagonal Latin square of order n. | [
"1",
"0",
"0",
"8",
"15",
"0",
"23",
"128",
"133",
"716"
]
| [
"nonn",
"more",
"hard"
]
| 8 | 1 | 4 | [
"A090741",
"A091323",
"A287644",
"A287645",
"A309210",
"A309598",
"A309599",
"A357514",
"A383684"
]
| null | Eduard I. Vatutin, May 05 2025 | 2025-06-29T22:35:43 | oeisdata/seq/A383/A383684.seq | a920706048696d89204a21bd7896376d |
A383685 | The lesser of two consecutive primes whose gap equals the difference between their digital roots. | [
"2",
"3",
"5",
"11",
"13",
"19",
"29",
"37",
"41",
"47",
"59",
"67",
"73",
"83",
"101",
"103",
"109",
"127",
"137",
"149",
"163",
"173",
"191",
"193",
"227",
"229",
"239",
"263",
"271",
"281",
"307",
"311",
"347",
"353",
"379",
"397",
"419",
"433",
"443",
"461",
"463",
"487",
"499",
"541",
"569",
"587",
"599",
"613",
"617",
"641",
"643",
"659",
"677",
"739",
"757",
"769"
]
| [
"nonn",
"base",
"easy"
]
| 11 | 1 | 1 | [
"A000040",
"A001223",
"A010888",
"A383679",
"A383685",
"A383686",
"A383687"
]
| null | Stefano Spezia, May 05 2025 | 2025-05-07T11:26:25 | oeisdata/seq/A383/A383685.seq | 26648c491c68d1348c76a61da1e9c4b9 |
A383686 | The greater of two consecutive primes whose gap equals the difference between their digital roots. | [
"3",
"5",
"7",
"13",
"17",
"23",
"31",
"41",
"43",
"53",
"61",
"71",
"79",
"89",
"103",
"107",
"113",
"131",
"139",
"151",
"167",
"179",
"193",
"197",
"229",
"233",
"241",
"269",
"277",
"283",
"311",
"313",
"349",
"359",
"383",
"401",
"421",
"439",
"449",
"463",
"467",
"491",
"503",
"547",
"571",
"593",
"601",
"617",
"619",
"643",
"647",
"661",
"683",
"743",
"761",
"773"
]
| [
"nonn",
"base",
"easy"
]
| 9 | 1 | 1 | [
"A000040",
"A001223",
"A010888",
"A383680",
"A383685",
"A383686",
"A383687"
]
| null | Stefano Spezia, May 05 2025 | 2025-05-07T11:26:32 | oeisdata/seq/A383/A383686.seq | e4442d613feb9824d22bf99030cfa94e |
A383687 | Disjunctive union of A383685 and A383686. | [
"2",
"7",
"11",
"17",
"19",
"23",
"29",
"31",
"37",
"43",
"47",
"53",
"59",
"61",
"67",
"71",
"73",
"79",
"83",
"89",
"101",
"107",
"109",
"113",
"127",
"131",
"137",
"139",
"149",
"151",
"163",
"167",
"173",
"179",
"191",
"197",
"227",
"233",
"239",
"241",
"263",
"269",
"271",
"277",
"281",
"283",
"307",
"313",
"347",
"349",
"353",
"359",
"379",
"383",
"397",
"401",
"419"
]
| [
"nonn",
"base",
"easy"
]
| 10 | 1 | 1 | [
"A000040",
"A001223",
"A010888",
"A383681",
"A383685",
"A383686",
"A383687"
]
| null | Stefano Spezia, May 05 2025 | 2025-05-07T11:26:38 | oeisdata/seq/A383/A383687.seq | 7ce8042a68a8dd559f84c23d204deaaa |
A383688 | Partial sums of A383442. | [
"0",
"1",
"3",
"2",
"0",
"-3",
"0",
"4",
"9",
"4",
"0",
"6",
"13",
"21",
"14",
"8",
"17",
"27",
"38",
"28",
"19",
"11",
"0",
"-12",
"-25",
"-39",
"-25",
"-12",
"0",
"15",
"31",
"48",
"66",
"48",
"33",
"17",
"0",
"19",
"39",
"60",
"82",
"105",
"83",
"64",
"44",
"23",
"47",
"72",
"98",
"125",
"153",
"126",
"102",
"79",
"53",
"28",
"0",
"-29",
"-59",
"-90",
"-122",
"-155",
"-122",
"-92",
"-63",
"-31"
]
| [
"sign"
]
| 7 | 0 | 3 | [
"A383442",
"A383443",
"A383688"
]
| null | Paolo Xausa, May 05 2025 | 2025-05-05T11:45:26 | oeisdata/seq/A383/A383688.seq | fc4d5ed4f5b78458eeb5786f7f512f6c |
A383689 | a(n) is the smallest integer k such that the Diophantine equation x^3 + y^3 + z^3 = k^n, where 0 < x < y < z has exactly n integer solutions. | [
"36",
"188",
"54",
"144",
"90",
"63",
"99"
]
| [
"nonn",
"hard",
"more"
]
| 27 | 1 | 1 | [
"A383689",
"A383879"
]
| null | Zhining Yang, May 12 2025 | 2025-06-07T11:56:45 | oeisdata/seq/A383/A383689.seq | 19a4275a36da425130cc83f92e8b2998 |
A383690 | Positions of digits in the decimal expansion of Pi where the cumulative sum of even digits equals the cumulative sum of odd digits (positions 1, 2, 3, ... refer to the digits 3, 1, 4, ...). | [
"3",
"268",
"375",
"376",
"402"
]
| [
"nonn",
"base",
"more"
]
| 30 | 1 | 1 | [
"A000796",
"A175813",
"A383690"
]
| null | Gonzalo Martínez, May 09 2025 | 2025-05-20T16:49:38 | oeisdata/seq/A383/A383690.seq | 43c2840f56a942a0a405f98288824775 |
A383691 | Square numbers with distinct digits from 1-9 that have an initial string of two or more digits forming a square number. | [
"169",
"256",
"361",
"3249",
"16384",
"18496",
"36481",
"81796",
"237169",
"729316",
"2537649",
"3481956",
"5184729",
"36517849",
"81432576",
"254817369",
"361874529",
"529874361"
]
| [
"nonn",
"base",
"fini",
"full"
]
| 18 | 1 | 1 | [
"A036744",
"A036745",
"A352329",
"A383691"
]
| null | Hilarie Orman, May 05 2025 | 2025-05-07T11:55:12 | oeisdata/seq/A383/A383691.seq | 6c4a0b60add9b411f7b0340ae28229ad |
A383692 | a(n) = round(Chi(n)) where Chi(x) is the cosh integral function. | [
"1",
"2",
"5",
"10",
"20",
"43",
"96",
"220",
"519",
"1246",
"3036",
"7480",
"18599",
"46596",
"117478",
"297780",
"758319",
"1938952",
"4975454",
"12807826",
"33063593",
"85572336",
"221983185",
"577057696",
"1502975453",
"3921470496",
"10248248560",
"26822559296",
"70299597879",
"184486604704",
"484727787984"
]
| [
"nonn"
]
| 10 | 1 | 2 | [
"A383542",
"A383692"
]
| null | Kritsada Moomuang, May 05 2025 | 2025-05-10T23:00:20 | oeisdata/seq/A383/A383692.seq | b47a558e2c9ec30eb6cb02d5a97cbcdc |
A383693 | Exponential unitary abundant numbers: numbers k such that A322857(k) > 2*k. | [
"900",
"1764",
"4356",
"4500",
"4900",
"6084",
"6300",
"8820",
"9900",
"10404",
"11700",
"12348",
"12996",
"14700",
"15300",
"17100",
"19044",
"19404",
"20700",
"21780",
"22500",
"22932",
"26100",
"27900",
"29988",
"30276",
"30420",
"30492",
"31500",
"33300",
"33516",
"34596",
"36900",
"38700",
"40572",
"42300",
"42588",
"44100",
"47700",
"47916",
"49284",
"49500"
]
| [
"nonn",
"easy"
]
| 9 | 1 | 1 | [
"A005117",
"A013929",
"A129575",
"A209061",
"A322857",
"A322858",
"A361255",
"A383693",
"A383694",
"A383697",
"A383698"
]
| null | Amiram Eldar, May 05 2025 | 2025-05-07T10:49:38 | oeisdata/seq/A383/A383693.seq | 4899c7cf47fb84d56f8c2402c36931db |
A383694 | Primitive exponential unitary abundant numbers: the powerful terms of A383693. | [
"900",
"1764",
"4356",
"4500",
"4900",
"6084",
"10404",
"12348",
"12996",
"19044",
"22500",
"30276",
"34596",
"44100",
"47916",
"49284",
"60516",
"66564",
"79092",
"79524",
"86436",
"88200",
"101124",
"108900",
"112500",
"125316",
"132300",
"133956",
"152100",
"161604",
"176400",
"176868",
"181476",
"191844",
"213444",
"217800",
"220500"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A001694",
"A005117",
"A322857",
"A328136",
"A383693",
"A383694",
"A383698"
]
| null | Amiram Eldar, May 05 2025 | 2025-05-07T10:49:58 | oeisdata/seq/A383/A383694.seq | e63833edfb3a0ef50ed1b5e0d65b7780 |
A383695 | Exponential infinitary abundant numbers that are not exponential unitary abundant: numbers k such that A361175(k) > 2*k >= A322857(k). | [
"476985600",
"815673600",
"1018886400",
"1177862400",
"1493049600",
"2014214400",
"2373638400",
"2712326400",
"3756614400",
"3863865600",
"4744454400",
"5218617600",
"5246841600",
"6234681600",
"7928121600",
"8108755200",
"8245036800",
"8972409600",
"9062726400",
"9824774400",
"10502150400",
"10603756800"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A005117",
"A013929",
"A129575",
"A322857",
"A361175",
"A383695",
"A383696"
]
| null | Amiram Eldar, May 05 2025 | 2025-05-07T10:50:08 | oeisdata/seq/A383/A383695.seq | e1afdd28a2e931f7791ffadf4865e21b |
A383696 | Primitive exponential infinitary abundant numbers that are not primitive exponential unitary abundant: the powerful terms of A383695. | [
"476985600",
"815673600",
"1018886400",
"1177862400",
"1493049600",
"2014214400",
"2373638400",
"2712326400",
"3756614400",
"3863865600",
"4744454400",
"5218617600",
"6234681600",
"7928121600",
"9824774400",
"10502150400",
"12669753600",
"14227718400",
"15040569600",
"17614598400",
"19443513600",
"22356230400"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A001694",
"A005117",
"A322857",
"A361175",
"A383695",
"A383696"
]
| null | Amiram Eldar, May 06 2025 | 2025-05-07T10:50:28 | oeisdata/seq/A383/A383696.seq | 5603d5af129049619302e3c7ad24854d |
A383697 | Exponential squarefree exponential abundant numbers: numbers k such that A361174(k) > 2*k. | [
"900",
"1764",
"4356",
"4500",
"4900",
"6084",
"6300",
"8820",
"9900",
"10404",
"11700",
"12348",
"12996",
"14700",
"15300",
"17100",
"19044",
"19404",
"20700",
"21780",
"22932",
"26100",
"27900",
"29988",
"30276",
"30420",
"30492",
"31500",
"33300",
"33516",
"34596",
"36900",
"38700",
"40572",
"42300",
"42588",
"44100",
"47700",
"47916",
"49284",
"49500"
]
| [
"nonn",
"easy"
]
| 8 | 1 | 1 | [
"A005117",
"A013929",
"A129575",
"A209061",
"A361174",
"A383693",
"A383697",
"A383698"
]
| null | Amiram Eldar, May 06 2025 | 2025-05-07T10:50:33 | oeisdata/seq/A383/A383697.seq | fe91ace94c4abc36ea1a31ec2a2df8fb |
A383698 | Primitive exponential squarefree exponential abundant numbers: the powerful terms of A383697. | [
"900",
"1764",
"4356",
"4500",
"4900",
"6084",
"10404",
"12348",
"12996",
"19044",
"30276",
"34596",
"44100",
"47916",
"49284",
"60516",
"66564",
"79092",
"79524",
"88200",
"101124",
"108900",
"112500",
"125316",
"132300",
"133956",
"152100",
"161604",
"176868",
"181476",
"191844",
"213444",
"217800",
"220500",
"224676",
"246924"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A001694",
"A005117",
"A361174",
"A383694",
"A383697",
"A383698"
]
| null | Amiram Eldar, May 06 2025 | 2025-05-07T10:50:45 | oeisdata/seq/A383/A383698.seq | d8f9ac995b18aacf4ba9d4ee6208bbe8 |
A383699 | Primitive exponential 3-abundant numbers: the powerful terms of A328135. | [
"901800900",
"1542132900",
"1926332100",
"2153888100",
"2690496900",
"2822796900",
"3942584100",
"4487660100",
"4600908900",
"5127992100",
"6267888900",
"6742052100",
"7162236900",
"7305120900",
"8421732900",
"8969984100",
"9866448900",
"10203020100",
"10718460900",
"11723411700",
"11787444900",
"12528324900"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A001694",
"A051377",
"A307112",
"A328135",
"A328136",
"A383699"
]
| null | Amiram Eldar, May 06 2025 | 2025-05-07T10:50:52 | oeisdata/seq/A383/A383699.seq | 31c1b1451df86e0ad4ba69ab4ad9ae6b |
A383700 | Coefficient of x^2 in expansion of (x+1) * (x+5) * ... * (x+4*n-3). | [
"0",
"0",
"1",
"15",
"254",
"5130",
"122119",
"3365089",
"105599276",
"3722336388",
"145717348221",
"6275071262691",
"294890141047050",
"15020233818893550",
"824373714907080675",
"48505985450168267925",
"3046201904592803410200",
"203381159927362120499400",
"14385952383695375700375225"
]
| [
"nonn"
]
| 16 | 0 | 4 | [
"A290319",
"A383700"
]
| null | Seiichi Manyama, May 06 2025 | 2025-05-12T03:51:17 | oeisdata/seq/A383/A383700.seq | 8ade0f64f57b03a5a67f2b8974b0dcea |
A383701 | Coefficient of x^3 in expansion of (x+1) * (x+5) * ... * (x+4*n-3). | [
"0",
"0",
"0",
"1",
"28",
"730",
"20460",
"633619",
"21740040",
"823020596",
"34174098440",
"1546855384261",
"75883563554436",
"4013184755214414",
"227719025845257492",
"13804358188086757719",
"890571834923460488784",
"60933371174617735181160",
"4407783770975985847999440",
"336154167664942342604334345"
]
| [
"nonn"
]
| 12 | 0 | 5 | [
"A290319",
"A383701"
]
| null | Seiichi Manyama, May 06 2025 | 2025-05-07T06:03:36 | oeisdata/seq/A383/A383701.seq | 6de792f1da9c26732fd14fef017ddd50 |
A383702 | Coefficient of x^2 in expansion of (x+3) * (x+7) * ... * (x+4*n-1). | [
"0",
"0",
"1",
"21",
"446",
"10670",
"290599",
"8951355",
"308846124",
"11822475564",
"497794079421",
"22881487815153",
"1140642637297866",
"61312161303209466",
"3535773901817957955",
"217787248332803277495",
"14271822475100747003160",
"991517953843097370650520",
"72799719644532661375481145"
]
| [
"nonn"
]
| 20 | 0 | 4 | [
"A225471",
"A383702"
]
| null | Seiichi Manyama, May 06 2025 | 2025-05-08T08:58:42 | oeisdata/seq/A383/A383702.seq | fef4d6f29edd77a1caf5b12752f79414 |
A383703 | Coefficient of x^3 in expansion of (x+3) * (x+7) * ... * (x+4*n-1). | [
"0",
"0",
"0",
"1",
"36",
"1130",
"36660",
"1280419",
"48644344",
"2011398164",
"90267003960",
"4379275249701",
"228707424551100",
"12804721289403966",
"765571832220427596",
"48704512002823186119",
"3286171504510664002992",
"234445313277315235203624",
"17637135196532479070107824",
"1395584859384468591633567945"
]
| [
"nonn"
]
| 15 | 0 | 5 | [
"A225471",
"A383703"
]
| null | Seiichi Manyama, May 06 2025 | 2025-05-07T11:54:40 | oeisdata/seq/A383/A383703.seq | 5cb1f68d8c2589960cabcbca96c90222 |
A383704 | a(n) = [x^n] Product_{k=0..2*n-1} (x - (-1)^k * (2*k+1)). | [
"1",
"2",
"-34",
"-540",
"26614",
"805980",
"-66399124",
"-2972817848",
"343902030758",
"20389669252524",
"-3039312653124540",
"-224361715353976200",
"40941662601331486396",
"3617518823154571788440",
"-781104190733806836937320",
"-80375840650247250199417200",
"20044038897159722534821833990"
]
| [
"sign"
]
| 14 | 0 | 2 | [
"A293318",
"A383704"
]
| null | Seiichi Manyama, May 06 2025 | 2025-05-07T14:57:15 | oeisdata/seq/A383/A383704.seq | f2183dd962beb9e7a5311df92a8494a1 |
A383705 | Numerator of Dirichlet g.f.: Sum_{n>=1} a(n)/n^s = zeta(s)^(2/3). | [
"1",
"2",
"2",
"5",
"2",
"4",
"2",
"40",
"5",
"4",
"2",
"10",
"2",
"4",
"4",
"110",
"2",
"10",
"2",
"10",
"4",
"4",
"2",
"80",
"5",
"4",
"40",
"10",
"2",
"8",
"2",
"308",
"4",
"4",
"4",
"25",
"2",
"4",
"4",
"80",
"2",
"8",
"2",
"10",
"10",
"4",
"2",
"220",
"5",
"10",
"4",
"10",
"2",
"80",
"4",
"80",
"4",
"4",
"2",
"20",
"2",
"4",
"10",
"2618",
"4",
"8",
"2",
"10",
"4",
"8",
"2",
"200",
"2",
"4",
"10",
"10",
"4"
]
| [
"nonn",
"frac",
"mult"
]
| 11 | 1 | 2 | [
"A046643",
"A256688",
"A256689",
"A383657",
"A383705"
]
| null | Vaclav Kotesovec, May 06 2025 | 2025-05-06T17:10:31 | oeisdata/seq/A383/A383705.seq | 945115330a03ca398334a52da11bb2cc |
A383706 | Number of ways to choose disjoint strict integer partitions, one of each prime index of n. | [
"1",
"1",
"1",
"0",
"2",
"1",
"2",
"0",
"0",
"1",
"3",
"0",
"4",
"1",
"1",
"0",
"5",
"0",
"6",
"0",
"2",
"2",
"8",
"0",
"2",
"2",
"0",
"0",
"10",
"1",
"12",
"0",
"2",
"3",
"2",
"0",
"15",
"3",
"2",
"0",
"18",
"1",
"22",
"0",
"0",
"5",
"27",
"0",
"2",
"0",
"3",
"0",
"32",
"0",
"3",
"0",
"4",
"5",
"38",
"0",
"46",
"7",
"0",
"0",
"4",
"1",
"54",
"0",
"5",
"1",
"64",
"0",
"76",
"8",
"0",
"0",
"3",
"1",
"89",
"0",
"0",
"10"
]
| [
"nonn"
]
| 9 | 1 | 5 | [
"A000009",
"A000041",
"A048767",
"A048768",
"A055396",
"A056239",
"A061395",
"A098859",
"A112798",
"A122111",
"A130091",
"A179009",
"A209229",
"A217605",
"A239455",
"A279375",
"A279790",
"A299200",
"A317141",
"A351293",
"A351294",
"A351295",
"A357982",
"A381432",
"A381433",
"A381454",
"A382525",
"A382771",
"A382876",
"A382912",
"A382913",
"A383533",
"A383706",
"A383707",
"A383708",
"A383710",
"A383711",
"A384005"
]
| null | Gus Wiseman, May 15 2025 | 2025-05-18T09:58:29 | oeisdata/seq/A383/A383706.seq | 83adabfa3a6ceb782b7f9e49578d60ad |
A383707 | Heinz numbers of maximally refined strict integer partitions. | [
"1",
"2",
"3",
"6",
"10",
"14",
"15",
"30",
"42",
"66",
"70",
"78",
"105",
"110",
"182",
"210",
"330",
"390"
]
| [
"nonn",
"more"
]
| 19 | 1 | 2 | [
"A048767",
"A055396",
"A056239",
"A061395",
"A112798",
"A130091",
"A179009",
"A299200",
"A351294",
"A351295",
"A357982",
"A381432",
"A381454",
"A382525",
"A383706",
"A383707",
"A384320",
"A384321",
"A384349",
"A384389",
"A384390",
"A384723"
]
| null | Gus Wiseman, May 15 2025 | 2025-06-10T23:15:46 | oeisdata/seq/A383/A383707.seq | c889eb36ce1b9fe0b775419df9c77dcc |
A383708 | Number of integer partitions of n such that it is possible to choose a family of pairwise disjoint strict integer partitions, one of each part. | [
"1",
"1",
"2",
"2",
"3",
"5",
"5",
"7",
"8",
"13",
"14",
"18",
"22",
"27",
"36",
"41",
"50",
"61",
"73",
"86"
]
| [
"nonn",
"more"
]
| 10 | 0 | 3 | [
"A044813",
"A047966",
"A048767",
"A048768",
"A089259",
"A091602",
"A098859",
"A116540",
"A130091",
"A217605",
"A239455",
"A242882",
"A317141",
"A351013",
"A351293",
"A351294",
"A351295",
"A381432",
"A381433",
"A381441",
"A382771",
"A382912",
"A382913",
"A383013",
"A383533",
"A383706",
"A383708",
"A383710",
"A383711"
]
| null | Gus Wiseman, May 07 2025 | 2025-05-08T22:55:53 | oeisdata/seq/A383/A383708.seq | d5a67b8c0664c598df38bd6f9cf01132 |
A383709 | Number of integer partitions of n with distinct multiplicities (Wilf) and distinct 0-appended differences. | [
"1",
"1",
"2",
"1",
"2",
"2",
"3",
"4",
"4",
"4",
"5",
"6",
"5",
"7",
"8",
"6",
"8",
"9",
"9",
"10",
"9",
"10",
"12",
"12",
"11",
"12",
"14",
"13",
"14",
"15",
"14",
"16",
"16",
"16",
"18",
"17",
"17",
"19",
"20",
"19",
"19",
"21",
"21",
"22",
"22",
"21",
"24",
"24",
"23",
"25",
"25",
"25",
"26",
"27",
"27",
"27",
"28",
"28",
"30",
"30",
"28",
"31",
"32",
"31",
"32",
"32",
"33",
"34",
"34",
"34"
]
| [
"nonn"
]
| 6 | 0 | 3 | [
"A047966",
"A048767",
"A098859",
"A130091",
"A130092",
"A239455",
"A320348",
"A325324",
"A325325",
"A325349",
"A325351",
"A325367",
"A325368",
"A325388",
"A336866",
"A351293",
"A351294",
"A351295",
"A381431",
"A383506",
"A383507",
"A383512",
"A383513",
"A383530",
"A383531",
"A383532",
"A383534",
"A383709",
"A383712"
]
| null | Gus Wiseman, May 15 2025 | 2025-05-16T22:59:23 | oeisdata/seq/A383/A383709.seq | 3596390cc58632a74f66fdccc37af3d7 |
A383710 | Number of integer partitions of n such that it is not possible to choose a family of pairwise disjoint strict integer partitions, one of each part. | [
"0",
"0",
"1",
"1",
"3",
"4",
"6",
"10",
"15",
"22",
"29",
"42",
"59",
"79",
"108",
"140",
"190",
"247",
"324",
"417",
"541"
]
| [
"nonn",
"more"
]
| 7 | 0 | 5 | [
"A044813",
"A047966",
"A048767",
"A048768",
"A089259",
"A098859",
"A116540",
"A130091",
"A217605",
"A239455",
"A242882",
"A317141",
"A318361",
"A351293",
"A351294",
"A351295",
"A381432",
"A381433",
"A381454",
"A382912",
"A382913",
"A383013",
"A383533",
"A383706",
"A383708",
"A383710",
"A383711"
]
| null | Gus Wiseman, May 07 2025 | 2025-05-08T22:57:09 | oeisdata/seq/A383/A383710.seq | 576688f6abce4994bad7ace3becf8b2e |
A383711 | Number of integer partitions of n with no ones such that it is not possible to choose a family of pairwise disjoint strict integer partitions, one of each part. | [
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"1",
"3",
"3",
"4",
"6",
"10",
"11",
"17",
"19",
"30",
"36",
"51",
"61",
"84",
"96",
"133",
"160",
"209",
"253",
"325",
"393",
"488",
"598",
"744"
]
| [
"nonn",
"more"
]
| 6 | 0 | 9 | [
"A044813",
"A047966",
"A048767",
"A048768",
"A089259",
"A098859",
"A116540",
"A130091",
"A217605",
"A239455",
"A242882",
"A317141",
"A318361",
"A351293",
"A351294",
"A351295",
"A381432",
"A381433",
"A381441",
"A381454",
"A382912",
"A382913",
"A383013",
"A383533",
"A383706",
"A383708",
"A383710",
"A383711"
]
| null | Gus Wiseman, May 07 2025 | 2025-05-08T22:55:58 | oeisdata/seq/A383/A383711.seq | e3f0b00093473aedb97364e21c4afaea |
A383712 | Heinz numbers of integer partitions with distinct multiplicities (Wilf) and distinct 0-appended differences. | [
"1",
"2",
"3",
"4",
"5",
"7",
"9",
"11",
"13",
"17",
"19",
"20",
"23",
"25",
"28",
"29",
"31",
"37",
"41",
"43",
"44",
"45",
"47",
"49",
"50",
"52",
"53",
"59",
"61",
"67",
"68",
"71",
"73",
"75",
"76",
"79",
"83",
"89",
"92",
"97",
"98",
"99",
"101",
"103",
"107",
"109",
"113",
"116",
"117",
"121",
"124",
"127",
"131",
"137",
"139",
"148",
"149",
"151",
"153",
"157",
"163",
"164"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A000040",
"A000720",
"A001222",
"A001223",
"A005117",
"A047966",
"A048767",
"A055396",
"A056239",
"A061395",
"A098859",
"A112798",
"A122111",
"A130091",
"A130092",
"A238745",
"A239455",
"A320348",
"A325324",
"A325325",
"A325349",
"A325355",
"A325366",
"A325367",
"A325368",
"A325388",
"A336866",
"A351293",
"A351294",
"A351295",
"A383506",
"A383507",
"A383512",
"A383513",
"A383530",
"A383531",
"A383532",
"A383709",
"A383712"
]
| null | Gus Wiseman, May 15 2025 | 2025-05-16T22:59:12 | oeisdata/seq/A383/A383712.seq | fbe9a692a1d5dd96461396a0535b3d30 |
A383713 | Triangle read by rows: T(n,k) is the number of compositions of n with k parts all in standard order. | [
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"2",
"1",
"0",
"0",
"0",
"1",
"3",
"1",
"0",
"0",
"0",
"1",
"3",
"4",
"1",
"0",
"0",
"0",
"0",
"4",
"6",
"5",
"1",
"0",
"0",
"0",
"0",
"2",
"10",
"10",
"6",
"1",
"0",
"0",
"0",
"0",
"1",
"9",
"20",
"15",
"7",
"1",
"0",
"0",
"0",
"0",
"1",
"7",
"25",
"35",
"21",
"8",
"1",
"0",
"0",
"0",
"0",
"0",
"7",
"26",
"55",
"56",
"28",
"9",
"1",
"0",
"0",
"0",
"0",
"0",
"4",
"29",
"71",
"105",
"84",
"36",
"10",
"1"
]
| [
"nonn",
"easy",
"tabl"
]
| 10 | 0 | 14 | [
"A000110",
"A047998",
"A107429",
"A126347",
"A278984",
"A383253",
"A383713"
]
| null | John Tyler Rascoe, May 06 2025 | 2025-05-07T11:18:39 | oeisdata/seq/A383/A383713.seq | d1c58539c427c1194d10b0e57befaa68 |
A383714 | Integers k such that there exists an integer 0<m<k such that m*sigma(m)^2 + k*sigma(k)^2 = (m+k)^3. | [
"21",
"231",
"284",
"1210",
"2499",
"2924",
"5564",
"6368",
"10856",
"14595",
"18416",
"66992",
"71145",
"76084",
"87633",
"88730"
]
| [
"nonn",
"more",
"changed"
]
| 108 | 1 | 1 | [
"A002046",
"A063990",
"A259180",
"A383239",
"A383483",
"A383484",
"A383714"
]
| null | S. I. Dimitrov, May 14 2025 | 2025-07-10T12:14:32 | oeisdata/seq/A383/A383714.seq | d3f8ca73a377ce309769b77bbc0168fe |
A383715 | Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) = (-1)^floor((k+1)/2) * A099927(n,k). | [
"1",
"1",
"-1",
"1",
"-2",
"-1",
"1",
"-5",
"-5",
"1",
"1",
"-12",
"-30",
"12",
"1",
"1",
"-29",
"-174",
"174",
"29",
"-1",
"1",
"-70",
"-1015",
"2436",
"1015",
"-70",
"-1",
"1",
"-169",
"-5915",
"34307",
"34307",
"-5915",
"-169",
"1",
"1",
"-408",
"-34476",
"482664",
"1166438",
"-482664",
"-34476",
"408",
"1",
"1",
"-985",
"-200940",
"6791772",
"39618670",
"-39618670",
"-6791772",
"200940",
"985",
"-1"
]
| [
"sign",
"tabl"
]
| 21 | 0 | 5 | [
"A055870",
"A099927",
"A383715"
]
| null | Seiichi Manyama, May 07 2025 | 2025-05-07T09:40:44 | oeisdata/seq/A383/A383715.seq | 1d31b7d2eda769709050767dc7e4be41 |
A383717 | Dirichlet g.f.: Product_{p prime} (1 + 1/p^(s-1) + 1/p^(2*s-1)). | [
"1",
"2",
"3",
"2",
"5",
"6",
"7",
"0",
"3",
"10",
"11",
"6",
"13",
"14",
"15",
"0",
"17",
"6",
"19",
"10",
"21",
"22",
"23",
"0",
"5",
"26",
"0",
"14",
"29",
"30",
"31",
"0",
"33",
"34",
"35",
"6",
"37",
"38",
"39",
"0",
"41",
"42",
"43",
"22",
"15",
"46",
"47",
"0",
"7",
"10",
"51",
"26",
"53",
"0",
"55",
"0",
"57",
"58",
"59",
"30",
"61",
"62",
"21",
"0",
"65",
"66",
"67",
"34",
"69",
"70",
"71",
"0",
"73"
]
| [
"nonn",
"mult",
"easy"
]
| 13 | 1 | 2 | [
"A007947",
"A056552",
"A335341",
"A336649",
"A383717"
]
| null | Vaclav Kotesovec, May 07 2025 | 2025-05-07T08:17:40 | oeisdata/seq/A383/A383717.seq | 2a706aab59bb78576a51b8bfeb93331d |
A383718 | a(n) is the multinomial coefficient (length of n in binary) choose (the lengths of runs in n's binary expansion). | [
"1",
"1",
"2",
"1",
"3",
"6",
"3",
"1",
"4",
"12",
"24",
"12",
"6",
"12",
"4",
"1",
"5",
"20",
"60",
"30",
"60",
"120",
"60",
"20",
"10",
"30",
"60",
"30",
"10",
"20",
"5",
"1",
"6",
"30",
"120",
"60",
"180",
"360",
"180",
"60",
"120",
"360",
"720",
"360",
"180",
"360",
"120",
"30",
"15",
"60",
"180",
"90",
"180",
"360",
"180",
"60",
"20",
"60",
"120",
"60",
"15",
"30",
"6",
"1"
]
| [
"nonn",
"base"
]
| 11 | 0 | 3 | [
"A000111",
"A000975",
"A023758",
"A101211",
"A368070",
"A383718"
]
| null | Natalia L. Skirrow, Apr 20 2025 | 2025-06-02T16:49:53 | oeisdata/seq/A383/A383718.seq | aac1e505820a58cc6a0190c3001908a9 |
A383719 | a(n) = Pell(n) * Pell(n-1) * Pell(n-2) * Pell(n-3) * Pell(n-4) / 3480. | [
"1",
"70",
"5915",
"482664",
"39618670",
"3248730940",
"266442347522",
"21851425660680",
"1792084691254935",
"146972777186757522",
"12053560080255418725",
"988538895611708641200",
"81072243052956528402380",
"6648912468496274313591800",
"545291894670184984544154100",
"44720584275276797753993516592"
]
| [
"nonn",
"easy"
]
| 24 | 5 | 2 | [
"A000129",
"A099927",
"A383719"
]
| null | Seiichi Manyama, May 07 2025 | 2025-05-10T11:28:26 | oeisdata/seq/A383/A383719.seq | 7992ca2f9a5990749e16fc492db0009e |
A383720 | a(0)=3, a(1)=5, a(2)=35; a(n) = 5*a(n-1) + 5*a(n-2) - a(n-3) for n > 2. | [
"3",
"5",
"35",
"197",
"1155",
"6725",
"39203",
"228485",
"1331715",
"7761797",
"45239075",
"263672645",
"1536796803",
"8957108165",
"52205852195",
"304278004997",
"1773462177795",
"10336495061765",
"60245508192803",
"351136554095045",
"2046573816377475",
"11928306344169797",
"69523264248641315"
]
| [
"nonn",
"easy"
]
| 22 | 0 | 1 | [
"A000129",
"A002203",
"A047946",
"A084158",
"A383720"
]
| null | Seiichi Manyama, May 07 2025 | 2025-07-03T10:57:28 | oeisdata/seq/A383/A383720.seq | ca1fe4414de534f348ee8b3cb4e5ec3e |
A383721 | a(n) is the number of distinct rectangles with integer area that can be inscribed in a cube with edge length 4*n, as shown in the linked figure "Cube with inscribed rectangle". | [
"1",
"2",
"2",
"2",
"1",
"4",
"1",
"2",
"2",
"3",
"1",
"5",
"1",
"3",
"4",
"2",
"1",
"4",
"1",
"4",
"3",
"2",
"1",
"5",
"1",
"2",
"2",
"4",
"1",
"8",
"1",
"2",
"3",
"2",
"3",
"6",
"1",
"2",
"3",
"5",
"1",
"7",
"1",
"3",
"6",
"2",
"1",
"5",
"1",
"3",
"2",
"3",
"1",
"4",
"3",
"5",
"2",
"2",
"1",
"11",
"1",
"2",
"5",
"2",
"2",
"6",
"1",
"3",
"2",
"7",
"1",
"7",
"1",
"2",
"4",
"2",
"3",
"6",
"1",
"5",
"2",
"2",
"1",
"10",
"2",
"2",
"2"
]
| [
"nonn"
]
| 10 | 1 | 2 | [
"A361795",
"A373710",
"A375473",
"A383721"
]
| null | Felix Huber, May 08 2025 | 2025-05-14T00:00:31 | oeisdata/seq/A383/A383721.seq | 10754eb2e407162574f26765921fadc8 |
A383722 | a(n) = A378762(A382679(n)). | [
"1",
"5",
"3",
"6",
"2",
"4",
"14",
"8",
"12",
"10",
"15",
"9",
"13",
"7",
"11",
"27",
"17",
"25",
"19",
"23",
"21",
"28",
"20",
"26",
"18",
"24",
"16",
"22",
"44",
"30",
"42",
"32",
"40",
"34",
"38",
"36",
"45",
"35",
"43",
"33",
"41",
"31",
"39",
"29",
"37",
"65",
"47",
"63",
"49",
"61",
"51",
"59",
"53",
"57",
"55",
"66",
"54",
"64",
"52",
"62",
"50",
"60",
"48",
"58",
"46",
"56"
]
| [
"nonn",
"tabf"
]
| 8 | 1 | 2 | [
"A000027",
"A000384",
"A016813",
"A376214",
"A378684",
"A379342",
"A379343",
"A380200",
"A380245",
"A380815",
"A380817",
"A381662",
"A381663",
"A381664",
"A381968",
"A382499",
"A382679",
"A382680",
"A383722"
]
| null | Boris Putievskiy, May 07 2025 | 2025-05-11T21:57:11 | oeisdata/seq/A383/A383722.seq | 488376bb289957b7e6c77974daec46b8 |
A383723 | a(n) = A378762(A376214(n)). | [
"1",
"2",
"3",
"6",
"5",
"4",
"9",
"8",
"7",
"10",
"15",
"12",
"13",
"14",
"11",
"20",
"17",
"18",
"19",
"16",
"21",
"28",
"23",
"26",
"25",
"24",
"27",
"22",
"35",
"30",
"33",
"32",
"31",
"34",
"29",
"36",
"45",
"38",
"43",
"40",
"41",
"42",
"39",
"44",
"37",
"54",
"47",
"52",
"49",
"50",
"51",
"48",
"53",
"46",
"55",
"66",
"57",
"64",
"59",
"62",
"61",
"60",
"63",
"58",
"65",
"56"
]
| [
"nonn",
"tabf"
]
| 8 | 1 | 2 | [
"A000027",
"A000384",
"A016813",
"A376214",
"A378684",
"A379342",
"A379343",
"A380200",
"A380245",
"A380815",
"A380817",
"A381662",
"A381663",
"A381664",
"A381968",
"A382499",
"A382679",
"A382680",
"A383723"
]
| null | Boris Putievskiy, May 07 2025 | 2025-05-11T21:57:03 | oeisdata/seq/A383/A383723.seq | 33a8afdc433c62bb90ba29aa1e0a9e66 |
A383724 | a(n) = A378762(A382680(n)). | [
"1",
"5",
"3",
"6",
"2",
"4",
"12",
"8",
"14",
"10",
"15",
"7",
"13",
"9",
"11",
"23",
"17",
"25",
"19",
"27",
"21",
"28",
"16",
"26",
"18",
"24",
"20",
"22",
"38",
"30",
"40",
"32",
"42",
"34",
"44",
"36",
"45",
"29",
"43",
"31",
"41",
"33",
"39",
"35",
"37",
"57",
"47",
"59",
"49",
"61",
"51",
"63",
"53",
"65",
"55",
"66",
"46",
"64",
"48",
"62",
"50",
"60",
"52",
"58",
"54",
"56"
]
| [
"nonn",
"tabf"
]
| 8 | 1 | 2 | [
"A000027",
"A000384",
"A016813",
"A376214",
"A378684",
"A379342",
"A379343",
"A380200",
"A380245",
"A380815",
"A380817",
"A381662",
"A381663",
"A381664",
"A381968",
"A382499",
"A382679",
"A382680",
"A383724"
]
| null | Boris Putievskiy, May 07 2025 | 2025-05-11T21:49:18 | oeisdata/seq/A383/A383724.seq | 4cf22b9eb289d3bd3949893edd029218 |
A383725 | a(n) is the least number k such that omega(k) = n and the largest prime factor of k equals the sum of its remaining prime factors, where omega(k) = A001221(k). | [
"30",
"3135",
"3570",
"844305",
"1231230",
"463798335",
"1089218130",
"410825520105",
"905980145070",
"818186519485335",
"1461885412557570",
"2023416377587710105",
"3676255934199278430",
"6175645531427513476335",
"14590719651042312667890",
"29263451149172039260325865",
"67794672364404337821058590"
]
| [
"nonn"
]
| 21 | 3 | 1 | [
"A001221",
"A002110",
"A068873",
"A102330",
"A365795",
"A382469",
"A383725",
"A383726",
"A383728",
"A383729"
]
| null | Paolo Xausa, May 07 2025 | 2025-05-11T11:56:17 | oeisdata/seq/A383/A383725.seq | cb8e16c951e947408719b86db2ed501c |
A383726 | Square array read by ascending antidiagonals, where row n lists numbers m such that omega(m) = n and the largest prime factor of m equals the sum of its remaining distinct prime factors, where omega(m) = A001221(m). | [
"30",
"3135",
"60",
"3570",
"6279",
"70",
"844305",
"7140",
"8855",
"90",
"1231230",
"1218945",
"8970",
"9405",
"120"
]
| [
"nonn",
"tabl",
"hard",
"more"
]
| 11 | 3 | 1 | [
"A001221",
"A365795",
"A382469",
"A383725",
"A383726",
"A383727",
"A383728",
"A383729"
]
| null | Paolo Xausa, May 07 2025 | 2025-05-11T11:56:35 | oeisdata/seq/A383/A383726.seq | eb40dafbbab5d923f852dfff8c289c06 |
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