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timestamp[us]date 1999-12-11 03:00:00
2025-07-14 02:38:35
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A381715 | Number of multisets that can be obtained by taking the sum of each block of a multiset partition of the prime indices of n into distinct constant blocks. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1"
]
| [
"nonn"
]
| 10 | 1 | 8 | [
"A000688",
"A000720",
"A001055",
"A001222",
"A002846",
"A003963",
"A005117",
"A006171",
"A045778",
"A046099",
"A050326",
"A050342",
"A050361",
"A055396",
"A056239",
"A061395",
"A112798",
"A213242",
"A213385",
"A279784",
"A293511",
"A295935",
"A299202",
"A300383",
"A300385",
"A317141",
"A317142",
"A355731",
"A362421",
"A381441",
"A381452",
"A381453",
"A381455",
"A381635",
"A381636",
"A381715",
"A381716",
"A381870"
]
| null | Gus Wiseman, Mar 10 2025 | 2025-03-11T08:24:18 | oeisdata/seq/A381/A381715.seq | ca347a84863817e29852cf7f11b42304 |
A381716 | Number of multisets that can be obtained by taking the sum of each block of a multiset partition of the prime indices of n into constant blocks with distinct sums. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"0",
"1",
"1",
"0",
"4",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"0",
"1",
"1",
"1"
]
| [
"nonn"
]
| 5 | 1 | 8 | [
"A000688",
"A000720",
"A001055",
"A001222",
"A002846",
"A005117",
"A006171",
"A050361",
"A055396",
"A056239",
"A061395",
"A112798",
"A213242",
"A265947",
"A279784",
"A293511",
"A295935",
"A299202",
"A300383",
"A300385",
"A317141",
"A362421",
"A381453",
"A381455",
"A381633",
"A381634",
"A381635",
"A381636",
"A381715",
"A381716"
]
| null | Gus Wiseman, Mar 10 2025 | 2025-03-11T08:24:23 | oeisdata/seq/A381/A381716.seq | fcd897bbb7ee12f221fd9b00ce907596 |
A381717 | Number of integer partitions of n that cannot be partitioned into constant multisets with distinct block-sums. | [
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"3",
"2",
"3",
"6",
"7",
"10",
"15",
"15",
"28",
"37",
"47",
"64",
"71",
"97",
"139",
"173",
"215",
"273",
"361",
"439",
"551",
"691",
"853",
"1078",
"1325",
"1623",
"2046",
"2458",
"2998",
"3697",
"4527",
"5472",
"6590",
"7988",
"9590",
"11598",
"13933",
"16560",
"19976",
"23822",
"28420",
"33797",
"40088",
"47476",
"56369",
"66678"
]
| [
"nonn"
]
| 15 | 0 | 9 | [
"A000009",
"A000041",
"A000688",
"A001055",
"A002846",
"A045778",
"A047966",
"A050361",
"A130091",
"A213242",
"A213427",
"A265947",
"A279786",
"A300383",
"A317141",
"A317142",
"A326535",
"A353864",
"A355743",
"A381453",
"A381455",
"A381633",
"A381635",
"A381636",
"A381716",
"A381717",
"A381806",
"A381990",
"A381991",
"A381992",
"A381993",
"A382079",
"A382876"
]
| null | Gus Wiseman, Mar 16 2025 | 2025-04-27T09:09:10 | oeisdata/seq/A381/A381717.seq | ca6c8b6588a5a629f8df73b7fd91044e |
A381718 | Number of normal multiset partitions of weight n into sets with distinct sums. | [
"1",
"1",
"2",
"6",
"23",
"106",
"549",
"3184",
"20353",
"141615",
"1063399",
"8554800",
"73281988",
"665141182",
"6369920854",
"64133095134",
"676690490875",
"7462023572238",
"85786458777923",
"1025956348473929",
"12739037494941490"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A000110",
"A000670",
"A001055",
"A007716",
"A019536",
"A034691",
"A035310",
"A045778",
"A050320",
"A050326",
"A055932",
"A089259",
"A116539",
"A116540",
"A255903",
"A255906",
"A270995",
"A275780",
"A279785",
"A296119",
"A317532",
"A317583",
"A318360",
"A321469",
"A326517",
"A326518",
"A326519",
"A333217",
"A381633",
"A381635",
"A381718",
"A382203",
"A382204",
"A382214",
"A382216",
"A382428",
"A382429"
]
| null | Gus Wiseman, Mar 26 2025 | 2025-04-05T18:13:56 | oeisdata/seq/A381/A381718.seq | 68e3f3937ec0bfaf45fd212325bf2fcb |
A381719 | Numbers whose prime indices cannot be partitioned into sets with a common sum. | [
"12",
"18",
"20",
"24",
"28",
"40",
"44",
"45",
"48",
"50",
"52",
"54",
"56",
"60",
"63",
"68",
"72",
"75",
"76",
"80",
"84",
"88",
"90",
"92",
"96",
"98",
"99",
"104",
"108",
"112",
"116",
"117",
"120",
"124",
"126",
"132",
"135",
"136",
"140",
"144",
"147",
"148",
"152",
"153",
"156",
"160",
"162",
"164",
"168",
"171",
"172",
"175",
"176",
"184",
"188",
"189",
"192"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A000009",
"A000041",
"A000720",
"A000961",
"A001055",
"A001222",
"A045778",
"A050320",
"A050326",
"A055396",
"A056239",
"A061395",
"A089259",
"A112798",
"A116540",
"A270995",
"A279788",
"A293243",
"A293511",
"A296119",
"A300383",
"A302478",
"A317141",
"A318360",
"A321455",
"A326518",
"A326534",
"A358914",
"A381078",
"A381454",
"A381633",
"A381634",
"A381635",
"A381717",
"A381719",
"A381806",
"A381871",
"A381990",
"A381992",
"A381993",
"A381994",
"A381995",
"A382080",
"A382429",
"A383308"
]
| null | Gus Wiseman, Apr 22 2025 | 2025-04-25T08:45:42 | oeisdata/seq/A381/A381719.seq | d243c661a65efc4097f05c6015b50473 |
A381720 | Integers whose Hamming weight is a cube. | [
"0",
"1",
"2",
"4",
"8",
"16",
"32",
"64",
"128",
"255",
"256",
"383",
"447",
"479",
"495",
"503",
"507",
"509",
"510",
"512",
"639",
"703",
"735",
"751",
"759",
"763",
"765",
"766",
"831",
"863",
"879",
"887",
"891",
"893",
"894",
"927",
"943",
"951",
"955",
"957",
"958",
"975",
"983",
"987",
"989",
"990",
"999",
"1003",
"1005",
"1006",
"1011",
"1013",
"1014"
]
| [
"nonn",
"base"
]
| 40 | 1 | 3 | [
"A000079",
"A000120",
"A000578",
"A023690",
"A084561",
"A344602",
"A381720"
]
| null | Ctibor O. Zizka, Mar 05 2025 | 2025-05-19T16:32:40 | oeisdata/seq/A381/A381720.seq | 9fdb903b5feadbcfeb8af05cc168cd05 |
A381721 | Sum of the legs of the unique primitive Pythagorean triple whose inradius is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers. | [
"17",
"7",
"31",
"49",
"127",
"287",
"721",
"1799",
"4607",
"11857",
"30751",
"79999",
"208657",
"544967",
"1424671",
"3726449",
"9750527",
"25518367",
"66793681",
"174844999",
"457712767",
"1198247057",
"3136953631",
"8212492799",
"21500328977",
"56288177287",
"147363690271",
"385802064049",
"1010041159807",
"2644319243807",
"6922913058001",
"18124414244999",
"47450320478207"
]
| [
"nonn",
"easy"
]
| 16 | 0 | 1 | [
"A000032",
"A380821",
"A380823",
"A380824",
"A381721"
]
| null | Miguel-Ángel Pérez García-Ortega, Mar 05 2025 | 2025-06-16T09:44:12 | oeisdata/seq/A381/A381721.seq | 6791260facb101a832096f9da833f786 |
A381722 | Number of minimum connected dominating sets in the n-triangular honeycomb queen graph. | [
"1",
"3",
"12",
"6",
"70",
"3",
"116",
"3",
"135",
"3",
"177",
"3"
]
| [
"nonn",
"more"
]
| 13 | 1 | 2 | null | null | Eric W. Weisstein, Mar 05 2025 | 2025-03-30T09:52:16 | oeisdata/seq/A381/A381722.seq | a3e8b49e3b344530cc33c2ebdcd230d2 |
A381723 | a(n) = pos(M(n)), where M(n) is the n X n matrix with numbers 1, 2, ..., n^2 in order across rows, and pos(M(n)) is the positive part of the determinant of M(n); see A380661. | [
"1",
"4",
"225",
"27728",
"7240350",
"3439197360",
"2686774125000",
"3213645578293248",
"5578750547986764960",
"13484491722080225280000",
"43904082301794970311672000",
"187409206411313292409598115840",
"1025421491750171253824589270768000",
"7056011383804251291488039375527526400"
]
| [
"nonn"
]
| 17 | 1 | 2 | [
"A232773",
"A380661",
"A380662",
"A381723"
]
| null | Clark Kimberling, Mar 09 2025 | 2025-03-26T08:28:14 | oeisdata/seq/A381/A381723.seq | 756f6a2c86f411912e06a3274a9c690c |
A381724 | a(n) = pos(M(n)), where M(n) is the n X n matrix with every term = 4, and pos(M(n)) is the positive part of the determinant of M(n); see A380661. | [
"4",
"16",
"192",
"3072",
"61440",
"1474560",
"41287680",
"1321205760",
"47563407360",
"1902536294400",
"83711596953600",
"4018156653772800",
"208944145996185600",
"11700872175786393600",
"702052330547183616000",
"44931349155019751424000",
"3055331742541343096832000"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A001710",
"A002966",
"A032108",
"A051711",
"A380661",
"A381724"
]
| null | Clark Kimberling, Mar 05 2025 | 2025-03-11T13:20:54 | oeisdata/seq/A381/A381724.seq | bbb617547bb8e7a9938b2327ea22125c |
A381725 | Numbers k such that 5^k - 4^k is a semiprime. | [
"2",
"5",
"7",
"11",
"13",
"19",
"31",
"41",
"79",
"83",
"113",
"157",
"173",
"233",
"281",
"317",
"359",
"373"
]
| [
"nonn",
"hard",
"more"
]
| 10 | 1 | 1 | [
"A001222",
"A001358",
"A005060",
"A059802",
"A082869",
"A381725"
]
| null | Zak Seidov and Robert Israel, Mar 05 2025 | 2025-03-06T01:53:32 | oeisdata/seq/A381/A381725.seq | baff0d3fcee17d20d33652f3dd6c6e76 |
A381726 | Number of minimum connected dominating sets in the n X n black bishop graph. | [
"1",
"2",
"1",
"1",
"2",
"13",
"83",
"513",
"4052",
"41197",
"462069",
"5597201",
"76094134",
"1153902701",
"18981358311",
"336018968449",
"6413439874792",
"131386321421901",
"2867812411156521",
"66426533670738769",
"1629082910078009770",
"42175861619149917325",
"1148999152027728530363",
"32856688248674995989889"
]
| [
"nonn"
]
| 19 | 1 | 2 | [
"A072590",
"A132609",
"A289145",
"A303141",
"A323500",
"A381726",
"A381727"
]
| null | Eric W. Weisstein, Mar 05 2025 | 2025-03-22T10:24:35 | oeisdata/seq/A381/A381726.seq | b80f06638c02893b794465367c09bdbf |
A381727 | Number of minimum connected dominating sets in the n X n white bishop graph. | [
"2",
"4",
"1",
"4",
"13",
"64",
"513",
"4480",
"41197",
"444416",
"5597201",
"77253632",
"1153902701",
"18870222848",
"336018968449",
"6428081455104",
"131386321421901",
"2865273888571392",
"66426533670738769",
"1629643279560867840",
"42175861619149917325",
"1148845693539400548352",
"32856688248674995989889"
]
| [
"nonn"
]
| 16 | 2 | 1 | [
"A072590",
"A132609",
"A289169",
"A303144",
"A323501",
"A381726",
"A381727"
]
| null | Eric W. Weisstein, Mar 05 2025 | 2025-03-22T11:17:08 | oeisdata/seq/A381/A381727.seq | eb36783201de99f2e189d8ef96990ac1 |
A381728 | Number of minimum dominating sets in the n-Mycielski graph. | [
"1",
"2",
"5",
"60",
"1560",
"84240"
]
| [
"nonn",
"more"
]
| 4 | 1 | 2 | null | null | Eric W. Weisstein, Mar 05 2025 | 2025-03-05T13:43:00 | oeisdata/seq/A381/A381728.seq | d31a7b01cfbc588611aac48f1589a29b |
A381729 | Number of minimum connected dominating sets in the n-Lucas cube graph. | [
"1",
"1",
"1",
"4",
"5",
"90",
"210",
"272",
"72"
]
| [
"nonn",
"more",
"changed"
]
| 12 | 1 | 4 | null | null | Eric W. Weisstein, Mar 05 2025 | 2025-07-03T09:18:41 | oeisdata/seq/A381/A381729.seq | e0701d88175edb6ddebb918f998e7700 |
A381730 | Number of minimum connected dominating sets in the n X n grid graph. | [
"1",
"4",
"2",
"16",
"126",
"24",
"800",
"16288",
"16",
"87216",
"3554000",
"16",
"13400336",
"882342944",
"16",
"2376303680"
]
| [
"nonn",
"more"
]
| 21 | 1 | 2 | [
"A287690",
"A347632",
"A369692",
"A381474",
"A381730"
]
| null | Eric W. Weisstein, Mar 05 2025 | 2025-03-21T14:39:32 | oeisdata/seq/A381/A381730.seq | bdbe4481be2bf82f6f207e314cf3d64c |
A381731 | a(n) is the least number k with squarefree neighbors such that the number of non-unitary divisors of k (A048105) is equal to n, or 0 if no such k exists. | [
"2",
"4",
"12",
"16",
"32",
"36",
"112",
"256",
"72",
"0",
"180",
"144",
"216",
"16384",
"768",
"65536",
"432",
"1600",
"3072",
"900",
"864",
"1296",
"720",
"12544",
"1080",
"67108864",
"2592",
"268435456",
"1440",
"9216",
"196608",
"5184",
"2160",
"17179869184",
"2880",
"36864",
"10368",
"3600",
"6300"
]
| [
"nonn"
]
| 28 | 0 | 1 | [
"A048105",
"A280892",
"A309181",
"A381731"
]
| null | Juri-Stepan Gerasimov, Mar 05 2025 | 2025-03-25T22:34:41 | oeisdata/seq/A381/A381731.seq | cc526df507a75d09f6651c7ba3a687f8 |
A381732 | Proceeding from left to right, between any two consecutive digits (d_i, d_i+1) of an integer k, write down apart the lacking consecutive digits, in increasing order if d_i <d_i+1 or decreasing order if d_i>d_i+1. If abs(d_i - d_i+1) = 0 or 1 no digit is added. Sequence lists integers k that divide such resulting numbers. | [
"27",
"737",
"909",
"1845",
"1912",
"7078",
"27412",
"90009",
"870129",
"990099",
"6852899",
"9090909",
"17388261",
"70168376",
"70787078",
"96096078",
"96707298",
"162533711",
"358006673",
"737737737",
"1050889491",
"2238028254",
"3281718034",
"4249370147",
"9009009009",
"11819327599",
"12178217823",
"13851266943",
"18768863945"
]
| [
"nonn",
"base"
]
| 23 | 1 | 1 | null | null | Paolo P. Lava, Mar 05 2025 | 2025-03-29T19:08:42 | oeisdata/seq/A381/A381732.seq | a69ec372ed838102e4b0378e053a5c4c |
A381733 | Number of divisors d of n such that 2^omega(n + d) = tau(n + d), where omega = A001221 and tau = A000005. | [
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"3",
"2",
"2",
"1",
"1",
"1",
"2",
"1",
"3",
"2",
"2",
"1",
"2",
"2",
"1",
"1",
"4",
"2",
"3",
"1",
"2",
"2",
"2",
"2",
"4",
"2",
"2",
"2",
"2",
"2",
"1",
"1",
"3",
"1",
"2",
"1",
"1",
"0",
"2",
"1",
"3",
"1",
"2",
"2",
"3",
"2",
"2",
"1",
"5",
"2",
"1",
"2",
"2",
"4",
"3",
"1",
"4",
"2",
"3",
"1",
"3",
"2",
"1",
"1",
"4",
"2",
"2",
"1",
"2",
"1",
"2",
"1",
"5",
"3",
"2",
"1",
"2",
"1",
"4",
"1",
"4",
"2",
"2",
"2",
"2",
"1",
"1",
"2",
"4"
]
| [
"nonn"
]
| 9 | 1 | 4 | [
"A000005",
"A001221",
"A005117",
"A381136",
"A381138",
"A381733"
]
| null | Juri-Stepan Gerasimov, Mar 05 2025 | 2025-03-15T04:33:10 | oeisdata/seq/A381/A381733.seq | 2069d05ade3b2a3cd67e4258466b23c0 |
A381734 | Population of elementary triangular automaton rule 190 at generation n, starting from a lone 1 cell at generation 0. | [
"1",
"4",
"10",
"19",
"28",
"37",
"58",
"73",
"88",
"115",
"136",
"163",
"178",
"247",
"280",
"307",
"334",
"391",
"400",
"463",
"526",
"595",
"622",
"679",
"754",
"811",
"862",
"925",
"1036",
"1057",
"1168",
"1249",
"1318",
"1321",
"1468",
"1531",
"1618",
"1723",
"1840",
"1939",
"2032",
"2155",
"2230",
"2323",
"2572",
"2617",
"2722",
"2785",
"2926",
"2935"
]
| [
"nonn"
]
| 15 | 0 | 2 | [
"A372581",
"A380012",
"A380670",
"A381734",
"A381735"
]
| null | Paul Cousin, Mar 05 2025 | 2025-05-21T01:27:30 | oeisdata/seq/A381/A381734.seq | c1379fa88f35eae6682aa7f599d48372 |
A381735 | Third center column of elementary triangular automaton rule 190, starting from a lone 1 cell. | [
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1"
]
| [
"nonn"
]
| 14 | 0 | null | [
"A380173",
"A380668",
"A381734",
"A381735"
]
| null | Paul Cousin, Mar 05 2025 | 2025-05-21T01:27:22 | oeisdata/seq/A381/A381735.seq | 5d5f8ad82633bc76b28e75bd753b6179 |
A381736 | Integers k = p*q*r, where p < q < r are distinct primes and p*q > r. | [
"30",
"70",
"105",
"154",
"165",
"182",
"195",
"231",
"273",
"286",
"357",
"374",
"385",
"399",
"418",
"429",
"442",
"455",
"494",
"561",
"595",
"598",
"627",
"646",
"663",
"665",
"715",
"741",
"759",
"782",
"805",
"874",
"897",
"935",
"957",
"969",
"986",
"1001",
"1015",
"1023",
"1045",
"1054",
"1085",
"1102",
"1105",
"1131",
"1173",
"1178",
"1209"
]
| [
"nonn"
]
| 45 | 1 | 1 | [
"A007304",
"A164596",
"A381736",
"A382022"
]
| null | Matthew Goers, Mar 05 2025 | 2025-04-22T06:32:24 | oeisdata/seq/A381/A381736.seq | 7350543e108ec9cc4eab5da81eb366cf |
A381737 | Orders k of Hermite polynomials whose maximal coefficient in absolute value appears twice. | [
"8",
"13",
"34",
"43",
"76",
"89",
"134",
"151",
"208",
"229",
"298",
"323",
"404",
"433",
"526",
"559",
"664",
"701",
"818",
"859",
"988",
"1033",
"1174",
"1223",
"1376",
"1429",
"1594",
"1651",
"1828",
"1889",
"2078",
"2143",
"2344",
"2413",
"2626",
"2699",
"2924",
"3001",
"3238",
"3319",
"3568",
"3653",
"3914",
"4003",
"4276",
"4369",
"4654",
"4751",
"5048"
]
| [
"nonn"
]
| 28 | 1 | 1 | [
"A060821",
"A277281",
"A381524",
"A381737"
]
| null | Mike Sheppard, Mar 05 2025 | 2025-03-16T18:11:54 | oeisdata/seq/A381/A381737.seq | c94c1a0e223930009dd5836c5be14f7f |
A381738 | Numbers k such that k^2 is abundant. | [
"6",
"10",
"12",
"14",
"18",
"20",
"24",
"28",
"30",
"36",
"40",
"42",
"44",
"48",
"50",
"52",
"54",
"56",
"60",
"66",
"68",
"70",
"72",
"76",
"78",
"80",
"84",
"88",
"90",
"92",
"96",
"98",
"100",
"102",
"104",
"105",
"108",
"110",
"112",
"114",
"116",
"120",
"124",
"126",
"130",
"132",
"136",
"138",
"140",
"144",
"150",
"152",
"154",
"156",
"160",
"162",
"168",
"170",
"174"
]
| [
"nonn",
"easy"
]
| 12 | 1 | 1 | [
"A005101",
"A063734",
"A174830",
"A334166",
"A363171",
"A381738",
"A381739",
"A381740",
"A381741",
"A381742"
]
| null | Amiram Eldar, Mar 05 2025 | 2025-03-06T01:43:56 | oeisdata/seq/A381/A381738.seq | 50fddf5170ca76a44d921768ac95ebce |
A381739 | Number k such that k^2 is abundant, and d^2 is nonabundant for any proper divisor d of k. | [
"6",
"10",
"14",
"44",
"52",
"68",
"76",
"92",
"105",
"116",
"124",
"286",
"296",
"328",
"344",
"374",
"376",
"418",
"424",
"442",
"472",
"488",
"495",
"506",
"536",
"568",
"584",
"585",
"632",
"664",
"712",
"776",
"808",
"824",
"856",
"872",
"904",
"1016",
"2096",
"2145",
"2192",
"2224",
"2384",
"2416",
"2512",
"2608",
"2672",
"2768",
"2805",
"2864",
"2896",
"3056"
]
| [
"nonn",
"easy"
]
| 9 | 1 | 1 | [
"A005101",
"A263837",
"A381738",
"A381739",
"A381741"
]
| null | Amiram Eldar, Mar 05 2025 | 2025-03-06T01:45:38 | oeisdata/seq/A381/A381739.seq | e7abec0aab31b7746af1474e64597418 |
A381740 | Squarefree numbers k such that k^2 is abundant. | [
"6",
"10",
"14",
"30",
"42",
"66",
"70",
"78",
"102",
"105",
"110",
"114",
"130",
"138",
"154",
"170",
"174",
"182",
"186",
"190",
"210",
"222",
"230",
"238",
"246",
"258",
"266",
"282",
"286",
"290",
"310",
"318",
"322",
"330",
"354",
"366",
"370",
"374",
"390",
"402",
"406",
"410",
"418",
"426",
"430",
"434",
"438",
"442",
"462",
"470",
"474",
"498",
"506",
"510"
]
| [
"nonn",
"easy"
]
| 10 | 1 | 1 | [
"A005117",
"A013661",
"A087248",
"A381738",
"A381740",
"A381741"
]
| null | Amiram Eldar, Mar 05 2025 | 2025-03-06T01:45:17 | oeisdata/seq/A381/A381740.seq | 9fd649b94742cd760eab607760375eab |
A381741 | Squarefree numbers k such that k^2 is abundant, and d^2 is nonabundant for any proper divisor d of k. | [
"6",
"10",
"14",
"105",
"286",
"374",
"418",
"442",
"506",
"2145",
"2805",
"3135",
"3315",
"3705",
"3795",
"4485",
"4785",
"4845",
"5115",
"5655",
"6045",
"6105",
"6765",
"7095",
"7755",
"8745",
"9735",
"10065",
"11362",
"14326",
"14858",
"15314",
"17342",
"18278",
"18538",
"18734",
"19778",
"20026",
"20254",
"21242",
"22126",
"22678",
"23218"
]
| [
"nonn",
"easy"
]
| 9 | 1 | 1 | [
"A005101",
"A005117",
"A263837",
"A381738",
"A381739",
"A381740",
"A381741"
]
| null | Amiram Eldar, Mar 06 2025 | 2025-03-06T01:44:40 | oeisdata/seq/A381/A381741.seq | c4fa663e07188b9bb39f0d9fd912633c |
A381742 | Numbers k such that k^2 is abundant but d*k is nonabundant for any proper divisor d of k. | [
"14",
"124",
"585",
"1016",
"16748",
"32085",
"33892",
"37882",
"39962",
"41925",
"46665",
"121605",
"134589",
"181305",
"212175",
"388455",
"495465",
"522488",
"524224",
"544065",
"839865",
"1061565",
"1152921",
"1165515",
"1243275",
"1247103",
"1335411",
"1676829",
"1943638",
"2151075",
"2290869",
"2478075",
"2625514",
"2673998"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A005101",
"A091191",
"A174265",
"A263837",
"A341358",
"A379949",
"A379950",
"A381738",
"A381742"
]
| null | Amiram Eldar, Mar 06 2025 | 2025-03-06T01:44:06 | oeisdata/seq/A381/A381742.seq | d95a5722de98dfbe47eba01a06364f7e |
A381743 | The number of divisors d of n such that d*n is abundant. | [
"0",
"0",
"0",
"0",
"0",
"3",
"0",
"0",
"0",
"2",
"0",
"6",
"0",
"1",
"0",
"0",
"0",
"6",
"0",
"6",
"0",
"0",
"0",
"8",
"0",
"0",
"0",
"5",
"0",
"8",
"0",
"0",
"0",
"0",
"0",
"9",
"0",
"0",
"0",
"8",
"0",
"8",
"0",
"4",
"0",
"0",
"0",
"10",
"0",
"3",
"0",
"4",
"0",
"8",
"0",
"8",
"0",
"0",
"0",
"12",
"0",
"0",
"0",
"0",
"0",
"8",
"0",
"2",
"0",
"8",
"0",
"12",
"0",
"0",
"0",
"2",
"0",
"8",
"0",
"10",
"0",
"0",
"0",
"12",
"0",
"0"
]
| [
"nonn",
"easy"
]
| 10 | 1 | 6 | [
"A000005",
"A000396",
"A002182",
"A005101",
"A341358",
"A381738",
"A381742",
"A381743"
]
| null | Amiram Eldar, Mar 06 2025 | 2025-03-06T01:54:44 | oeisdata/seq/A381/A381743.seq | 94900797ec47b33d421ad583b728fb04 |
A381744 | Expansion of exp( Sum_{k>=1} binomial(6*k-1,2*k) * x^k/k ). | [
"1",
"10",
"215",
"5942",
"186111",
"6283192",
"222992692",
"8201608382",
"309834609743",
"11950890428170",
"468707758663887",
"18634632264615272",
"749325132218313540",
"30422303269317412048",
"1245346665979469486376",
"51343805279989437688334",
"2130090659402456357279919",
"88858984785475871013971710"
]
| [
"nonn",
"easy"
]
| 19 | 0 | 2 | [
"A006013",
"A079489",
"A182960",
"A381744",
"A381745",
"A381746"
]
| null | Seiichi Manyama, Mar 05 2025 | 2025-03-06T08:15:55 | oeisdata/seq/A381/A381744.seq | f62666fe7e1aa7b1e2be44e19fd31d54 |
A381745 | Expansion of exp( Sum_{k>=1} binomial(8*k-1,2*k) * x^k/k ). | [
"1",
"21",
"903",
"49525",
"3070308",
"204928371",
"14369906538",
"1043861319189",
"77866470852108",
"5929621690613108",
"459076176165983247",
"36026517938705145267",
"2859318461620989381900",
"229114879928544260792946",
"18509862380800289696106372",
"1506048000721264678984095445",
"123303480420582227597300406588"
]
| [
"nonn",
"easy"
]
| 20 | 0 | 2 | [
"A006632",
"A079489",
"A381744",
"A381745",
"A381746",
"A381751"
]
| null | Seiichi Manyama, Mar 05 2025 | 2025-03-06T08:44:05 | oeisdata/seq/A381/A381745.seq | 73705129c760f9d34482b1da43d5b87c |
A381746 | Expansion of exp( Sum_{k>=1} binomial(10*k-1,2*k) * x^k/k ). | [
"1",
"36",
"2586",
"235884",
"24284907",
"2689924444",
"312907382800",
"37699275223260",
"4663450108073401",
"588854988193808392",
"75589352418472567340",
"9834912295258236849604",
"1294095251234713917535805",
"171909332777340128148714400",
"23024035140764003881788203616"
]
| [
"nonn",
"easy"
]
| 19 | 0 | 2 | [
"A079489",
"A118971",
"A381744",
"A381745",
"A381746",
"A381752"
]
| null | Seiichi Manyama, Mar 05 2025 | 2025-03-06T08:44:01 | oeisdata/seq/A381/A381746.seq | b6f8c641a0eae5b21fd30b11c38e2f42 |
A381747 | a(n) is the number of solutions to tau(x) + tau(n-x) = tau(n) where 1 <= x <= floor(n/2). | [
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"3",
"0",
"1",
"0",
"2",
"1",
"2",
"0",
"2",
"0",
"1",
"1",
"3",
"0",
"1",
"0",
"4",
"0",
"3",
"0",
"3",
"0",
"3",
"1",
"4",
"0",
"1",
"0",
"2",
"1",
"2",
"0",
"3",
"0",
"5",
"6",
"4",
"0",
"0",
"0",
"5",
"0",
"5",
"0",
"5",
"1",
"4",
"0",
"4",
"0",
"2",
"0",
"3",
"6",
"4",
"0",
"5",
"0",
"8",
"1",
"5",
"0",
"3",
"0",
"5",
"8",
"8",
"0",
"5",
"0",
"3",
"0",
"5",
"0",
"3",
"1",
"5",
"0",
"6"
]
| [
"nonn",
"easy"
]
| 17 | 1 | 10 | [
"A000005",
"A000430",
"A211225",
"A381747",
"A382074"
]
| null | Felix Huber, Mar 30 2025 | 2025-04-26T08:27:25 | oeisdata/seq/A381/A381747.seq | 1f793a77f257c0b10bbfb462c3cd5091 |
A381748 | a(n) is the number of primes (counted with multiplicity) in row n of A051599. | [
"1",
"2",
"2",
"4",
"2",
"4",
"2",
"6",
"2",
"4",
"4",
"4",
"4",
"4",
"2",
"2",
"2",
"2",
"2",
"6",
"2",
"4",
"2",
"2",
"2",
"4",
"4",
"6",
"2",
"8",
"6",
"6",
"2",
"2",
"2",
"2",
"4",
"4",
"2",
"2",
"2",
"2",
"4",
"2",
"2",
"4",
"2",
"6",
"2",
"4",
"4",
"8",
"2",
"4",
"4",
"2",
"2",
"4",
"4",
"2",
"2",
"2",
"2",
"10",
"2",
"2",
"4",
"4",
"2",
"4",
"2",
"2",
"2",
"2",
"2",
"2",
"4",
"2",
"4"
]
| [
"nonn"
]
| 18 | 0 | 2 | [
"A051599",
"A381748"
]
| null | Vladimir Igorevich Lukyanchikov, Mar 06 2025 | 2025-03-16T21:37:08 | oeisdata/seq/A381/A381748.seq | 4d92c2ee62dd782718dc872282b632a9 |
A381749 | Triangle read by rows: T(n,k), n >= k, is the maximum number of kings on a n X k chessboard so that no king attacks more than one other king. | [
"1",
"2",
"2",
"2",
"4",
"4",
"3",
"4",
"6",
"8",
"4",
"6",
"8",
"10",
"12",
"4",
"6",
"8",
"11",
"14",
"16",
"5",
"8",
"10",
"13",
"16",
"18",
"21",
"6",
"8",
"12",
"14",
"18",
"20",
"24",
"26",
"6",
"10",
"12",
"16",
"20",
"22",
"26",
"30",
"33",
"7",
"10",
"14",
"18",
"22",
"25",
"29",
"32",
"36",
"40",
"8",
"12",
"16",
"20",
"24",
"28",
"32",
"36",
"40",
"44",
"48",
"8",
"12",
"16",
"21",
"26"
]
| [
"nonn",
"tabl",
"easy"
]
| 21 | 1 | 2 | [
"A260090",
"A381749"
]
| null | Yifan Xie, Mar 06 2025 | 2025-03-22T17:16:27 | oeisdata/seq/A381/A381749.seq | 4c0bd75886e4732a79f87610ed30369d |
A381750 | Nonprime-powers k such that, for any prime p dividing k and m = 1+floor(log k/log p), rad(p^m (mod k)) divides k, where rad = A007947. | [
"6",
"12",
"14",
"24",
"39",
"56",
"62",
"112",
"120",
"155",
"254",
"992",
"1984",
"3279",
"5219",
"16256",
"16382",
"19607",
"32512",
"70643",
"97655",
"208919",
"262142",
"363023",
"402233",
"712979",
"1040603",
"1048574",
"1508597",
"2265383",
"2391483",
"4685519",
"5207819",
"6728903",
"21243689",
"25239899",
"56328959",
"61035155",
"67100672"
]
| [
"nonn"
]
| 23 | 1 | 1 | [
"A000961",
"A007947",
"A024619",
"A139257",
"A381525",
"A381750",
"A381799"
]
| null | Michael De Vlieger, Mar 27 2025 | 2025-05-30T23:15:45 | oeisdata/seq/A381/A381750.seq | 57862c0484b461a2c64c5f8bfa6a897d |
A381751 | Expansion of exp( Sum_{k>=1} binomial(8*k-1,2*k-1) * x^k/k ). | [
"1",
"7",
"252",
"12866",
"767460",
"50005591",
"3449225652",
"247579862356",
"18301102679444",
"1383742325041292",
"106516121515030768",
"8319491960857739258",
"657680525420544788060",
"52522142073165048614002",
"4230907373618147894630904",
"343379827862952363210331624",
"28051180121294369965012932980"
]
| [
"nonn",
"easy"
]
| 12 | 0 | 2 | [
"A006013",
"A079489",
"A182960",
"A381745",
"A381751",
"A381752",
"A381753",
"A381757",
"A381758"
]
| null | Seiichi Manyama, Mar 06 2025 | 2025-03-06T08:27:50 | oeisdata/seq/A381/A381751.seq | a264d42596cb175022faed48b8d87949 |
A381752 | Expansion of exp( Sum_{k>=1} binomial(10*k-1,2*k-1) * x^k/k ). | [
"1",
"9",
"525",
"44067",
"4338765",
"467396050",
"53346810991",
"6339179481480",
"775994115988525",
"97182642466115275",
"12392633418043399130",
"1603634650155295053250",
"210047857493659698690575",
"27795006677556725604853840",
"3710220786174094422360657000",
"498998879378383167317202612400"
]
| [
"nonn",
"easy"
]
| 9 | 0 | 2 | [
"A006013",
"A079489",
"A182960",
"A381746",
"A381751",
"A381752",
"A381753",
"A381757",
"A381758"
]
| null | Seiichi Manyama, Mar 06 2025 | 2025-03-06T08:27:54 | oeisdata/seq/A381/A381752.seq | 748528136c7cfe422889c6ade7c0af9c |
A381753 | Expansion of exp( Sum_{k>=1} binomial(5*k-1,2*k-1) * x^k/k ). | [
"1",
"4",
"50",
"846",
"16495",
"349240",
"7803823",
"181135830",
"4324897697",
"105543188190",
"2620784850325",
"66005699547352",
"1682046970846570",
"43291586055360034",
"1123707191010320955",
"29382536610737191930",
"773229801368332554273",
"20463493681189771623960"
]
| [
"nonn",
"easy"
]
| 14 | 0 | 2 | [
"A006013",
"A060941",
"A079489",
"A182960",
"A381751",
"A381752",
"A381753",
"A381757",
"A381758"
]
| null | Seiichi Manyama, Mar 06 2025 | 2025-03-07T10:47:16 | oeisdata/seq/A381/A381753.seq | caaa742f2346449c1b7c6db3aa727ac0 |
A381754 | Numbers k such that k and 3*k have the same number of zeros in their binary expansions. | [
"0",
"1",
"2",
"4",
"8",
"16",
"19",
"32",
"35",
"38",
"39",
"53",
"64",
"67",
"70",
"71",
"76",
"78",
"79",
"101",
"105",
"106",
"117",
"128",
"131",
"134",
"135",
"140",
"142",
"143",
"152",
"156",
"158",
"159",
"197",
"201",
"202",
"209",
"210",
"212",
"229",
"233",
"234",
"245",
"256",
"259",
"262",
"263",
"268",
"270",
"271",
"280",
"284",
"286",
"287",
"301",
"304"
]
| [
"nonn",
"base",
"easy"
]
| 30 | 1 | 3 | [
"A023416",
"A077459",
"A381754",
"A381934"
]
| null | Barak Manos, Mar 06 2025 | 2025-04-07T09:50:05 | oeisdata/seq/A381/A381754.seq | 2d91cf403437dfe2bc69e79efee901dd |
A381755 | Numbers of minimum connected dominating sets in the n-Pell graph. | [
"2",
"2",
"3",
"46",
"628"
]
| [
"nonn",
"more"
]
| 7 | 1 | 1 | null | null | Eric W. Weisstein, Mar 06 2025 | 2025-06-24T18:32:37 | oeisdata/seq/A381/A381755.seq | 333372b2894b5037d79aabbf83bb97eb |
A381756 | Decimal expansion of the smallest angular distance between two vertices of the equilateral square antiprism measured along the circumscribing sphere. | [
"1",
"3",
"0",
"6",
"5",
"2",
"7",
"1",
"6",
"1",
"7",
"1",
"7",
"4",
"3",
"7",
"2",
"7",
"5",
"5",
"3",
"4",
"1",
"6",
"4",
"6",
"9",
"0",
"5",
"9",
"8",
"6",
"9",
"4",
"7",
"4",
"4",
"1",
"6",
"2",
"8",
"6",
"1",
"3",
"9",
"0",
"1",
"9",
"9",
"9",
"2",
"7",
"8",
"9",
"0",
"3",
"1",
"9",
"6",
"8",
"8",
"6",
"5",
"8",
"5",
"8",
"9",
"7",
"4",
"5",
"3",
"6",
"9",
"4",
"0",
"3",
"0",
"6",
"5",
"2",
"9",
"1",
"1",
"4",
"4",
"9",
"1",
"2",
"9",
"1",
"0"
]
| [
"nonn",
"cons"
]
| 6 | 1 | 2 | [
"A086178",
"A381756"
]
| null | R. J. Mathar, Mar 06 2025 | 2025-03-06T08:27:46 | oeisdata/seq/A381/A381756.seq | 6c8473bc4dec56714b83bd088988fdc4 |
A381757 | Expansion of exp( Sum_{k>=1} binomial(7*k-1,2*k-1) * x^k/k ). | [
"1",
"6",
"161",
"6062",
"265868",
"12720904",
"643915209",
"33905228350",
"1838102210977",
"101910583801012",
"5751779249830131",
"329359930638541776",
"19087504000780665541",
"1117418973753045781944",
"65982722733895652916539",
"3925378032146863676341770",
"235048328495265879957413946"
]
| [
"nonn",
"easy"
]
| 9 | 0 | 2 | [
"A006013",
"A079489",
"A182960",
"A300386",
"A381751",
"A381752",
"A381753",
"A381757",
"A381758"
]
| null | Seiichi Manyama, Mar 06 2025 | 2025-03-06T08:28:03 | oeisdata/seq/A381/A381757.seq | f7e583030319b6043f02a8c072002989 |
A381758 | Expansion of exp( Sum_{k>=1} binomial(9*k-1,2*k-1) * x^k/k ). | [
"1",
"8",
"372",
"24732",
"1925394",
"163883548",
"14773987638",
"1386341339430",
"133994232166575",
"13248555929274096",
"1333732204895318366",
"136243562694021684648",
"14087033746990654649067",
"1471456489458490198994856",
"155042502964505871862313879",
"16459391575059417875255359878"
]
| [
"nonn",
"easy"
]
| 11 | 0 | 2 | [
"A006013",
"A079489",
"A182960",
"A300387",
"A381751",
"A381752",
"A381753",
"A381757",
"A381758"
]
| null | Seiichi Manyama, Mar 06 2025 | 2025-03-06T08:28:09 | oeisdata/seq/A381/A381758.seq | 62046a2f19977a1eb6f2ba4534cd77aa |
A381759 | Number of words of length 2n+1 with one 0 entry and two entries of each of 1..n so that there are exactly k numbers between two equal k's and so that the first element does not exceed the last. | [
"1",
"1",
"3",
"5",
"11",
"38",
"182",
"938",
"4158",
"23384",
"160104",
"1063772",
"6987380",
"53746000",
"479965824",
"4182552416",
"35963592624",
"351432650816",
"3860219984448",
"41614300175968"
]
| [
"nonn",
"more"
]
| 21 | 1 | 3 | [
"A014552",
"A176127",
"A381759",
"A381760"
]
| null | Zhao Hui Du, Mar 06 2025 | 2025-03-15T04:21:36 | oeisdata/seq/A381/A381759.seq | 7f4919a5f995b25609c789601e87cff1 |
A381760 | Number of words of length 2n+1 with one 0 entry and two entries of each of 1..n so that there are exactly k numbers between two equal k's and so that the first element is not 0 and also does not exceed the last. | [
"1",
"1",
"1",
"3",
"11",
"38",
"130",
"638",
"4158",
"23384",
"124520",
"847484",
"6987380",
"53746000",
"400346544",
"3529108816",
"35963592624",
"351432650816",
"3346590201888",
"36341624453568"
]
| [
"nonn",
"more"
]
| 21 | 1 | 4 | [
"A014552",
"A176127",
"A381759",
"A381760"
]
| null | Zhao Hui Du, Mar 06 2025 | 2025-03-15T04:22:11 | oeisdata/seq/A381/A381760.seq | ab820898c815fc958f242cb4caa2a9c2 |
A381761 | Number of minimum connected dominating sets in the n-Keller graph. | [
"0",
"40",
"80816",
"42002944"
]
| [
"nonn",
"more"
]
| 4 | 1 | 2 | null | null | Eric W. Weisstein, Mar 06 2025 | 2025-03-06T09:09:48 | oeisdata/seq/A381/A381761.seq | d26cb41d312f4fd4daa0cfa2125eb63f |
A381762 | Numbers k such that S(k) sets a new record, where S(k) denotes the sum of the reciprocals of odd elements in the Collatz sequence which starts at k. | [
"1",
"3",
"7",
"9",
"559",
"745",
"993"
]
| [
"nonn",
"more"
]
| 19 | 1 | 2 | [
"A127789",
"A304174",
"A381762"
]
| null | Barak Manos, Mar 06 2025 | 2025-03-15T12:28:00 | oeisdata/seq/A381/A381762.seq | 3c6d25cfd636cb2a98bef6c9db5d5d06 |
A381763 | a(n) is the greatest k >= 0 such that Omega(n-i) = Omega(n+i) for 1 <= i <= k, where Omega = A001222. | [
"0",
"0",
"1",
"2",
"1",
"0",
"0",
"0",
"0",
"0",
"3",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
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"1",
"0",
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"0",
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"1",
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"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"2",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"3",
"0",
"0",
"2",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0"
]
| [
"nonn"
]
| 7 | 2 | 4 | [
"A001222",
"A381763",
"A381768"
]
| null | Robert Israel, Mar 06 2025 | 2025-03-07T06:29:53 | oeisdata/seq/A381/A381763.seq | c10dababdb44a041ff6ac222996270b9 |
A381764 | Nearest integer not equal to n with the same Hamming weight (number of 1 bits) as n. | [
"2",
"1",
"5",
"2",
"6",
"5",
"11",
"4",
"10",
"9",
"13",
"10",
"14",
"13",
"23",
"8",
"18",
"17",
"21",
"18",
"22",
"21",
"27",
"20",
"26",
"25",
"29",
"26",
"30",
"29",
"47",
"16",
"34",
"33",
"37",
"34",
"38",
"37",
"43",
"36",
"42",
"41",
"45",
"42",
"46",
"45",
"55",
"40",
"50",
"49",
"53",
"50",
"54",
"53",
"59",
"52",
"58",
"57",
"61",
"58",
"62",
"61",
"95",
"32",
"66",
"65",
"69",
"66"
]
| [
"nonn"
]
| 39 | 1 | 1 | [
"A000120",
"A055010",
"A057168",
"A243109",
"A381764"
]
| null | Chai Wah Wu, Mar 06 2025 | 2025-06-20T12:40:17 | oeisdata/seq/A381/A381764.seq | 695c36a673a003c4fdd3beaa765a1968 |
A381765 | Number of connected simple graphs on n unlabeled vertices whose degree sequence is consecutive. | [
"1",
"1",
"1",
"2",
"5",
"16",
"75",
"544",
"6920",
"159228",
"6961507",
"577826609",
"90529308665"
]
| [
"nonn",
"more"
]
| 41 | 0 | 4 | [
"A001349",
"A005177",
"A381586",
"A381765"
]
| null | John P. McSorley, Mar 25 2025 | 2025-04-02T03:56:04 | oeisdata/seq/A381/A381765.seq | fbb491c4d02b5f619ae78943e862a5e0 |
A381766 | Starting from the n-th prime, a(n) is the minimum number > 1 of consecutive primes whose sum is the average of a twin prime pair. | [
"57",
"180",
"2",
"2",
"4",
"2",
"8",
"2",
"100",
"2",
"16",
"18",
"26",
"12",
"160",
"4",
"70",
"70",
"2",
"12",
"6",
"4",
"76",
"202",
"2",
"4",
"4",
"10",
"24",
"2",
"14",
"18",
"22",
"8",
"8",
"48",
"4",
"72",
"132",
"224",
"180",
"142",
"10",
"96",
"24",
"10",
"24",
"124",
"76",
"2",
"164",
"34",
"196",
"120",
"34",
"24",
"128",
"118",
"8",
"6",
"34",
"2",
"2",
"8",
"116",
"18",
"552",
"6"
]
| [
"nonn"
]
| 47 | 1 | 1 | [
"A014574",
"A065091",
"A381766",
"A381868"
]
| null | Abhiram R Devesh, Mar 08 2025 | 2025-04-02T13:21:04 | oeisdata/seq/A381/A381766.seq | ebed093123239a392fc70c3baaf7035b |
A381767 | a(n) = ceiling(n^(n/(n-1))) with a(1)=1. | [
"1",
"4",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"16",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"32",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"40",
"41",
"42",
"43",
"44",
"45",
"47",
"48",
"49",
"50",
"51",
"52",
"53",
"54",
"55",
"56",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"64",
"65",
"66",
"67",
"68",
"69",
"70",
"71"
]
| [
"nonn"
]
| 40 | 1 | 2 | [
"A381767",
"A382131"
]
| null | Mike Sheppard, Mar 06 2025 | 2025-05-25T21:26:21 | oeisdata/seq/A381/A381767.seq | a162771fb0d43a25d552849dc1744803 |
A381768 | a(n) is the least positive number k for which A381763(k) = n. | [
"1",
"4",
"5",
"12",
"604",
"1338",
"432",
"11700",
"421098"
]
| [
"nonn",
"more"
]
| 5 | 0 | 2 | [
"A001222",
"A381763",
"A381768"
]
| null | Zak Seidov and Robert Israel, Mar 06 2025 | 2025-03-07T06:31:10 | oeisdata/seq/A381/A381768.seq | 0456ebcd61f465d7e5c7745b3c13e3a1 |
A381769 | a(n) is the area of the largest rectangle that can be formed from n sticks whose lengths are 1, 2, ..., n. | [
"0",
"0",
"0",
"0",
"3",
"12",
"25",
"49",
"81",
"121",
"182",
"272",
"380",
"506",
"676",
"900",
"1156",
"1444",
"1806",
"2256",
"2756",
"3306",
"3969",
"4761",
"5625",
"6561",
"7656",
"8930",
"10302",
"11772",
"13456",
"15376",
"17424",
"19600",
"22052",
"24806",
"27722",
"30800",
"34225",
"38025",
"42025",
"46225",
"50850",
"55932",
"61256",
"66822",
"72900",
"79524",
"86436",
"93636"
]
| [
"nonn",
"easy",
"nice"
]
| 77 | 0 | 5 | null | null | Ali Sada and Daniel Mondot, Mar 06 2025 | 2025-03-12T07:47:51 | oeisdata/seq/A381/A381769.seq | 58d86166ab57a0beb0c5881a9d2e5d44 |
A381770 | a(n) is the least k > 0 such that the factorial base expansion of k*n has digits in nonincreasing order. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"5",
"1",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"1",
"1",
"6",
"3",
"2",
"2",
"3",
"1",
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"1",
"1",
"3",
"3",
"2",
"3",
"3",
"2",
"2",
"14",
"2",
"2",
"2",
"2",
"2",
"2",
"1",
"6",
"3",
"2",
"2",
"8",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"5",
"1",
"1",
"1",
"1",
"4",
"8",
"4",
"6",
"6",
"8",
"1",
"6",
"4",
"2",
"2",
"9",
"1",
"8",
"1",
"1",
"7",
"8",
"1",
"5",
"1"
]
| [
"nonn",
"base"
]
| 10 | 0 | 8 | [
"A223475",
"A351987",
"A381770",
"A381771"
]
| null | Rémy Sigrist, Mar 07 2025 | 2025-03-10T11:11:23 | oeisdata/seq/A381/A381770.seq | 728478ae6ce89e7216fa02aefa35481a |
A381771 | For any n > 0, a(n) is the least positive multiple of n whose factorial base expansion has digits in nonincreasing order; a(0) = 0. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"14",
"8",
"9",
"20",
"22",
"12",
"65",
"14",
"15",
"16",
"17",
"18",
"57",
"20",
"21",
"22",
"23",
"24",
"150",
"78",
"54",
"56",
"87",
"30",
"62",
"32",
"33",
"102",
"105",
"72",
"111",
"114",
"78",
"80",
"574",
"84",
"86",
"88",
"90",
"92",
"94",
"48",
"294",
"150",
"102",
"104",
"424",
"54",
"110",
"56",
"57",
"116",
"118",
"60",
"305",
"62",
"63"
]
| [
"nonn",
"base"
]
| 10 | 0 | 3 | [
"A223474",
"A351987",
"A381770",
"A381771"
]
| null | Rémy Sigrist, Mar 07 2025 | 2025-03-10T11:11:27 | oeisdata/seq/A381/A381771.seq | 502a06d225c645b2863896beeb91fb5c |
A381772 | Expansion of ( (1/x) * Series_Reversion( x/((1+x) * C(x))^2 ) )^(1/2), where C(x) is the g.f. of A000108. | [
"1",
"2",
"11",
"83",
"727",
"6940",
"70058",
"735502",
"7949031",
"87851819",
"988307647",
"11279719247",
"130286197186",
"1520108988221",
"17889102534329",
"212095541328931",
"2531001870925559",
"30376237591559863",
"366417240105654587",
"4440000077166319993",
"54020150448778625847",
"659665548217188211288"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A000108",
"A007852",
"A054727",
"A060941",
"A069271",
"A274052",
"A381772",
"A381773",
"A381774",
"A381775",
"A381780"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:48:52 | oeisdata/seq/A381/A381772.seq | 94a0ca5d964633921140567a0a2fb3d5 |
A381773 | Expansion of ( (1/x) * Series_Reversion( x/((1+x) * C(x))^3 ) )^(1/3), where C(x) is the g.f. of A000108. | [
"1",
"2",
"15",
"157",
"1913",
"25427",
"357546",
"5229980",
"78765793",
"1213181593",
"19021747383",
"302595975502",
"4871780511910",
"79232327379407",
"1299767617080662",
"21481625997258747",
"357350097625089497",
"5978708468143961925",
"100537111802285439375",
"1698302173359384479307"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A000108",
"A054727",
"A060941",
"A212071",
"A234461",
"A381772",
"A381773",
"A381774",
"A381775",
"A381779",
"A381780",
"A381782",
"A381783",
"A381786"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:48:57 | oeisdata/seq/A381/A381773.seq | c955ee20a23ab26c186f870ee6738831 |
A381774 | Expansion of ( (1/x) * Series_Reversion( x/((1+x) * C(x))^4 ) )^(1/4), where C(x) is the g.f. of A000108. | [
"1",
"2",
"19",
"255",
"3995",
"68344",
"1237526",
"23316295",
"452385355",
"8977539540",
"181374792040",
"3718002102747",
"77138798530854",
"1616741658725930",
"34179703551312530",
"728019711835819493",
"15608122038151106507",
"336551042553481867640",
"7293934071668996347055"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A000108",
"A054727",
"A060941",
"A381772",
"A381773",
"A381774",
"A381775"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:49:01 | oeisdata/seq/A381/A381774.seq | bf999ad1ab077602e7bed8affcca432f |
A381775 | Expansion of ( (1/x) * Series_Reversion( x/((1+x) * C(x))^6 ) )^(1/6), where C(x) is the g.f. of A000108. | [
"1",
"2",
"27",
"523",
"11871",
"294668",
"7747698",
"212054604",
"5978347887",
"172421233231",
"5063192676597",
"150872475295522",
"4550458484780442",
"138652322209300991",
"4261638256558924407",
"131973650298641750844",
"4113788296015093994719",
"128973000885015536107140"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A000108",
"A054727",
"A060941",
"A381772",
"A381773",
"A381774",
"A381775"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-08T02:30:52 | oeisdata/seq/A381/A381775.seq | 4be212dc44fe9287ff8da2be8130ff44 |
A381776 | Empty polygon numbers: a(n) is the smallest number of points in the plane (with no three of them collinear) such that an empty convex n-gon cannot be avoided. | [
"3",
"5",
"10",
"30"
]
| [
"nonn",
"bref",
"fini",
"full",
"nice"
]
| 22 | 3 | 1 | [
"A003182",
"A003186",
"A330333",
"A348260",
"A381776"
]
| null | Paolo Xausa, Mar 07 2025 | 2025-03-07T08:22:56 | oeisdata/seq/A381/A381776.seq | 6779e8362b608d818c26bfcbba0e50f5 |
A381777 | Self-convolution of A001190. | [
"0",
"0",
"1",
"2",
"3",
"6",
"11",
"22",
"44",
"92",
"193",
"414",
"896",
"1966",
"4347",
"9700",
"21787",
"49262",
"111976",
"255824",
"586996",
"765220",
"1187129",
"2186146",
"3966763",
"7642844",
"14733649",
"29037924",
"57062745",
"113051998",
"222948526",
"438614648",
"853410655",
"1637949306",
"3069032471",
"5548974602",
"9438433065"
]
| [
"nonn",
"easy"
]
| 5 | 0 | 4 | [
"A001190",
"A381777"
]
| null | Stefano Spezia, Mar 07 2025 | 2025-03-07T09:05:14 | oeisdata/seq/A381/A381777.seq | de260e7d6f957e1a6e7730362df8467c |
A381778 | G.f. A(x) satisfies A(x) = (1 + x*A(x)) * C(x*A(x)^2), where C(x) is the g.f. of A000108. | [
"1",
"2",
"9",
"60",
"474",
"4105",
"37681",
"360122",
"3545320",
"35705553",
"366126614",
"3809497971",
"40119258081",
"426829897847",
"4580629916321",
"49527776299522",
"539025763347730",
"5900193301962178",
"64913644702760248",
"717433047054489969",
"7961616716665723173",
"88679610762886209459"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A000108",
"A054727",
"A381778",
"A381779"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:47:44 | oeisdata/seq/A381/A381778.seq | 0ea1be9bb26b0db6efa1b00c543c782f |
A381779 | G.f. A(x) satisfies A(x) = (1 + x*A(x)) * C(x*A(x)^3), where C(x) is the g.f. of A000108. | [
"1",
"2",
"11",
"95",
"977",
"11028",
"132029",
"1646428",
"21155077",
"278127359",
"3723466202",
"50586670945",
"695676081162",
"9665426437561",
"135464096419620",
"1912922793362142",
"27190770354633287",
"388734441118885467",
"5586079818959767743",
"80638973170989453862",
"1168864771263296930809"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A000108",
"A054727",
"A381778",
"A381779"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:47:40 | oeisdata/seq/A381/A381779.seq | b4e72b9ad5478006ff83ef06034c98ec |
A381780 | G.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * C(x*A(x)^3), where C(x) is the g.f. of A000108. | [
"1",
"2",
"13",
"122",
"1348",
"16317",
"209366",
"2797461",
"38509302",
"542367569",
"7778173646",
"113196865436",
"1667497600735",
"24816081138489",
"372551391235504",
"5635157636123317",
"85797446797707896",
"1313857342649814042",
"20222887980813290849",
"312694810135597988049",
"4854881337618505385339"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A000108",
"A007852",
"A069271",
"A381772",
"A381780"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:47:35 | oeisdata/seq/A381/A381780.seq | cdf5b05e93d77f1447c13575ad15fead |
A381781 | a(n) = k where k*Pi is the solution to sin(x) = 0 obtained using Newton's method starting from x = n. | [
"0",
"0",
"1",
"1",
"1",
"3",
"2",
"2",
"5",
"3",
"3",
"74",
"4",
"4",
"2",
"5",
"5",
"4",
"6",
"6",
"6",
"7",
"7",
"7",
"8",
"8",
"8",
"10",
"9",
"9",
"13",
"10",
"10",
"30",
"11",
"11",
"9",
"12",
"12",
"11",
"13",
"13",
"13",
"14",
"14",
"14",
"15",
"15",
"15",
"25",
"16",
"16",
"14",
"17",
"17",
"32",
"18",
"18",
"16",
"19",
"19",
"18",
"20",
"20",
"17",
"21",
"21",
"21",
"22",
"22",
"22",
"25",
"23",
"23",
"26"
]
| [
"sign",
"easy"
]
| 51 | 0 | 6 | [
"A082964",
"A381473",
"A381781",
"A381892",
"A381893"
]
| null | Simcha Z. Katzoff, Mar 07 2025 | 2025-03-25T19:49:39 | oeisdata/seq/A381/A381781.seq | a2c69ea1cc4b278fe987cb89bc056b39 |
A381782 | G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * C(x), where C(x) is the g.f. of A000108. | [
"1",
"2",
"9",
"52",
"342",
"2437",
"18331",
"143320",
"1153308",
"9489487",
"79470647",
"675149665",
"5804359859",
"50402807459",
"441433999816",
"3894774605660",
"34585663823538",
"308867647484634",
"2772256164853972",
"24994569816424301",
"226261997160303326",
"2055711320495566962"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A000108",
"A212071",
"A381773",
"A381782",
"A381783"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:47:29 | oeisdata/seq/A381/A381782.seq | 2ac8ce22b4ff90ea3b4b5fbd2298530c |
A381783 | G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * C(x*A(x)), where C(x) is the g.f. of A000108. | [
"1",
"2",
"11",
"79",
"645",
"5682",
"52643",
"505575",
"4987933",
"50250625",
"514787110",
"5346336739",
"56161123273",
"595667090038",
"6370314162095",
"68616488830785",
"743733580011957",
"8106009997644507",
"88783190884441892",
"976705067814061730",
"10787334777299825522",
"119569153425125828365"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A000108",
"A212071",
"A381773",
"A381782",
"A381783"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:47:24 | oeisdata/seq/A381/A381783.seq | b792f6ea314a9232f06739c879d88d30 |
A381784 | G.f. A(x) satisfies A(x) = (1 + x*A(x)^4) * C(x*A(x)^2), where C(x) is the g.f. of A000108. | [
"1",
"2",
"15",
"153",
"1799",
"22969",
"309479",
"4331175",
"62349575",
"917335467",
"13732751589",
"208509835114",
"3203279694575",
"49701110565986",
"777708690091907",
"12258870836704797",
"194475105262057575",
"3102607480658510165",
"49746656826517452788",
"801205735002960886531",
"12956005807148939155717"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A000108",
"A234461",
"A381774",
"A381784"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:47:20 | oeisdata/seq/A381/A381784.seq | d5118f8abef03e4cd85965c1a97a46ce |
A381785 | G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)^2), where C(x) is the g.f. of A000108. | [
"1",
"2",
"7",
"45",
"335",
"2731",
"23573",
"211741",
"1958571",
"18529392",
"178459000",
"1743868792",
"17246702932",
"172302244669",
"1736302280083",
"17627794322287",
"180133941044517",
"1851310247393202",
"19123511540724822",
"198437973436950204",
"2067524004169000212",
"21620908821378509071"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A000108",
"A212071",
"A381772",
"A381778",
"A381784",
"A381785"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:47:49 | oeisdata/seq/A381/A381785.seq | daaf7149c3c93e77cbf30349374b5959 |
A381786 | G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)^3), where C(x) is the g.f. of A000108. | [
"1",
"2",
"9",
"76",
"744",
"7986",
"90836",
"1075714",
"13122656",
"163769229",
"2080985186",
"26832199993",
"350187469872",
"4617094718728",
"61406081813812",
"822834184073768",
"11098254270705028",
"150555545320009712",
"2052839917410937693",
"28118478688846531072",
"386727880988105218913",
"5338557108832658927346"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A000108",
"A234461",
"A381773",
"A381779",
"A381780",
"A381786"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:48:03 | oeisdata/seq/A381/A381786.seq | 4c0fc5f3ba3f4a0f7a4c29892077ff01 |
A381787 | G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)), where C(x) is the g.f. of A000108. | [
"1",
"2",
"5",
"22",
"112",
"623",
"3664",
"22405",
"141002",
"907228",
"5940663",
"39459873",
"265228359",
"1800608563",
"12328843910",
"85040632504",
"590371016188",
"4121775003434",
"28921911896836",
"203854515625194",
"1442669458817907",
"10247020573880520",
"73024240955785936",
"521973882076798493"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A000108",
"A167422",
"A381785",
"A381786",
"A381787"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-07T10:48:48 | oeisdata/seq/A381/A381787.seq | 416d45089eff515bb466baa52ee67db4 |
A381788 | Greedy expansion of Pi-3 in a base with place values 1/(10^k-1), k >= 1, using digits {0,1,2,...,8,9,A=10}. | [
"1",
"3",
"0",
"1",
"7",
"8",
"5",
"0",
"1",
"4",
"6",
"6",
"5",
"9",
"4",
"7",
"1",
"5",
"1",
"9",
"5",
"6",
"1",
"3",
"4",
"8",
"9",
"3",
"4",
"2",
"2",
"7",
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"2",
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"8",
"6",
"2",
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"3",
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"8",
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"1",
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"2",
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"8",
"6",
"3",
"1",
"2",
"5",
"9",
"1",
"2",
"9",
"1",
"5",
"5",
"5",
"0",
"6",
"9",
"6",
"8",
"0",
"7",
"7",
"9",
"7",
"4",
"0",
"9",
"8",
"2",
"8",
"5",
"7",
"4",
"1",
"9",
"5",
"5",
"7",
"5",
"2",
"8",
"3",
"1",
"1",
"0",
"8",
"8",
"5"
]
| [
"nonn",
"base"
]
| 32 | 1 | 2 | [
"A000796",
"A073668",
"A381788"
]
| null | Simon Plouffe, Mar 07 2025 | 2025-03-18T14:43:07 | oeisdata/seq/A381/A381788.seq | 549f952476b96daf7f851bf2e9f5a3b9 |
A381789 | Number of connected dominating sets in the n-Pell graph. | [
"3",
"12",
"852",
"63845729"
]
| [
"nonn",
"more"
]
| 13 | 1 | 1 | null | null | Eric W. Weisstein, Mar 07 2025 | 2025-03-07T14:07:46 | oeisdata/seq/A381/A381789.seq | 4e334356e8395dbe30218e53a2c0bd38 |
A381790 | a(n) = 3*2^n + 2*n - 2. | [
"1",
"6",
"14",
"28",
"54",
"104",
"202",
"396",
"782",
"1552",
"3090",
"6164",
"12310",
"24600",
"49178",
"98332",
"196638",
"393248",
"786466",
"1572900",
"3145766",
"6291496",
"12582954",
"25165868",
"50331694",
"100663344",
"201326642",
"402653236",
"805306422",
"1610612792",
"3221225530",
"6442451004",
"12884901950"
]
| [
"nonn",
"easy"
]
| 8 | 0 | 2 | null | null | Eric W. Weisstein, Mar 07 2025 | 2025-03-08T01:48:21 | oeisdata/seq/A381/A381790.seq | 67b52caab4cc119e9255ff0b37b75ed4 |
A381791 | a(n) = 2*(4 + 17*2^(n-1)). | [
"25",
"42",
"76",
"144",
"280",
"552",
"1096",
"2184",
"4360",
"8712",
"17416",
"34824",
"69640",
"139272",
"278536",
"557064",
"1114120",
"2228232",
"4456456",
"8912904",
"17825800",
"35651592",
"71303176",
"142606344",
"285212680",
"570425352",
"1140850696",
"2281701384",
"4563402760",
"9126805512",
"18253611016"
]
| [
"nonn",
"easy"
]
| 8 | 0 | 1 | null | null | Eric W. Weisstein, Mar 07 2025 | 2025-03-08T01:34:37 | oeisdata/seq/A381/A381791.seq | cfb416211bc4ca30e3db316f4c545bfd |
A381792 | Numbers k such that k + prime(k) is prime and k + semiprime(k) is semiprime. | [
"4",
"6",
"18",
"24",
"34",
"72",
"96",
"98",
"116",
"130",
"150",
"172",
"200",
"206",
"270",
"290",
"350",
"356",
"362",
"386",
"410",
"420",
"450",
"504",
"508",
"554",
"576",
"618",
"666",
"682",
"720",
"738",
"754",
"782",
"784",
"808",
"820",
"832",
"858",
"892",
"960",
"962",
"984",
"1016",
"1050",
"1102",
"1110",
"1154",
"1162",
"1168",
"1176",
"1184",
"1206",
"1256",
"1284",
"1296",
"1302",
"1360"
]
| [
"nonn"
]
| 14 | 1 | 1 | [
"A000040",
"A001222",
"A001358",
"A064402",
"A100915",
"A381792"
]
| null | Zak Seidov and Robert Israel, Mar 07 2025 | 2025-03-10T11:01:24 | oeisdata/seq/A381/A381792.seq | 4fe5b5a74e0845b3ae30653c771e738a |
A381793 | Smallest k>1 such that 10*k^(5*2^n)+1 is prime. | [
"6",
"11",
"649",
"792",
"1034",
"12386",
"21813",
"87318",
"35387",
"207339",
"67958"
]
| [
"nonn",
"base",
"hard",
"more"
]
| 28 | 0 | 1 | [
"A020714",
"A089319",
"A381793",
"A381815"
]
| null | Jakub Buczak, Mar 07 2025 | 2025-03-16T15:03:15 | oeisdata/seq/A381/A381793.seq | 19739fa328e63146734153c694dafd2a |
A381794 | Number of connected dominating sets in the n-trapezohedral graph. | [
"8",
"36",
"115",
"436",
"1604",
"6067",
"22936",
"87332",
"334075",
"1285148",
"4969452",
"19310763",
"75372496",
"295346604",
"1161269763",
"4579368004",
"18103226292",
"71715416035",
"284593621544",
"1131006389780",
"4500107172363",
"17922831610316",
"71439705155420",
"284943217164891",
"1137130012887584"
]
| [
"nonn",
"easy"
]
| 12 | 1 | 1 | [
"A000032",
"A370089",
"A381190",
"A381794"
]
| null | Eric W. Weisstein, Mar 07 2025 | 2025-03-20T19:34:31 | oeisdata/seq/A381/A381794.seq | 40addb72b77d0e3b145d74e4c1d7e8d9 |
A381795 | Number of connected dominating sets in the n-triangular honeycomb bishop graph. | [
"1",
"4",
"28",
"504",
"19488",
"1488192",
"217706592"
]
| [
"nonn",
"more"
]
| 4 | 1 | 2 | null | null | Eric W. Weisstein, Mar 07 2025 | 2025-03-07T14:07:28 | oeisdata/seq/A381/A381795.seq | e0b645b235e396afbf3df1225e41a138 |
A381796 | Number of connected dominating sets in the n-triangular honeycomb obtuse knight graph. | [
"1",
"0",
"0",
"0",
"0",
"223634",
"46217016"
]
| [
"nonn",
"more"
]
| 4 | 1 | 6 | null | null | Eric W. Weisstein, Mar 07 2025 | 2025-03-07T14:07:25 | oeisdata/seq/A381/A381796.seq | 1e2172a859481a2199e5dd0d7442ad3e |
A381797 | Number of connected dominating sets in the n X n X n grid graph. | [
"1",
"115",
"22463410"
]
| [
"nonn",
"bref",
"more"
]
| 4 | 1 | 2 | null | null | Eric W. Weisstein, Mar 07 2025 | 2025-03-07T14:07:19 | oeisdata/seq/A381/A381797.seq | 653a52166898224b150413a881f42be9 |
A381798 | Number of residues r such that p^m is congruent to r (mod n), where prime p | n and m >= 0. | [
"1",
"2",
"2",
"3",
"2",
"4",
"2",
"4",
"3",
"6",
"2",
"6",
"2",
"5",
"7",
"5",
"2",
"9",
"2",
"7",
"8",
"12",
"2",
"7",
"3",
"14",
"4",
"7",
"2",
"11",
"2",
"6",
"8",
"10",
"11",
"11",
"2",
"20",
"5",
"9",
"2",
"14",
"2",
"14",
"12",
"13",
"2",
"10",
"3",
"23",
"19",
"15",
"2",
"22",
"7",
"8",
"20",
"30",
"2",
"12",
"2",
"7",
"11",
"7",
"9",
"18",
"2",
"11",
"14",
"23",
"2",
"12",
"2",
"38",
"24",
"22",
"14",
"17"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A000961",
"A381798",
"A381799"
]
| null | Michael De Vlieger, Mar 07 2025 | 2025-03-14T20:05:08 | oeisdata/seq/A381/A381798.seq | 2e283572d331e673ffed93edf727e73b |
A381799 | Irregular triangle read by rows, where row n is a list of residues of powers of prime factors of n (mod n). | [
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"2",
"0",
"1",
"1",
"2",
"3",
"4",
"0",
"1",
"0",
"1",
"2",
"4",
"0",
"1",
"3",
"1",
"2",
"4",
"5",
"6",
"8",
"0",
"1",
"1",
"2",
"3",
"4",
"8",
"9",
"0",
"1",
"1",
"2",
"4",
"7",
"8",
"1",
"3",
"5",
"6",
"9",
"10",
"12",
"0",
"1",
"2",
"4",
"8",
"0",
"1",
"1",
"2",
"3",
"4",
"8",
"9",
"10",
"14",
"16",
"0",
"1",
"1",
"2",
"4",
"5",
"8",
"12",
"16",
"1",
"3",
"6",
"7",
"9",
"12",
"15",
"18"
]
| [
"nonn",
"tabf"
]
| 6 | 1 | 8 | [
"A024619",
"A038566",
"A121998",
"A381798",
"A381799"
]
| null | Michael De Vlieger, Mar 07 2025 | 2025-03-14T20:06:38 | oeisdata/seq/A381/A381799.seq | 56858f1da5380b7e4c154652a3f96883 |
A381800 | a(n) = number of distinct residues r mod n of numbers k such that rad(k) | n, where rad = A007947. | [
"1",
"2",
"2",
"3",
"2",
"5",
"2",
"4",
"3",
"7",
"2",
"8",
"2",
"6",
"8",
"5",
"2",
"12",
"2",
"9",
"9",
"13",
"2",
"11",
"3",
"15",
"4",
"9",
"2",
"19",
"2",
"6",
"9",
"11",
"12",
"16",
"2",
"21",
"6",
"12",
"2",
"24",
"2",
"16",
"15",
"14",
"2",
"16",
"3",
"28",
"20",
"17",
"2",
"31",
"8",
"12",
"21",
"31",
"2",
"28",
"2",
"8",
"13",
"7",
"10",
"32",
"2",
"13",
"15",
"35",
"2",
"20",
"2",
"39",
"29",
"24"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A000005",
"A010846",
"A024619",
"A051953",
"A381798",
"A381800",
"A381801"
]
| null | Michael De Vlieger, Mar 07 2025 | 2025-03-14T20:16:41 | oeisdata/seq/A381/A381800.seq | 64dfcc2fcb25fd196a33187cbd2615f7 |
A381801 | Irregular triangle read by rows: row n lists the residues r mod n of numbers k such that rad(k) | n, where rad = A007947. | [
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"2",
"0",
"1",
"0",
"1",
"2",
"3",
"4",
"0",
"1",
"0",
"1",
"2",
"4",
"0",
"1",
"3",
"0",
"1",
"2",
"4",
"5",
"6",
"8",
"0",
"1",
"0",
"1",
"2",
"3",
"4",
"6",
"8",
"9",
"0",
"1",
"0",
"1",
"2",
"4",
"7",
"8",
"0",
"1",
"3",
"5",
"6",
"9",
"10",
"12",
"0",
"1",
"2",
"4",
"8",
"0",
"1",
"0",
"1",
"2",
"3",
"4",
"6",
"8",
"9",
"10",
"12",
"14",
"16",
"0",
"1",
"0",
"1",
"2",
"4",
"5",
"8",
"10",
"12",
"16"
]
| [
"nonn",
"tabf"
]
| 7 | 1 | 8 | [
"A007947",
"A038566",
"A121998",
"A162306",
"A381799",
"A381800",
"A381801"
]
| null | Michael De Vlieger, Mar 07 2025 | 2025-03-14T20:11:52 | oeisdata/seq/A381/A381801.seq | 5d05c6b0182384bd39127ba07c620130 |
A381802 | a(n) = number of distinct residues r mod n of numbers k congruent to r (mod n) such that rad(k) does not divide n, where rad = A007947. | [
"0",
"0",
"1",
"1",
"3",
"1",
"5",
"4",
"6",
"3",
"9",
"4",
"11",
"8",
"7",
"11",
"15",
"6",
"17",
"11",
"12",
"9",
"21",
"13",
"22",
"11",
"23",
"19",
"27",
"11",
"29",
"26",
"24",
"23",
"23",
"20",
"35",
"17",
"33",
"28",
"39",
"18",
"41",
"28",
"30",
"32",
"45",
"32",
"46",
"22",
"31",
"35",
"51",
"23",
"47",
"44",
"36",
"27",
"57",
"32",
"59",
"54",
"50",
"57",
"55",
"34",
"65",
"55",
"54",
"35"
]
| [
"nonn"
]
| 7 | 1 | 5 | [
"A000010",
"A381800",
"A381801",
"A381802"
]
| null | Michael De Vlieger, Mar 14 2025 | 2025-03-22T19:05:15 | oeisdata/seq/A381/A381802.seq | 509b0d5536c4419d560c0775f144c769 |
A381803 | Number of residues r in {0..n-1} that are not coprime to n and not in row n of A381801. | [
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"3",
"0",
"4",
"0",
"1",
"0",
"4",
"1",
"0",
"0",
"6",
"3",
"0",
"6",
"8",
"0",
"4",
"0",
"11",
"5",
"8",
"0",
"9",
"0",
"0",
"10",
"13",
"0",
"7",
"0",
"9",
"7",
"11",
"0",
"17",
"5",
"3",
"0",
"12",
"0",
"6",
"8",
"21",
"1",
"0",
"0",
"17",
"0",
"25",
"15",
"26",
"8",
"15",
"0",
"24",
"11",
"12",
"0",
"29",
"0",
"0",
"7",
"17",
"3",
"22",
"0",
"32",
"23"
]
| [
"nonn"
]
| 7 | 1 | 14 | [
"A000010",
"A038566",
"A051953",
"A121998",
"A381800",
"A381802",
"A381803"
]
| null | Michael De Vlieger, Mar 24 2025 | 2025-04-03T22:43:40 | oeisdata/seq/A381/A381803.seq | 39f625e827b167b825028a8a3c11435f |
A381804 | Number of residues r mod n congruent to k such that rad(k) | n but rad(r) does not divide n, with rad = A007947. | [
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"3",
"0",
"0",
"2",
"0",
"1",
"4",
"6",
"0",
"0",
"0",
"8",
"0",
"1",
"0",
"1",
"0",
"0",
"3",
"3",
"7",
"2",
"0",
"13",
"0",
"1",
"0",
"5",
"0",
"7",
"7",
"6",
"0",
"1",
"0",
"16",
"14",
"8",
"0",
"15",
"3",
"1",
"15",
"23",
"0",
"2",
"0",
"0",
"5",
"0",
"5",
"10",
"0",
"3",
"9",
"15",
"0",
"2",
"0",
"30",
"20",
"14",
"10",
"10",
"0",
"3",
"0",
"14",
"0"
]
| [
"nonn"
]
| 4 | 1 | 15 | [
"A010846",
"A243623",
"A381800",
"A381804"
]
| null | Michael De Vlieger, Mar 14 2025 | 2025-03-22T19:06:02 | oeisdata/seq/A381/A381804.seq | 126f9be99dede6b99e742d28a44d8ff2 |
A381805 | Smallest composite squarefree number that is coprime to n. | [
"6",
"15",
"10",
"15",
"6",
"35",
"6",
"15",
"10",
"21",
"6",
"35",
"6",
"15",
"14",
"15",
"6",
"35",
"6",
"21",
"10",
"15",
"6",
"35",
"6",
"15",
"10",
"15",
"6",
"77",
"6",
"15",
"10",
"15",
"6",
"35",
"6",
"15",
"10",
"21",
"6",
"55",
"6",
"15",
"14",
"15",
"6",
"35",
"6",
"21",
"10",
"15",
"6",
"35",
"6",
"15",
"10",
"15",
"6",
"77",
"6",
"15",
"10",
"15",
"6",
"35",
"6",
"15",
"10",
"33",
"6",
"35"
]
| [
"nonn",
"easy"
]
| 7 | 1 | 1 | [
"A002110",
"A007947",
"A051250",
"A053669",
"A120944",
"A380539",
"A381805",
"A382248"
]
| null | Michael De Vlieger, Mar 31 2025 | 2025-04-05T10:58:12 | oeisdata/seq/A381/A381805.seq | 11931575f1f960a0ded576539045e410 |
A381806 | Numbers that cannot be written as a product of squarefree numbers with distinct sums of prime indices. | [
"4",
"8",
"9",
"16",
"24",
"25",
"27",
"32",
"40",
"48",
"49",
"54",
"56",
"64",
"72",
"80",
"81",
"88",
"96",
"104",
"108",
"112",
"121",
"125",
"128",
"135",
"136",
"144",
"152",
"160",
"162",
"169",
"176",
"184",
"189",
"192",
"200",
"208",
"216",
"224",
"232",
"240",
"243",
"248",
"250",
"256",
"272",
"288",
"289",
"296",
"297",
"304",
"320",
"324",
"328",
"336"
]
| [
"nonn"
]
| 18 | 1 | 1 | [
"A000688",
"A000720",
"A001055",
"A001222",
"A003963",
"A005117",
"A045778",
"A050320",
"A050326",
"A055396",
"A056239",
"A061395",
"A089259",
"A112798",
"A116540",
"A270995",
"A279785",
"A292444",
"A293243",
"A293511",
"A296119",
"A299202",
"A300383",
"A300385",
"A317141",
"A318360",
"A321469",
"A358914",
"A381078",
"A381441",
"A381454",
"A381633",
"A381634",
"A381635",
"A381636",
"A381716",
"A381718",
"A381806",
"A381870",
"A381990",
"A381992",
"A382075"
]
| null | Gus Wiseman, Mar 12 2025 | 2025-03-28T14:13:20 | oeisdata/seq/A381/A381806.seq | 2dc3404ec381099a0bfe5a735a84938d |
A381807 | Number of multisets that can be obtained by choosing a constant partition of each m = 0..n and taking the multiset union. | [
"1",
"1",
"2",
"4",
"12",
"24",
"92",
"184",
"704",
"2016",
"7600",
"15200",
"80664",
"161328",
"601696",
"2198824",
"9868544",
"19737088",
"102010480",
"204020960"
]
| [
"nonn",
"more"
]
| 11 | 0 | 3 | [
"A000005",
"A000009",
"A000041",
"A000688",
"A001970",
"A006171",
"A018818",
"A050361",
"A058694",
"A066723",
"A066843",
"A152827",
"A213385",
"A265947",
"A279784",
"A295935",
"A299200",
"A300383",
"A317141",
"A321467",
"A321468",
"A321470",
"A321471",
"A321514",
"A327486",
"A355537",
"A355731",
"A355733",
"A355741",
"A355742",
"A355744",
"A355746",
"A355747",
"A381453",
"A381455",
"A381635",
"A381636",
"A381715",
"A381716",
"A381807",
"A381808"
]
| null | Gus Wiseman, Mar 13 2025 | 2025-06-04T21:09:59 | oeisdata/seq/A381/A381807.seq | 1d2470894bee1a484fe09dee4f7594f4 |
A381808 | Number of multisets that can be obtained by choosing a strict integer partition of m for each m = 0..n and taking the multiset union. | [
"1",
"1",
"1",
"2",
"4",
"12",
"38",
"145",
"586",
"2619",
"12096",
"58370",
"285244",
"1436815",
"7281062",
"37489525",
"193417612"
]
| [
"nonn",
"more"
]
| 8 | 0 | 4 | [
"A000005",
"A000009",
"A000041",
"A001970",
"A018818",
"A050342",
"A058694",
"A066723",
"A066843",
"A116539",
"A152827",
"A213385",
"A265947",
"A279785",
"A296120",
"A299200",
"A300383",
"A317141",
"A318361",
"A321467",
"A321468",
"A321470",
"A321471",
"A321514",
"A327486",
"A355537",
"A355731",
"A355733",
"A355741",
"A355742",
"A355744",
"A355746",
"A355747",
"A381453",
"A381455",
"A381718",
"A381807",
"A381808"
]
| null | Gus Wiseman, Mar 14 2025 | 2025-06-04T21:09:03 | oeisdata/seq/A381/A381808.seq | 5a3317f08921173ee202ea10a2c48d82 |
A381809 | Decimal expansion of zeta(3)/(8*Pi^2). | [
"0",
"1",
"5",
"2",
"2",
"4",
"2",
"2",
"8",
"5",
"2",
"9",
"1",
"9",
"6",
"6",
"3",
"5",
"3",
"9",
"0",
"1",
"2",
"5",
"7",
"6",
"5",
"2",
"3",
"5",
"5",
"7",
"7",
"3",
"8",
"8",
"3",
"2",
"3",
"5",
"0",
"0",
"2",
"4",
"1",
"7",
"7",
"2",
"4",
"8",
"6",
"9",
"6",
"8",
"1",
"2",
"6",
"4",
"8",
"5",
"9",
"4",
"4",
"9",
"2",
"9",
"5",
"1",
"8",
"9",
"0",
"8",
"9",
"7",
"2",
"4",
"6",
"8",
"4",
"4",
"9",
"3",
"3",
"8",
"8",
"9",
"7",
"2",
"9",
"2",
"4",
"4",
"0",
"4",
"3",
"7",
"2",
"4",
"7",
"9",
"8"
]
| [
"nonn",
"cons"
]
| 11 | 0 | 3 | [
"A002117",
"A002388",
"A276712",
"A381809"
]
| null | Stefano Spezia, May 05 2025 | 2025-05-05T11:45:17 | oeisdata/seq/A381/A381809.seq | 5ebe188da695c37d00acbe3d94c3c5cb |
A381810 | Array read by downward antidiagonals: A(n,k) is a generalization of odd columns of A125790 defined in Comments for n > 0, k >= 0. | [
"2",
"4",
"4",
"6",
"16",
"6",
"8",
"36",
"20",
"10",
"10",
"64",
"42",
"84",
"14",
"12",
"100",
"72",
"286",
"100",
"20",
"14",
"144",
"110",
"680",
"322",
"120",
"26",
"16",
"196",
"156",
"1330",
"744",
"364",
"140",
"36",
"18",
"256",
"210",
"2300",
"1430",
"816",
"406",
"656",
"46",
"20",
"324",
"272",
"3654",
"2444",
"1540",
"888",
"3396",
"740",
"60",
"22",
"400",
"342",
"5456",
"3850",
"2600",
"1650",
"10816",
"3682",
"840",
"74"
]
| [
"nonn",
"tabl"
]
| 36 | 1 | 1 | [
"A000123",
"A001511",
"A007814",
"A053645",
"A062383",
"A070939",
"A078121",
"A106400",
"A119387",
"A125790",
"A236206",
"A381810"
]
| null | Mikhail Kurkov, May 05 2025 | 2025-06-11T21:58:05 | oeisdata/seq/A381/A381810.seq | 6d7607d3aa9cca553143d170ac17445c |
A381811 | The largest nonnegative integer j for which each integer n,n+2,...,n+2j can be written as the sum of the squares for some partition of n. | [
"0",
"1",
"1",
"3",
"4",
"4",
"7",
"13",
"13",
"18",
"25",
"25",
"32",
"32",
"40",
"49",
"52",
"62",
"73",
"85",
"102",
"112",
"127",
"133",
"160",
"166",
"166",
"184",
"203",
"208",
"228",
"249",
"271",
"294",
"322",
"343",
"373",
"376",
"376",
"403",
"431",
"490",
"521",
"521",
"553",
"592",
"620",
"655",
"662",
"662",
"735",
"735",
"773",
"812",
"852",
"893",
"901",
"943",
"986"
]
| [
"nonn"
]
| 15 | 1 | 4 | [
"A000041",
"A069999",
"A381811",
"A383682"
]
| null | Noah A Rosenberg, May 05 2025 | 2025-05-12T00:18:12 | oeisdata/seq/A381/A381811.seq | bd2a803f79c9cb2e51fa6f4f30a060ab |
A381812 | Number of moves required to reach a position with the maximum number of heads in the game of blet with 2*n coins. | [
"1",
"1",
"2",
"5",
"3",
"6",
"11",
"7",
"10",
"17",
"11",
"16",
"25",
"15",
"22",
"33",
"21",
"28",
"41",
"27",
"34"
]
| [
"nonn",
"more"
]
| 27 | 2 | 3 | [
"A047206",
"A075273",
"A381812",
"A381813",
"A381814"
]
| null | Pontus von Brömssen, Mar 08 2025 | 2025-03-16T13:08:33 | oeisdata/seq/A381/A381812.seq | 64c2a4a19ace3888032a2142ddd59365 |
A381813 | Number of connected components, not counting isolated vertices, of the blet graph for n coins. | [
"3",
"2",
"1",
"7",
"2",
"5",
"8",
"8",
"6",
"50",
"12",
"30",
"61",
"62",
"47",
"417",
"102",
"303",
"682",
"696",
"532",
"4904",
"1250",
"3854",
"8911",
"9218",
"7147",
"66735",
"17298",
"53965",
"126348",
"131740",
"103080"
]
| [
"nonn",
"more"
]
| 19 | 3 | 1 | [
"A007039",
"A075273",
"A381812",
"A381813",
"A381814"
]
| null | Pontus von Brömssen, Mar 08 2025 | 2025-03-16T12:19:50 | oeisdata/seq/A381/A381813.seq | 82fea528c6f327617069eb7fb18db209 |
A381814 | Size of the largest component of the blet graph for n coins. | [
"2",
"5",
"20",
"8",
"56",
"56",
"74",
"180",
"660",
"220",
"2288",
"2002",
"2942",
"7280",
"24752",
"8568",
"93024",
"77520",
"120920",
"298452",
"1009470",
"346104",
"3845600",
"3289000",
"5067974",
"12432420",
"42921450",
"14307150",
"161280600",
"140244000",
"215188426",
"524512560",
"1835793960"
]
| [
"nonn",
"more"
]
| 17 | 3 | 1 | [
"A075273",
"A381812",
"A381813",
"A381814"
]
| null | Pontus von Brömssen, Mar 08 2025 | 2025-03-16T10:37:21 | oeisdata/seq/A381/A381814.seq | fa33f31aa051c1b74ddc6284c15dd222 |
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