sequence_id
stringlengths 7
7
| sequence_name
stringlengths 4
573
| sequence
listlengths 1
348
| keywords
listlengths 1
8
| score
int64 1
2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
int64 0
635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
| filename
stringlengths 29
29
| hash
stringlengths 32
32
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A365602
|
Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(3/5).
|
[
"1",
"3",
"21",
"246",
"3990",
"82800",
"2092560",
"62343600",
"2139137760",
"83064002160",
"3600715721040",
"172353630085920",
"9028586395211040",
"513740204261763840",
"31553316959017737600",
"2080500578006553619200",
"146577866381052082876800",
"10988979300484733769667200"
] |
[
"nonn"
] | 12 | 0 | 2 |
[
"A347022",
"A365586",
"A365601",
"A365602",
"A365603",
"A365604"
] | null |
Seiichi Manyama, Sep 11 2023
| 2023-09-13T02:12:40 |
oeisdata/seq/A365/A365602.seq
|
44e346af1685be0bb38e3596296b3966
|
A365603
|
Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(4/5).
|
[
"1",
"4",
"32",
"404",
"6924",
"150000",
"3927480",
"120582360",
"4246964280",
"168767136000",
"7468938047520",
"364284571992480",
"19412919898230240",
"1122216138563359680",
"69941868616009932480",
"4675040053248335097600",
"333605090142406849939200",
"25312518953112479346316800"
] |
[
"nonn"
] | 12 | 0 | 2 |
[
"A347022",
"A365587",
"A365601",
"A365602",
"A365603",
"A365604"
] | null |
Seiichi Manyama, Sep 11 2023
| 2023-09-13T02:12:26 |
oeisdata/seq/A365/A365603.seq
|
63e582c9cd6ddd1e2a1592b751db77b8
|
A365604
|
Expansion of e.g.f. 1 / (1 - 5 * log(1 + x)).
|
[
"1",
"5",
"45",
"610",
"11020",
"248870",
"6744350",
"213233400",
"7704814200",
"313199930400",
"14146162064400",
"702826758144000",
"38093116667766000",
"2236695336601458000",
"141433354184701746000",
"9582086196220281456000",
"692463727252196674560000"
] |
[
"nonn"
] | 14 | 0 | 2 |
[
"A094418",
"A320080",
"A347022",
"A365588",
"A365601",
"A365602",
"A365603",
"A365604"
] | null |
Seiichi Manyama, Sep 11 2023
| 2023-09-13T02:12:13 |
oeisdata/seq/A365/A365604.seq
|
778e5749d2b73a0eff4c0b345aef2dfe
|
A365605
|
Characteristic function of numbers without an inferior odd divisor > 1.
|
[
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0"
] |
[
"nonn"
] | 35 | 1 | null |
[
"A342081",
"A365605"
] | null |
Christian Krause, Sep 11 2023
| 2023-10-08T18:42:11 |
oeisdata/seq/A365/A365605.seq
|
a37b1fb763862f04ea20e8dd599aca12
|
A365606
|
Number of degree 2 vertices in the n-Sierpinski carpet graph.
|
[
"8",
"20",
"84",
"500",
"3540",
"26996",
"212052",
"1684724",
"13442772",
"107437172",
"859182420",
"6872514548",
"54977282004",
"439809752948",
"3518452514388",
"28147543587572",
"225180119118036",
"1801440264196724",
"14411520047331156",
"115292154179921396",
"922337214843187668",
"7378697662956950900",
"59029581136289955924"
] |
[
"nonn",
"easy"
] | 22 | 1 | 1 |
[
"A001018",
"A009964",
"A083233",
"A271939",
"A291066",
"A332705",
"A359452",
"A359453",
"A365606",
"A365607",
"A365608"
] | null |
Allan Bickle, Sep 12 2023
| 2025-02-16T08:34:06 |
oeisdata/seq/A365/A365606.seq
|
a764e2e8e8e4863f64ae6f7811e10f79
|
A365607
|
Number of degree 3 vertices in the n-Sierpinski carpet graph.
|
[
"0",
"40",
"328",
"2536",
"19912",
"158056",
"1260616",
"10073320",
"80551624",
"644308072",
"5154149704",
"41232252904",
"329855188936",
"2638833008488",
"21110638558792",
"168885031942888",
"1351080025960648",
"10808639518937704",
"86469114085259080",
"691752906483344872",
"5534023233270575560",
"44272185810376054120"
] |
[
"nonn",
"easy"
] | 24 | 1 | 2 |
[
"A001018",
"A009964",
"A083233",
"A271939",
"A291066",
"A332705",
"A359452",
"A359453",
"A365606",
"A365607",
"A365608"
] | null |
Allan Bickle, Sep 12 2023
| 2025-02-16T08:34:06 |
oeisdata/seq/A365/A365607.seq
|
295e8b96fa47a82b21176cb0df0df70c
|
A365608
|
Number of degree 4 vertices in the n-Sierpinski carpet graph.
|
[
"0",
"4",
"100",
"1060",
"9316",
"77092",
"624484",
"5019172",
"40223332",
"321996580",
"2576602468",
"20614709284",
"164923342948",
"1319403749668",
"10555281015652",
"84442401180196",
"675539668606564",
"5404318726347556",
"43234553943265636",
"345876443943580708",
"2767011588741012580",
"22136092821505201444",
"177088742906772914020"
] |
[
"nonn",
"easy"
] | 23 | 1 | 2 |
[
"A001018",
"A009964",
"A083233",
"A271939",
"A291066",
"A332705",
"A359452",
"A359453",
"A365606",
"A365607",
"A365608"
] | null |
Allan Bickle, Sep 12 2023
| 2025-02-16T08:34:06 |
oeisdata/seq/A365/A365608.seq
|
6f3512c2dc28356288af5d7d2325bd44
|
A365609
|
G.f. satisfies A(x) = 1 + x^2*A(x)^4*(1 + x*A(x)).
|
[
"1",
"0",
"1",
"1",
"4",
"9",
"27",
"78",
"231",
"715",
"2193",
"6954",
"21999",
"70840",
"228896",
"746650",
"2447757",
"8072208",
"26745627",
"89002364",
"297344960",
"996865397",
"3352918429",
"11310307593",
"38256171642",
"129718262583",
"440855654827",
"1501451066767",
"5123671576890",
"17516503865294"
] |
[
"nonn"
] | 25 | 0 | 5 |
[
"A001005",
"A025250",
"A055113",
"A217358",
"A365609",
"A365690"
] | null |
Seiichi Manyama, Sep 17 2023
| 2023-09-17T10:11:10 |
oeisdata/seq/A365/A365609.seq
|
ec01162d55ac7fd8ec5e99150b34b399
|
A365610
|
Least prime in which the frequency of every digit is n, or -1 if no such number exists.
|
[
"2",
"11",
"-1",
"10010101",
"1000011011",
"-1",
"10000101011101",
"1000000010111111",
"-1",
"10000000011111011101",
"1000000000101101111111",
"-1",
"10000000000001111011111111",
"1000000000000111111101110111",
"-1",
"10000000000000011101111111011111",
"1000000000000000010111111111111111",
"-1"
] |
[
"sign",
"base"
] | 24 | 1 | 1 |
[
"A000040",
"A004022",
"A087395",
"A365610"
] | null |
Jean-Marc Rebert, Sep 12 2023
| 2023-09-21T14:59:45 |
oeisdata/seq/A365/A365610.seq
|
9d297a6102f8f2fd11b8148bdc85d2b9
|
A365611
|
Numbers k such that 10^100000+k is prime.
|
[
"342909",
"346579",
"829767",
"871899",
"1475997",
"1751769",
"2155489",
"2483527",
"2503087",
"2686179",
"2688933",
"3667159",
"3938473",
"3979761",
"4293973",
"4858267",
"5113299",
"5169411",
"5354043",
"5717979",
"6080631",
"6308469",
"6512023",
"6596557",
"7115409",
"7235803",
"7867333",
"8743093",
"8955391"
] |
[
"nonn"
] | 10 | 1 | 1 |
[
"A000040",
"A365611",
"A365612"
] | null |
Robert Price, Sep 12 2023
| 2023-09-18T15:39:28 |
oeisdata/seq/A365/A365611.seq
|
db5292963d3c8ab9d9ee528ae5e99d82
|
A365612
|
Prime gaps: differences between consecutive primes, starting at 10^100000.
|
[
"3670",
"483188",
"42132",
"604098",
"275772",
"403720",
"328038",
"19560",
"183092",
"2754",
"978226",
"271314",
"41288",
"314212",
"564294",
"255032",
"56112",
"184632",
"363936",
"362652",
"227838",
"203554",
"84534",
"518852",
"120394",
"631530",
"875760",
"212298",
"224628",
"45968",
"39600",
"21462",
"138004"
] |
[
"nonn"
] | 11 | 1 | 1 |
[
"A001223",
"A365611",
"A365612"
] | null |
Robert Price, Sep 12 2023
| 2023-09-18T15:39:21 |
oeisdata/seq/A365/A365612.seq
|
92b66b17893070d073371579de1a235a
|
A365613
|
a(n) = number of partitions p of n such that the greatest multiplicity of the parts of p is a part of p.
|
[
"0",
"1",
"0",
"1",
"3",
"2",
"4",
"4",
"9",
"11",
"18",
"19",
"30",
"36",
"51",
"64",
"90",
"107",
"150",
"182",
"239",
"294",
"385",
"466",
"602",
"733",
"928",
"1129",
"1420",
"1714",
"2137",
"2578",
"3177",
"3826",
"4690",
"5617",
"6845",
"8181",
"9898",
"11803",
"14211",
"16878",
"20234",
"23974",
"28596",
"33795",
"40161",
"47311",
"56025",
"65845"
] |
[
"nonn"
] | 10 | 0 | 5 |
[
"A000041",
"A365613",
"A365614",
"A365615",
"A365616"
] | null |
Clark Kimberling, Sep 17 2023
| 2023-09-22T05:23:55 |
oeisdata/seq/A365/A365613.seq
|
56ca7d7e44ebed2325ca83459727d5da
|
A365614
|
a(n) = number of partitions p of n such that the least multiplicity of the parts of p is a part of p.
|
[
"0",
"1",
"0",
"1",
"3",
"4",
"6",
"10",
"13",
"20",
"27",
"36",
"52",
"71",
"94",
"126",
"170",
"216",
"286",
"367",
"473",
"603",
"771",
"963",
"1229",
"1529",
"1910",
"2371",
"2959",
"3623",
"4492",
"5487",
"6740",
"8200",
"10016",
"12099",
"14724",
"17722",
"21402",
"25687",
"30914",
"36892",
"44224",
"52630",
"62781",
"74497",
"88540",
"104646"
] |
[
"nonn"
] | 9 | 0 | 5 |
[
"A000041",
"A365613",
"A365614",
"A365615",
"A365616"
] | null |
Clark Kimberling, Sep 17 2023
| 2023-09-22T05:24:44 |
oeisdata/seq/A365/A365614.seq
|
66f4d82c738b3b734ba762e6d0bcd207
|
A365615
|
a(n) = number of partitions p of n such that the least multiplicity of the parts of p is not a part of p.
|
[
"1",
"0",
"2",
"2",
"2",
"3",
"5",
"5",
"9",
"10",
"15",
"20",
"25",
"30",
"41",
"50",
"61",
"81",
"99",
"123",
"154",
"189",
"231",
"292",
"346",
"429",
"526",
"639",
"759",
"942",
"1112",
"1355",
"1609",
"1943",
"2294",
"2784",
"3253",
"3915",
"4613",
"5498",
"6424",
"7691",
"8950",
"10631",
"12394",
"14637",
"17018",
"20108",
"23255",
"27351",
"31699"
] |
[
"nonn"
] | 11 | 0 | 3 |
[
"A000041",
"A365613",
"A365614",
"A365615",
"A365616"
] | null |
Clark Kimberling, Sep 17 2023
| 2023-09-22T05:25:00 |
oeisdata/seq/A365/A365615.seq
|
e6333fd2a4974b47aee3ed633f9bbc62
|
A365616
|
a(n) = number of partitions p of n such that the greatest multiplicity of the parts of p is not a part of p.
|
[
"1",
"0",
"2",
"2",
"2",
"5",
"7",
"11",
"13",
"19",
"24",
"37",
"47",
"65",
"84",
"112",
"141",
"190",
"235",
"308",
"388",
"498",
"617",
"789",
"973",
"1225",
"1508",
"1881",
"2298",
"2851",
"3467",
"4264",
"5172",
"6317",
"7620",
"9266",
"11132",
"13456",
"16117",
"19382",
"23127",
"27705",
"32940",
"39287",
"46579",
"55339",
"65397",
"77443",
"91248"
] |
[
"nonn"
] | 8 | 0 | 3 |
[
"A000041",
"A365613",
"A365614",
"A365615",
"A365616"
] | null |
Clark Kimberling, Sep 17 2023
| 2023-09-22T05:25:14 |
oeisdata/seq/A365/A365616.seq
|
77660308e895a5f8d6a02b5437e57659
|
A365617
|
Iterated Pochhammer symbol.
|
[
"1",
"1",
"2",
"24",
"421200",
"13257209623458438290962108800"
] |
[
"nonn"
] | 53 | 0 | 3 |
[
"A000142",
"A000407",
"A038155",
"A055462",
"A112332",
"A266083",
"A365617"
] | null |
Darío Clavijo, Sep 12 2023
| 2025-04-27T00:45:56 |
oeisdata/seq/A365/A365617.seq
|
294fea20575bfb548798579399b0d697
|
A365618
|
Table read by antidiagonals: T(n, k) = A000120(n) + A000120(k).
|
[
"0",
"1",
"1",
"1",
"2",
"1",
"2",
"2",
"2",
"2",
"1",
"3",
"2",
"3",
"1",
"2",
"2",
"3",
"3",
"2",
"2",
"2",
"3",
"2",
"4",
"2",
"3",
"2",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"1",
"4",
"3",
"4",
"2",
"4",
"3",
"4",
"1",
"2",
"2",
"4",
"4",
"3",
"3",
"4",
"4",
"2",
"2",
"2",
"3",
"2",
"5",
"3",
"4",
"3",
"5",
"2",
"3",
"2",
"3",
"3",
"3",
"3",
"4",
"4",
"4",
"4",
"3",
"3",
"3",
"3",
"2",
"4",
"3",
"4",
"2",
"5",
"4",
"5",
"2"
] |
[
"nonn",
"tabl",
"base",
"easy"
] | 55 | 0 | 5 |
[
"A000120",
"A365618",
"A367055"
] | null |
Mithra Karamchedu and Sophia Pi, Nov 03 2023
| 2024-01-20T09:11:12 |
oeisdata/seq/A365/A365618.seq
|
3ca8eed7ce29ad58c5616739cf19c125
|
A365619
|
a(n) is the least integer k such that A366110(k) = n, or 0 if there is no such k.
|
[
"0",
"0",
"0",
"0",
"0",
"454",
"0",
"13",
"0",
"0",
"0",
"19",
"0",
"16",
"0",
"17",
"15",
"22",
"6",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"23",
"0",
"396",
"0",
"0",
"0",
"46",
"0",
"148",
"40",
"0",
"8",
"0",
"0",
"652",
"0",
"15980",
"0",
"0",
"0",
"25",
"0",
"0",
"0",
"0",
"0",
"50",
"0",
"0",
"0",
"0",
"0",
"136",
"0",
"0",
"0",
"27",
"0",
"64",
"0",
"0",
"0",
"100",
"0",
"29",
"21",
"0",
"0",
"0",
"0",
"15574",
"0",
"0",
"0",
"0",
"0",
"346"
] |
[
"nonn"
] | 14 | 1 | 6 |
[
"A152454",
"A365619",
"A366110"
] | null |
Michel Marcus, Nov 02 2023
| 2023-11-04T14:01:23 |
oeisdata/seq/A365/A365619.seq
|
a22d533f7c3166a552fdfeb46956284a
|
A365620
|
Number of integer grid points on the circle around (0,0) with radius A088959(n).
|
[
"4",
"12",
"20",
"36",
"60",
"108",
"180",
"252",
"324",
"540",
"756",
"972",
"1620",
"2268",
"2916",
"4860",
"6804",
"8748",
"14580",
"20412",
"26244",
"43740",
"61236",
"72900",
"78732",
"102060",
"131220",
"183708",
"218700",
"236196",
"306180",
"393660",
"551124",
"656100",
"708588",
"918540"
] |
[
"nonn"
] | 25 | 1 | 1 |
[
"A046109",
"A071385",
"A365620"
] | null |
Günter Rote, Sep 12 2023
| 2023-09-25T08:55:42 |
oeisdata/seq/A365/A365620.seq
|
ad4e6bd884f3198ce67a0fddb33aad58
|
A365621
|
Minimum size of a set of polyominoes with n cells such that all other free polyominoes with n cells can be obtained by moving one cell of one of the polyominoes in the set.
|
[
"1",
"1",
"1",
"1",
"2",
"3",
"7"
] |
[
"nonn",
"more"
] | 21 | 1 | 5 |
[
"A098891",
"A365621",
"A367123",
"A367124",
"A367127",
"A367441"
] | null |
Pontus von Brömssen, Nov 14 2023
| 2023-11-19T11:36:10 |
oeisdata/seq/A365/A365621.seq
|
3330f0a27e07f7158ac27bf18fc0819d
|
A365622
|
Expansion of (1/x) * Series_Reversion( x*(1-x)^5/(1+x)^5 ).
|
[
"1",
"10",
"150",
"2670",
"52250",
"1086002",
"23533790",
"525825830",
"12026993010",
"280220428890",
"6627397194022",
"158692955007390",
"3839595257256330",
"93725694152075010",
"2305406918530451950",
"57085385625207424342",
"1421808255906105290210"
] |
[
"nonn"
] | 21 | 0 | 2 |
[
"A032349",
"A363006",
"A365622",
"A365843",
"A365847"
] | null |
Seiichi Manyama, Sep 20 2023
| 2023-09-20T10:00:46 |
oeisdata/seq/A365/A365622.seq
|
d80ea543caf781b9a9b6570eb50e352c
|
A365623
|
T(n,k) is the number of parking functions of length n with cars parking at most k spots away from their preferred spot; square array T(n,k), n>=0, k>=0, read by downward antidiagonals.
|
[
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"6",
"1",
"1",
"3",
"13",
"24",
"1",
"1",
"3",
"16",
"75",
"120",
"1",
"1",
"3",
"16",
"109",
"541",
"720",
"1",
"1",
"3",
"16",
"125",
"918",
"4683",
"5040",
"1",
"1",
"3",
"16",
"125",
"1171",
"9277",
"47293",
"40320",
"1",
"1",
"3",
"16",
"125",
"1296",
"12965",
"109438",
"545835",
"362880",
"1",
"1",
"3",
"16",
"125",
"1296",
"15511",
"166836",
"1475691",
"7087261",
"3628800"
] |
[
"nonn",
"tabl"
] | 50 | 0 | 6 |
[
"A000142",
"A000272",
"A000670",
"A264902",
"A365623",
"A365626",
"A365627"
] | null |
J. Carlos Martínez Mori, Sep 13 2023
| 2023-09-20T18:19:16 |
oeisdata/seq/A365/A365623.seq
|
f36ff3e5530d2cb7a854d879b3141d1a
|
A365624
|
a(n) is the length of the longest word w in the Thue-Morse sequence (A010060) in which every length-n factor of w is unique.
|
[
"2",
"5",
"8",
"12",
"16",
"18",
"24",
"26",
"32",
"34",
"36",
"38",
"48",
"50",
"52",
"54",
"64",
"66",
"68",
"70",
"72",
"74",
"76",
"78",
"96",
"98",
"100",
"102",
"104",
"106",
"108",
"110",
"128",
"130",
"132",
"134",
"136",
"138",
"140",
"142",
"144",
"146",
"148",
"150",
"152",
"154",
"156",
"158",
"192",
"194",
"196",
"198",
"200",
"202",
"204",
"206"
] |
[
"nonn"
] | 39 | 1 | 1 |
[
"A005942",
"A010060",
"A365624",
"A366408"
] | null |
Gandhar Joshi, Sep 13 2023
| 2024-12-19T11:46:19 |
oeisdata/seq/A365/A365624.seq
|
4ee41ff5e16e05473f1735faa6ae2163
|
A365625
|
a(0) = 0, a(1) = 1. let i = a(n-2) and j = a(n-1), then if i,j have a digit in common a(n) is the least novel number having no digit in common with either i or j. If i,j have no common digit, a(n) is the least novel number having a digit in common with at least one of i or j. All digits are decimal.
|
[
"0",
"1",
"10",
"2",
"11",
"12",
"3",
"13",
"4",
"14",
"5",
"15",
"6",
"16",
"7",
"17",
"8",
"18",
"9",
"19",
"20",
"21",
"33",
"22",
"23",
"40",
"24",
"31",
"25",
"26",
"30",
"27",
"28",
"34",
"29",
"32",
"41",
"35",
"36",
"42",
"37",
"38",
"44",
"39",
"43",
"50",
"45",
"61",
"46",
"52",
"47",
"48",
"51",
"49",
"53",
"54",
"60",
"55",
"56",
"70",
"57",
"62",
"58",
"59",
"63",
"64",
"71",
"65"
] |
[
"nonn",
"base",
"fini"
] | 12 | 0 | 3 |
[
"A001477",
"A365625"
] | null |
David James Sycamore, Sep 13 2023
| 2023-09-17T01:59:23 |
oeisdata/seq/A365/A365625.seq
|
81f4e3cdf6b1063f55e6fa244771af7c
|
A365626
|
Number of parking functions of length n with cars parking at most 3 spots away from their preferred spot.
|
[
"1",
"1",
"3",
"16",
"125",
"1171",
"12965",
"166836",
"2455121",
"40675881",
"749029635",
"15173252268",
"335303622765",
"8026962584007",
"206940524177025",
"5716136927184348",
"168418082791822545",
"5272347013042009125",
"174760355153742270543",
"6114528211048906800708",
"225195326302815011830005"
] |
[
"nonn"
] | 13 | 0 | 3 |
[
"A365623",
"A365626"
] | null |
J. Carlos Martínez Mori, Sep 13 2023
| 2023-09-14T13:45:44 |
oeisdata/seq/A365/A365626.seq
|
4b8be64c712157fe8afe72277973cb18
|
A365627
|
Number of parking functions of length n with cars parking at most 4 spots away from their preferred spot.
|
[
"1",
"1",
"3",
"16",
"125",
"1296",
"15511",
"212978",
"3321091",
"58196400",
"1134161181",
"24333706866",
"569786870013",
"14455456239756",
"394940662364775",
"11560567008386106",
"360947377705705971",
"11973823441677468648",
"420576028975783973061",
"15593290472977894193850"
] |
[
"nonn"
] | 6 | 0 | 3 |
[
"A365623",
"A365627"
] | null |
J. Carlos Martínez Mori, Sep 13 2023
| 2023-09-20T17:53:07 |
oeisdata/seq/A365/A365627.seq
|
98565459e87c1298924313d078fbaea0
|
A365628
|
a(n) = binomial(primorial(n), n).
|
[
"1",
"2",
"15",
"4060",
"78738660",
"545754554499462",
"1018081517447240182211275",
"1793004475784081302284255717158418120",
"1943305407393725342965469143054357602760779899437185",
"3772316402417100592416011698371929155605067111502494326520988270728160"
] |
[
"nonn"
] | 28 | 0 | 2 |
[
"A002110",
"A007318",
"A014062",
"A060604",
"A086687",
"A365628"
] | null |
Darío Clavijo, Sep 13 2023
| 2023-09-17T18:33:30 |
oeisdata/seq/A365/A365628.seq
|
cda7e8ee5bd0568696da42cd56638de7
|
A365629
|
Number of 4 X n mazes that can be navigated from the top left corner to the bottom right corner.
|
[
"1",
"216",
"28942",
"3329245",
"358911148",
"37502829018",
"3856945416544",
"393396697543644",
"39951066751274152",
"4047887027105625168",
"409638762069161924728",
"41428094401248851559736",
"4188336537335577744595384",
"423360539638841208001947048",
"42789587016771330584001089176"
] |
[
"nonn",
"easy",
"changed"
] | 44 | 1 | 2 |
[
"A349594",
"A349596",
"A365629",
"A373036"
] | null |
Eugene Nonko, Oct 25 2023
| 2025-07-15T10:23:51 |
oeisdata/seq/A365/A365629.seq
|
6592baeb267451f84dd95496a547fcb5
|
A365630
|
Number of partitions of n with exactly four part sizes.
|
[
"1",
"2",
"5",
"10",
"20",
"30",
"52",
"77",
"117",
"162",
"227",
"309",
"414",
"535",
"692",
"873",
"1100",
"1369",
"1661",
"2030",
"2438",
"2925",
"3450",
"4108",
"4759",
"5570",
"6440",
"7457",
"8491",
"9798",
"11020",
"12593",
"14125",
"15995",
"17820",
"20074",
"22182",
"24833",
"27379",
"30422",
"33351",
"36996",
"40346",
"44445",
"48336",
"53048",
"57494"
] |
[
"nonn"
] | 21 | 10 | 2 |
[
"A000005",
"A002133",
"A002134",
"A060177",
"A116608",
"A365630",
"A365631"
] | null |
Seiichi Manyama, Sep 13 2023
| 2023-09-15T18:41:41 |
oeisdata/seq/A365/A365630.seq
|
9cbf02108d085affc30103adb31fd6e7
|
A365631
|
Number of partitions of n with exactly five part sizes.
|
[
"1",
"2",
"5",
"10",
"20",
"36",
"58",
"95",
"147",
"222",
"323",
"462",
"636",
"889",
"1184",
"1584",
"2060",
"2686",
"3403",
"4353",
"5433",
"6768",
"8319",
"10230",
"12363",
"15011",
"17943",
"21467",
"25403",
"30044",
"35231",
"41294",
"48002",
"55718",
"64328",
"74086",
"84880",
"97071",
"110607",
"125692",
"142313",
"160728",
"181112",
"203438",
"228124"
] |
[
"nonn"
] | 22 | 15 | 2 |
[
"A000005",
"A002133",
"A002134",
"A060177",
"A116608",
"A364809",
"A365630",
"A365631"
] | null |
Seiichi Manyama, Sep 13 2023
| 2023-09-16T17:03:43 |
oeisdata/seq/A365/A365631.seq
|
daf949049f5b1c6120329aefc874b2a7
|
A365632
|
The number of divisors of n that are terms of A072873.
|
[
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"2",
"1",
"1",
"2",
"1",
"1",
"1"
] |
[
"nonn",
"easy",
"mult"
] | 13 | 1 | 4 |
[
"A072873",
"A327939",
"A365632",
"A365633",
"A365634"
] | null |
Amiram Eldar, Sep 14 2023
| 2023-09-20T05:41:08 |
oeisdata/seq/A365/A365632.seq
|
565883734d4a0e8c5e78dc492ac071b9
|
A365633
|
The sum of divisors of n that are terms of A072873.
|
[
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"7",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"3",
"1",
"1",
"4",
"3",
"1",
"1",
"1",
"7",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"7",
"1",
"1",
"1",
"3",
"1",
"4",
"1",
"3",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"15",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"7",
"4",
"1",
"1",
"3",
"1",
"1",
"1"
] |
[
"nonn",
"easy",
"mult"
] | 12 | 1 | 4 |
[
"A072873",
"A327939",
"A332653",
"A365632",
"A365633"
] | null |
Amiram Eldar, Sep 14 2023
| 2023-09-20T01:44:24 |
oeisdata/seq/A365/A365633.seq
|
0b17be19c3557a770926667e1a53605d
|
A365634
|
The number of divisors of n that are terms of A048102.
|
[
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"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",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"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",
"1"
] |
[
"nonn",
"easy",
"mult"
] | 13 | 1 | 4 |
[
"A048102",
"A365632",
"A365634",
"A365635"
] | null |
Amiram Eldar, Sep 14 2023
| 2024-09-05T16:23:07 |
oeisdata/seq/A365/A365634.seq
|
8b44a96a4c01f84027ae5fbee9aef088
|
A365635
|
The largest divisor of n that is a term of A048102.
|
[
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"27",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"27",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"4",
"27",
"1",
"1",
"4",
"1",
"1"
] |
[
"nonn",
"easy",
"mult"
] | 20 | 1 | 4 |
[
"A048102",
"A048103",
"A327939",
"A365634",
"A365635"
] | null |
Amiram Eldar, Sep 14 2023
| 2023-09-20T01:44:30 |
oeisdata/seq/A365/A365635.seq
|
2ac7b104be908bca2217082f78b1fc10
|
A365636
|
a(n) is the smallest multiple of n that is a term of A072873.
|
[
"1",
"4",
"27",
"4",
"3125",
"108",
"823543",
"16",
"27",
"12500",
"285311670611",
"108",
"302875106592253",
"3294172",
"84375",
"16",
"827240261886336764177",
"108",
"1978419655660313589123979",
"12500",
"22235661",
"1141246682444",
"20880467999847912034355032910567",
"432",
"3125",
"1211500426369012",
"27",
"3294172"
] |
[
"nonn",
"easy",
"mult"
] | 15 | 1 | 2 |
[
"A072873",
"A365636",
"A365637"
] | null |
Amiram Eldar, Sep 14 2023
| 2024-02-16T05:27:26 |
oeisdata/seq/A365/A365636.seq
|
f2aa89cb358a592bf1cee4e40a62612a
|
A365637
|
a(n) is the smallest number k such that k*n is a term of A072873.
|
[
"1",
"2",
"9",
"1",
"625",
"18",
"117649",
"2",
"3",
"1250",
"25937424601",
"9",
"23298085122481",
"235298",
"5625",
"1",
"48661191875666868481",
"6",
"104127350297911241532841",
"625",
"1058841",
"51874849202",
"907846434775996175406740561329",
"18",
"125",
"46596170244962",
"1",
"117649",
"88540901833145211536614766025207452637361"
] |
[
"nonn",
"easy",
"mult"
] | 16 | 1 | 2 |
[
"A072873",
"A365636",
"A365637"
] | null |
Amiram Eldar, Sep 14 2023
| 2025-04-27T00:46:00 |
oeisdata/seq/A365/A365637.seq
|
b4b3ab4b9e8509bc4c5ab0bc631fff68
|
A365638
|
Triangular array read by rows: T(n, k) is the number of ways that a k-element transitive tournament can occur as a subtournament of a larger tournament on n labeled vertices.
|
[
"1",
"1",
"1",
"2",
"4",
"2",
"8",
"24",
"24",
"6",
"64",
"256",
"384",
"192",
"24",
"1024",
"5120",
"10240",
"7680",
"1920",
"120",
"32768",
"196608",
"491520",
"491520",
"184320",
"23040",
"720",
"2097152",
"14680064",
"44040192",
"55050240",
"27525120",
"5160960",
"322560",
"5040",
"268435456",
"2147483648",
"7516192768",
"11274289152",
"7046430720",
"1761607680",
"165150720",
"5160960",
"40320"
] |
[
"nonn",
"easy",
"tabl"
] | 27 | 0 | 4 |
[
"A002866",
"A006125",
"A008279",
"A052670",
"A095340",
"A103904",
"A117260",
"A122027",
"A224886",
"A259105",
"A350608",
"A350609",
"A350610",
"A365638",
"A379614"
] | null |
Thomas Scheuerle, Sep 14 2023
| 2024-12-31T15:37:01 |
oeisdata/seq/A365/A365638.seq
|
da6489f427ce82763365c995f539ff20
|
A365639
|
Numbers k such that k! + k^3 + 1 is prime.
|
[
"0",
"1",
"2",
"4",
"6",
"16",
"28",
"42"
] |
[
"nonn",
"hard",
"more"
] | 23 | 1 | 3 |
[
"A000040",
"A000142",
"A000578",
"A001093",
"A038507",
"A073308",
"A080668",
"A365639"
] | null |
Darío Clavijo, Sep 14 2023
| 2024-03-06T01:00:18 |
oeisdata/seq/A365/A365639.seq
|
249d348f43c7baf20f4813c3953c854a
|
A365640
|
Prime powers of the form 2^k + 1.
|
[
"2",
"3",
"5",
"9",
"17",
"257",
"65537"
] |
[
"nonn"
] | 63 | 1 | 1 |
[
"A000961",
"A019434",
"A092506",
"A365640"
] | null |
Juri-Stepan Gerasimov, Nov 10 2023
| 2023-11-16T05:56:52 |
oeisdata/seq/A365/A365640.seq
|
d9bbfa4f636d72e051f43458be7c58e2
|
A365641
|
The minimum number of ways to label each triangle of a triangulation of an n-gon with one of its vertices so that different triangles get different labels (minimum taken over all triangulations).
|
[
"1",
"3",
"7",
"14",
"25",
"41",
"63",
"92",
"128",
"173",
"228",
"293",
"369",
"458",
"561",
"676",
"807",
"955",
"1119",
"1300"
] |
[
"nonn",
"more"
] | 13 | 2 | 2 | null | null |
Günter Rote, Sep 14 2023
| 2023-09-25T08:56:23 |
oeisdata/seq/A365/A365641.seq
|
2ce3aae36270416b34f28b0c77a17c51
|
A365642
|
a(1) = 1, a(2) = 2; a(n) = smallest k such that rad(k) | (a(n-2)+a(n-1)) and k != a(m), m < n, where rad(n) = A007947(n).
|
[
"1",
"2",
"3",
"5",
"4",
"9",
"13",
"8",
"7",
"15",
"11",
"16",
"27",
"43",
"10",
"53",
"21",
"32",
"2809",
"81",
"17",
"14",
"31",
"25",
"28",
"148877",
"45",
"19",
"64",
"83",
"49",
"6",
"55",
"61",
"29",
"12",
"41",
"7890481",
"18",
"179",
"197",
"47",
"122",
"169",
"97",
"38",
"75",
"113",
"94",
"23",
"39",
"62",
"101",
"163",
"22",
"37",
"59",
"24",
"6889",
"223",
"56",
"93",
"149"
] |
[
"nonn"
] | 12 | 1 | 2 |
[
"A007947",
"A365642"
] | null |
Michael De Vlieger, Nov 15 2023
| 2023-11-19T10:33:34 |
oeisdata/seq/A365/A365642.seq
|
42f4617bb992a2b27d0d29803e0104ee
|
A365643
|
Number of permutations whose reverse-complement shares the same recording tableau in the Robinson-Schensted correspondence.
|
[
"1",
"1",
"2",
"2",
"12",
"24",
"136",
"344",
"2872",
"7108",
"80672",
"211056",
"3032376"
] |
[
"nonn",
"more"
] | 30 | 0 | 3 |
[
"A059304",
"A365643"
] | null |
Dang-Son Nguyen, Sep 14 2023
| 2023-12-29T16:42:56 |
oeisdata/seq/A365/A365643.seq
|
e457534c71800dfb86ba7546296c3911
|
A365644
|
Array read by ascending antidiagonals: A(n, k) = k*(10^n - 1)/9 with k >= 0.
|
[
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"11",
"2",
"0",
"0",
"111",
"22",
"3",
"0",
"0",
"1111",
"222",
"33",
"4",
"0",
"0",
"11111",
"2222",
"333",
"44",
"5",
"0",
"0",
"111111",
"22222",
"3333",
"444",
"55",
"6",
"0",
"0",
"1111111",
"222222",
"33333",
"4444",
"555",
"66",
"7",
"0",
"0",
"11111111",
"2222222",
"333333",
"44444",
"5555",
"666",
"77",
"8",
"0"
] |
[
"nonn",
"base",
"easy",
"tabl"
] | 9 | 0 | 8 |
[
"A000004",
"A001477",
"A002275",
"A002276",
"A002277",
"A002278",
"A002279",
"A002280",
"A002281",
"A002282",
"A002283",
"A008593",
"A053422",
"A105279",
"A132583",
"A177769",
"A365644",
"A365645",
"A365646"
] | null |
Stefano Spezia, Sep 14 2023
| 2023-09-17T02:47:55 |
oeisdata/seq/A365/A365644.seq
|
4d45082edd3b15f5fac06341f4d088b0
|
A365645
|
a(n) = n*(1 + n)*(10^n - 1)/18.
|
[
"0",
"1",
"33",
"666",
"11110",
"166665",
"2333331",
"31111108",
"399999996",
"4999999995",
"61111111105",
"733333333326",
"8666666666658",
"101111111111101",
"1166666666666655",
"13333333333333320",
"151111111111111096",
"1699999999999999983",
"18999999999999999981",
"211111111111111111090",
"2333333333333333333310"
] |
[
"nonn",
"easy"
] | 12 | 0 | 3 |
[
"A365644",
"A365645"
] | null |
Stefano Spezia, Sep 14 2023
| 2023-09-17T05:40:05 |
oeisdata/seq/A365/A365645.seq
|
e1eacd4092b934258167ca33b3acec86
|
A365646
|
a(n) is the permanent of the n X n matrix M(n) whose generic M[i, j] = j*(10^i - 1)/9 with 1 <= i, j <= n.
|
[
"1",
"1",
"44",
"43956",
"781361856",
"217042789550400",
"868170290030441798400",
"47267044397174696636039097600",
"33612120124091913005718848881499750400",
"302509080814318135934642422882028113666502246400",
"33612120087118580872578956587618207930922159448149975040000"
] |
[
"nonn"
] | 13 | 0 | 3 |
[
"A365644",
"A365646"
] | null |
Stefano Spezia, Sep 14 2023
| 2023-09-17T10:01:45 |
oeisdata/seq/A365/A365646.seq
|
0cec8541c3e7286d35d3429504a9dd99
|
A365647
|
Dirichlet convolution of Dedekind psi function with reduced totient function.
|
[
"1",
"4",
"6",
"11",
"10",
"24",
"14",
"26",
"26",
"40",
"22",
"64",
"26",
"56",
"56",
"58",
"34",
"104",
"38",
"106",
"78",
"88",
"46",
"148",
"74",
"104",
"102",
"148",
"58",
"224",
"62",
"128",
"122",
"136",
"128",
"272",
"74",
"152",
"144",
"244",
"82",
"312",
"86",
"232",
"232",
"184",
"94",
"326",
"146",
"296",
"188",
"274",
"106",
"408",
"200",
"340",
"210",
"232",
"118"
] |
[
"nonn"
] | 10 | 1 | 2 |
[
"A000040",
"A001615",
"A002322",
"A365647",
"A365648"
] | null |
Torlach Rush, Sep 14 2023
| 2023-09-20T15:59:16 |
oeisdata/seq/A365/A365647.seq
|
62e3863d46f2e859db72e394fd7165e4
|
A365648
|
Dirichlet convolution of sigma with reduced totient function.
|
[
"1",
"4",
"6",
"12",
"10",
"24",
"14",
"30",
"27",
"40",
"22",
"70",
"26",
"56",
"56",
"70",
"34",
"108",
"38",
"116",
"78",
"88",
"46",
"172",
"75",
"104",
"108",
"162",
"58",
"224",
"62",
"158",
"122",
"136",
"128",
"310",
"74",
"152",
"144",
"284",
"82",
"312",
"86",
"254",
"242",
"184",
"94",
"396",
"147",
"300",
"188",
"300",
"106",
"432",
"200",
"396",
"210",
"232",
"118"
] |
[
"nonn"
] | 12 | 1 | 2 |
[
"A000040",
"A000203",
"A002322",
"A365647",
"A365648"
] | null |
Torlach Rush, Sep 14 2023
| 2023-09-20T15:59:47 |
oeisdata/seq/A365/A365648.seq
|
95415a19233cd6c243573131d9f5d257
|
A365649
|
Dirichlet convolution of sigma with Dedekind psi function.
|
[
"1",
"6",
"8",
"22",
"12",
"48",
"16",
"66",
"41",
"72",
"24",
"176",
"28",
"96",
"96",
"178",
"36",
"246",
"40",
"264",
"128",
"144",
"48",
"528",
"97",
"168",
"176",
"352",
"60",
"576",
"64",
"450",
"192",
"216",
"192",
"902",
"76",
"240",
"224",
"792",
"84",
"768",
"88",
"528",
"492",
"288",
"96",
"1424",
"177",
"582",
"288",
"616",
"108",
"1056",
"288",
"1056",
"320"
] |
[
"nonn",
"easy",
"mult"
] | 13 | 1 | 2 |
[
"A000040",
"A000203",
"A001615",
"A365647",
"A365648",
"A365649"
] | null |
Torlach Rush, Sep 14 2023
| 2023-09-20T16:00:11 |
oeisdata/seq/A365/A365649.seq
|
31ef04a7075994cf02ec00512d70769b
|
A365650
|
Number of free n-polyominoids, allowing both corner- and edge-connections.
|
[
"1",
"4",
"36",
"660",
"16687"
] |
[
"nonn",
"hard",
"more"
] | 11 | 1 | 2 |
[
"A000105",
"A030222",
"A075679",
"A365650",
"A365651",
"A365652",
"A366766"
] | null |
Pontus von Brömssen, Sep 17 2023
| 2023-11-04T18:24:35 |
oeisdata/seq/A365/A365650.seq
|
ba56a695280120eeaefa8083f1c87479
|
A365651
|
Number of fixed n-polyominoids, allowing both corner- and edge-connections.
|
[
"3",
"48",
"1072",
"27732",
"781200"
] |
[
"nonn",
"hard",
"more"
] | 10 | 1 | 1 |
[
"A001168",
"A006770",
"A075678",
"A365650",
"A365651",
"A365653",
"A366767"
] | null |
Pontus von Brömssen, Sep 17 2023
| 2023-12-04T16:43:38 |
oeisdata/seq/A365/A365651.seq
|
e0e3d8a881055bef8799fa0ab3070f71
|
A365652
|
Number of free n-polyominoids, allowing corner-connections only.
|
[
"1",
"2",
"19",
"293",
"6590",
"168753"
] |
[
"nonn",
"hard",
"more"
] | 12 | 1 | 2 |
[
"A075679",
"A365650",
"A365652",
"A365653",
"A366766"
] | null |
Pontus von Brömssen, Sep 17 2023
| 2023-11-04T18:24:49 |
oeisdata/seq/A365/A365652.seq
|
6541e6d31efd321460da6cd9b46dd526
|
A365653
|
Number of fixed n-polyominoids, allowing corner-connections only.
|
[
"3",
"30",
"554",
"12453",
"308313",
"8055534"
] |
[
"nonn",
"hard",
"more"
] | 10 | 1 | 1 |
[
"A075678",
"A365651",
"A365652",
"A365653",
"A366767"
] | null |
Pontus von Brömssen, Sep 17 2023
| 2023-12-04T16:43:51 |
oeisdata/seq/A365/A365653.seq
|
b3fc45fcc1aba04b2645ce590782b612
|
A365654
|
Number of free n-polyominoids, allowing right-angled connections only ("hard" polyominoids).
|
[
"1",
"1",
"5",
"16",
"90",
"537",
"3826",
"28655",
"225534"
] |
[
"nonn",
"hard",
"more"
] | 32 | 1 | 3 |
[
"A075679",
"A365559",
"A365654",
"A365655",
"A366766"
] | null |
Pontus von Brömssen, Sep 17 2023
| 2025-06-11T01:01:05 |
oeisdata/seq/A365/A365654.seq
|
6d2e3093a37e9911a68e9df3cc3f420c
|
A365655
|
Number of fixed n-polyominoids, allowing right-angled connections only ("hard" polyominoids).
|
[
"3",
"12",
"68",
"438",
"3054",
"22417",
"170610",
"1334316"
] |
[
"nonn",
"hard",
"more"
] | 13 | 1 | 1 |
[
"A075678",
"A365654",
"A365655",
"A366767"
] | null |
Pontus von Brömssen, Sep 17 2023
| 2023-12-04T16:44:24 |
oeisdata/seq/A365/A365655.seq
|
6031f583fbc04cf28dcab16a7fb08be5
|
A365656
|
Array T(n,k) read by antidiagonals (downward): T(n,1) = A005117(n) (squarefree numbers > 1); for k > 1, columns are nonsquarefree numbers (in descending order) with exactly the same prime factors as T(n,1).
|
[
"1",
"2",
"4",
"3",
"8",
"9",
"5",
"16",
"27",
"25",
"6",
"32",
"81",
"125",
"12",
"7",
"64",
"243",
"625",
"18",
"49",
"10",
"128",
"729",
"3125",
"24",
"343",
"20",
"11",
"256",
"2187",
"15625",
"36",
"2401",
"40",
"121",
"13",
"512",
"6561",
"78125",
"48",
"16807",
"50",
"1331",
"169",
"14",
"1024",
"19683",
"390625",
"54",
"117649",
"80",
"14641",
"2197",
"28",
"15"
] |
[
"nonn",
"tabf"
] | 32 | 0 | 2 |
[
"A002260",
"A005117",
"A007947",
"A065642",
"A284311",
"A284457",
"A365656"
] | null |
Michael De Vlieger, Nov 17 2023
| 2024-01-23T16:18:49 |
oeisdata/seq/A365/A365656.seq
|
b125fe58ae0571369d46356410b2c746
|
A365657
|
Integers k such that k^2 can be written as the sum of three positive fourth powers.
|
[
"481",
"1924",
"4329",
"7696",
"12025",
"17316",
"23569",
"24961",
"28721",
"30784",
"38961",
"48100",
"58201",
"65441",
"69121",
"69264",
"81289",
"94276",
"99844",
"108225",
"113241",
"114884",
"123136",
"139009",
"155844",
"173641",
"192400",
"212121",
"224649",
"232804",
"254449",
"258489",
"261764",
"276484",
"277056",
"300625",
"325156"
] |
[
"nonn"
] | 43 | 1 | 1 |
[
"A003828",
"A365657",
"A365688"
] | null |
Jud McCranie, Sep 14 2023
| 2023-09-28T22:21:24 |
oeisdata/seq/A365/A365657.seq
|
674b522712c57d2fd02be603824f5cad
|
A365658
|
Triangle read by rows where T(n,k) is the number of integer partitions of n with k distinct possible sums of nonempty submultisets.
|
[
"1",
"1",
"1",
"1",
"0",
"2",
"1",
"1",
"1",
"2",
"1",
"0",
"2",
"0",
"4",
"1",
"1",
"3",
"0",
"1",
"5",
"1",
"0",
"3",
"0",
"3",
"0",
"8",
"1",
"1",
"3",
"2",
"2",
"1",
"2",
"10",
"1",
"0",
"5",
"0",
"3",
"0",
"5",
"0",
"16",
"1",
"1",
"4",
"0",
"6",
"2",
"4",
"2",
"2",
"20",
"1",
"0",
"5",
"0",
"5",
"0",
"8",
"0",
"6",
"0",
"31",
"1",
"1",
"6",
"2",
"3",
"6",
"6",
"1",
"4",
"4",
"4",
"39",
"1",
"0",
"6",
"0",
"6",
"0",
"12",
"0",
"8",
"0",
"13",
"0",
"55"
] |
[
"nonn",
"tabl"
] | 13 | 1 | 6 |
[
"A000009",
"A000041",
"A000124",
"A046663",
"A108917",
"A122768",
"A126796",
"A137719",
"A299701",
"A304792",
"A364272",
"A364916",
"A365381",
"A365543",
"A365658",
"A365660",
"A365661"
] | null |
Gus Wiseman, Sep 16 2023
| 2025-04-08T13:21:27 |
oeisdata/seq/A365/A365658.seq
|
16b281793562fba593cd8a22e598c96f
|
A365659
|
Number of strict integer partitions of n that either have (1) length 2, or (2) greatest part n/2.
|
[
"0",
"0",
"0",
"1",
"1",
"2",
"3",
"3",
"4",
"4",
"6",
"5",
"8",
"6",
"10",
"7",
"12",
"8",
"15",
"9",
"18",
"10",
"21",
"11",
"25",
"12",
"29",
"13",
"34",
"14",
"40",
"15",
"46",
"16",
"53",
"17",
"62",
"18",
"71",
"19",
"82",
"20",
"95",
"21",
"109",
"22",
"125",
"23",
"144",
"24",
"165",
"25",
"189",
"26",
"217",
"27",
"248",
"28",
"283",
"29",
"324"
] |
[
"nonn"
] | 14 | 0 | 6 |
[
"A000009",
"A008967",
"A046663",
"A068911",
"A095944",
"A140106",
"A238628",
"A364272",
"A364914",
"A365046",
"A365376",
"A365377",
"A365543",
"A365544",
"A365659"
] | null |
Gus Wiseman, Sep 16 2023
| 2023-09-18T14:09:19 |
oeisdata/seq/A365/A365659.seq
|
5a3dc043b90db47dd90bb50dd605fb71
|
A365660
|
Number of integer partitions of 2n with exactly n distinct sums of nonempty submultisets.
|
[
"1",
"1",
"1",
"3",
"2",
"6",
"6",
"16",
"12",
"20",
"26",
"59",
"45",
"79",
"94",
"186",
"142",
"231",
"244",
"442",
"470",
"616",
"746",
"1340",
"1053",
"1548",
"1852",
"2780",
"2826",
"3874",
"4320",
"6617",
"6286",
"7924",
"9178",
"13180",
"13634",
"17494",
"20356",
"28220",
"29176",
"37188",
"41932",
"56037"
] |
[
"nonn",
"more"
] | 17 | 0 | 4 |
[
"A000009",
"A000041",
"A000124",
"A002219",
"A008967",
"A046663",
"A095944",
"A122768",
"A126796",
"A299701",
"A304792",
"A364272",
"A364349",
"A364911",
"A365376",
"A365377",
"A365543",
"A365658",
"A365660",
"A365661",
"A365663"
] | null |
Gus Wiseman, Sep 16 2023
| 2023-09-21T11:11:01 |
oeisdata/seq/A365/A365660.seq
|
bcd0801c0cd24cf6e15c3b07ee874388
|
A365661
|
Triangle read by rows where T(n,k) is the number of strict integer partitions of n with a submultiset summing to k.
|
[
"1",
"1",
"1",
"1",
"0",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"0",
"1",
"2",
"3",
"1",
"1",
"1",
"1",
"3",
"4",
"2",
"2",
"1",
"2",
"2",
"4",
"5",
"2",
"2",
"2",
"2",
"2",
"2",
"5",
"6",
"3",
"2",
"3",
"1",
"3",
"2",
"3",
"6",
"8",
"3",
"3",
"4",
"3",
"3",
"4",
"3",
"3",
"8",
"10",
"5",
"4",
"5",
"4",
"3",
"4",
"5",
"4",
"5",
"10",
"12",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"12"
] |
[
"nonn",
"tabl"
] | 11 | 0 | 7 |
[
"A000009",
"A000124",
"A002219",
"A006827",
"A046663",
"A108796",
"A108917",
"A122768",
"A237258",
"A275972",
"A299701",
"A304792",
"A364272",
"A364349",
"A364916",
"A365311",
"A365376",
"A365381",
"A365541",
"A365543",
"A365661",
"A365663"
] | null |
Gus Wiseman, Sep 16 2023
| 2025-04-05T23:17:49 |
oeisdata/seq/A365/A365661.seq
|
ea97f18a874d17ae5c6253e72b677f26
|
A365662
|
Number of ordered pairs of disjoint strict integer partitions of n.
|
[
"1",
"0",
"0",
"2",
"2",
"6",
"8",
"14",
"18",
"32",
"42",
"66",
"92",
"136",
"190",
"280",
"374",
"532",
"744",
"1014",
"1366",
"1896",
"2512",
"3384",
"4526",
"6006",
"7910",
"10496",
"13648",
"17842",
"23338",
"30116",
"38826",
"50256",
"64298",
"82258",
"105156",
"133480",
"169392",
"214778",
"270620",
"340554",
"428772",
"536302",
"670522"
] |
[
"nonn"
] | 14 | 0 | 4 |
[
"A000009",
"A000041",
"A000124",
"A000244",
"A000302",
"A000712",
"A001255",
"A002219",
"A006827",
"A032302",
"A046663",
"A054440",
"A064914",
"A108796",
"A122768",
"A237258",
"A260664",
"A260669",
"A276024",
"A284640",
"A304792",
"A364272",
"A364349",
"A365661",
"A365662",
"A365663"
] | null |
Gus Wiseman, Sep 19 2023
| 2025-04-24T06:23:37 |
oeisdata/seq/A365/A365662.seq
|
3d0dfa6683a8db4b6fde383301cacb25
|
A365663
|
Triangle read by rows where T(n,k) is the number of strict integer partitions of n without a subset summing to k.
|
[
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"2",
"2",
"2",
"2",
"2",
"3",
"2",
"2",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"4",
"3",
"5",
"3",
"4",
"3",
"5",
"5",
"4",
"5",
"5",
"4",
"5",
"5",
"5",
"6",
"5",
"6",
"7",
"6",
"5",
"6",
"5",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"8",
"9",
"8",
"8",
"8",
"11",
"8",
"8",
"8",
"9",
"8",
"10",
"11",
"10",
"10",
"10",
"10",
"10",
"10",
"10",
"10",
"11",
"10",
"12",
"13",
"11",
"13",
"11",
"12",
"15",
"12",
"11",
"13",
"11",
"13",
"12"
] |
[
"nonn",
"tabl"
] | 23 | 2 | 5 |
[
"A000009",
"A000124",
"A002219",
"A006827",
"A025147",
"A046663",
"A108796",
"A108917",
"A122768",
"A124506",
"A237258",
"A275972",
"A299701",
"A304792",
"A321142",
"A326083",
"A364272",
"A364349",
"A364350",
"A364839",
"A364916",
"A365311",
"A365376",
"A365381",
"A365541",
"A365543",
"A365661",
"A365663",
"A365922"
] | null |
Gus Wiseman, Sep 17 2023
| 2025-04-05T23:17:57 |
oeisdata/seq/A365/A365663.seq
|
32012be8e08cbc9b157e9c8a5ea4c858
|
A365664
|
Expansion of Sum_{0<i<j<k<l} q^(i+j+k+l)/( (1-q^i)*(1-q^j)*(1-q^k)*(1-q^l) )^2.
|
[
"1",
"3",
"9",
"22",
"51",
"97",
"188",
"330",
"568",
"918",
"1452",
"2233",
"3344",
"4884",
"7004",
"9856",
"13653",
"18699",
"25080",
"33462",
"43918",
"57304",
"73668",
"94482",
"119262",
"150285",
"187231",
"232560",
"285660",
"350746",
"425627",
"516477",
"620731",
"745503",
"887796",
"1056669",
"1247521",
"1472460",
"1726054",
"2021327"
] |
[
"nonn"
] | 36 | 10 | 2 |
[
"A000203",
"A001158",
"A001160",
"A002127",
"A002128",
"A010816",
"A013955",
"A060043",
"A365630",
"A365664",
"A365665",
"A365666"
] | null |
Seiichi Manyama, Sep 15 2023
| 2025-01-07T01:59:10 |
oeisdata/seq/A365/A365664.seq
|
84c85f10092ea1b01f2971e245a6b58b
|
A365665
|
Expansion of Sum_{0<i<j<k<l<m} q^(i+j+k+l+m)/( (1-q^i)*(1-q^j)*(1-q^k)*(1-q^l)*(1-q^m) )^2.
|
[
"1",
"3",
"9",
"22",
"51",
"108",
"208",
"390",
"693",
"1193",
"1977",
"3195",
"4995",
"7722",
"11583",
"17164",
"24882",
"35685",
"50205",
"70083",
"96300",
"131101",
"176358",
"235377",
"310651",
"407352",
"529074",
"682750",
"874038",
"1112085",
"1405521",
"1766259",
"2206413",
"2741431",
"3389052",
"4168089",
"5103450",
"6218469"
] |
[
"nonn"
] | 17 | 15 | 2 |
[
"A000203",
"A002127",
"A002128",
"A010816",
"A060043",
"A365631",
"A365664",
"A365665",
"A365667"
] | null |
Seiichi Manyama, Sep 15 2023
| 2023-09-15T10:29:04 |
oeisdata/seq/A365/A365665.seq
|
4f14f1e36eb506aee2a12a065ea2faa0
|
A365666
|
Expansion of Sum_{0<i<j<k<l} q^(2*(i+j+k+l)-4)/( (1-q^(2*i-1))*(1-q^(2*j-1))*(1-q^(2*k-1))*(1-q^(2*l-1)) )^2.
|
[
"1",
"2",
"4",
"8",
"14",
"24",
"40",
"64",
"100",
"144",
"212",
"304",
"424",
"588",
"800",
"1072",
"1422",
"1864",
"2408",
"3080",
"3950",
"4972",
"6224",
"7760",
"9564",
"11742",
"14344",
"17384",
"20968",
"25204",
"30112",
"35840",
"42548",
"50078",
"58888",
"69048",
"80474",
"93628",
"108608",
"125408",
"144536",
"166224",
"190348"
] |
[
"nonn"
] | 14 | 16 | 2 |
[
"A002131",
"A002132",
"A015128",
"A060046",
"A060047",
"A365666",
"A365667"
] | null |
Seiichi Manyama, Sep 15 2023
| 2023-09-15T10:10:19 |
oeisdata/seq/A365/A365666.seq
|
6ea6d9abf024441b5052d3a0fe790cdf
|
A365667
|
Expansion of Sum_{0<i<j<k<l<m} q^(2*(i+j+k+l+m)-5)/( (1-q^(2*i-1))*(1-q^(2*j-1))*(1-q^(2*k-1))*(1-q^(2*l-1))*(1-q^(2*m-1)) )^2.
|
[
"1",
"2",
"4",
"8",
"14",
"24",
"40",
"64",
"100",
"154",
"232",
"332",
"480",
"680",
"944",
"1304",
"1774",
"2384",
"3180",
"4200",
"5488",
"7120",
"9160",
"11680",
"14869",
"18740",
"23468",
"29280",
"36278",
"44720",
"54904",
"67040",
"81464",
"98658",
"118936",
"142792",
"170902",
"203760",
"242120",
"286624",
"338366",
"398160",
"467148"
] |
[
"nonn"
] | 13 | 25 | 2 |
[
"A002131",
"A002132",
"A015128",
"A060046",
"A060047",
"A365666",
"A365667"
] | null |
Seiichi Manyama, Sep 15 2023
| 2023-09-15T10:33:06 |
oeisdata/seq/A365/A365667.seq
|
49e7eb28bc718c206782b0be10632e38
|
A365668
|
G.f. A(x) satisfies: A(x) = x * (1 + A(x))^5 / (1 - 2 * A(x)).
|
[
"0",
"1",
"7",
"73",
"905",
"12354",
"179305",
"2715192",
"42414021",
"678476755",
"11058588574",
"182999237590",
"3066447596459",
"51926183715280",
"887204891847960",
"15276037569668880",
"264797324173666845",
"4617195655522976361",
"80930337327794271445",
"1425171253004955494215",
"25202145191953299213490"
] |
[
"nonn"
] | 48 | 0 | 3 |
[
"A001296",
"A002294",
"A064063",
"A365668",
"A365755",
"A366014",
"A366035",
"A366036",
"A366037"
] | null |
Ilya Gutkovskiy, Sep 26 2023
| 2025-02-16T08:34:06 |
oeisdata/seq/A365/A365668.seq
|
a095880d615c248207c9cad7c17d4b2f
|
A365669
|
Number of distinct circles created after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex.
|
[
"0",
"1",
"2",
"6",
"114",
"42103152"
] |
[
"nonn",
"more",
"hard"
] | 8 | 1 | 3 |
[
"A359569",
"A359570",
"A359571",
"A359619",
"A359931",
"A360350",
"A361622",
"A365669"
] | null |
Scott R. Shannon, Sep 15 2023
| 2023-10-05T08:37:00 |
oeisdata/seq/A365/A365669.seq
|
2f518381893ddf9e92c5d290853d6982
|
A365670
|
Number of perfect powers k which are not prime powers, and 1 < k < 10^n.
|
[
"0",
"1",
"14",
"72",
"257",
"873",
"2838",
"9085",
"28979",
"92145",
"292832",
"930124",
"2953569",
"9376798",
"29760901",
"94434276",
"299569798",
"950072891",
"3012393832",
"9549260877",
"30264906899",
"95902117819",
"303839485659",
"962486295193",
"3048497625289",
"9654373954803",
"30571355398031",
"96797106918709"
] |
[
"nonn"
] | 27 | 1 | 3 |
[
"A001597",
"A024619",
"A089579",
"A131605",
"A246655",
"A267574",
"A365670"
] | null |
Peter Luschny, Sep 16 2023
| 2024-08-15T02:02:09 |
oeisdata/seq/A365/A365670.seq
|
1fdd4254fdfa8b4ac610856904167db5
|
A365671
|
a(n) = denominator(4^n * n! * [x^n] sqrt(x / (e^x - 1))).
|
[
"1",
"1",
"3",
"1",
"5",
"3",
"21",
"3",
"45",
"5",
"11",
"1",
"91",
"35",
"45",
"3",
"17",
"3",
"1995",
"21",
"3465",
"165",
"115",
"45",
"2925",
"819",
"189",
"7",
"145",
"5",
"341",
"11",
"1309",
"119",
"1",
"1",
"9139",
"247",
"65",
"7",
"2255",
"495",
"148995",
"3465",
"108675",
"2415",
"1645",
"7",
"270725",
"5525",
"21879",
"429",
"583",
"33",
"4389",
"399",
"4959"
] |
[
"nonn",
"frac"
] | 6 | 0 | 3 |
[
"A126156",
"A241885",
"A365671"
] | null |
Peter Luschny, Sep 29 2023
| 2023-09-29T14:24:53 |
oeisdata/seq/A365/A365671.seq
|
4971ee5135c0b06e9bad6bdde94feaf3
|
A365672
|
Triangle read by rows. T(n, k) = 1 if k = 0, equals T(n, k-1) if k = n, and otherwise is (n - k + 1) * (2 * (n - k) + 1) * T(n, k - 1) + T(n - 1, k).
|
[
"1",
"1",
"1",
"1",
"7",
"7",
"1",
"22",
"139",
"139",
"1",
"50",
"889",
"5473",
"5473",
"1",
"95",
"3549",
"58708",
"357721",
"357721",
"1",
"161",
"10794",
"360940",
"5771821",
"34988647",
"34988647",
"1",
"252",
"27426",
"1595110",
"50434901",
"791512162",
"4784061619",
"4784061619"
] |
[
"nonn",
"tabl"
] | 9 | 0 | 5 |
[
"A000384",
"A126156",
"A365672",
"A365673"
] | null |
Peter Luschny, Sep 29 2023
| 2023-10-01T07:13:10 |
oeisdata/seq/A365/A365672.seq
|
ca5b1a424f63819a74f16a11a1fa4308
|
A365673
|
Array A(n, k) read by ascending antidiagonals. Polygonal number weighted generalized Catalan sequences.
|
[
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"4",
"1",
"1",
"1",
"4",
"15",
"8",
"1",
"1",
"1",
"5",
"34",
"105",
"16",
"1",
"1",
"1",
"6",
"61",
"496",
"945",
"32",
"1",
"1",
"1",
"7",
"96",
"1385",
"11056",
"10395",
"64",
"1",
"1",
"1",
"8",
"139",
"2976",
"50521",
"349504",
"135135",
"128",
"1",
"1",
"1",
"9",
"190",
"5473",
"151416",
"2702765",
"14873104",
"2027025",
"256",
"1"
] |
[
"nonn",
"tabl"
] | 38 | 0 | 9 |
[
"A000012",
"A000217",
"A000290",
"A000326",
"A000364",
"A000384",
"A001147",
"A001477",
"A001498",
"A002105",
"A009766",
"A011782",
"A060058",
"A080956",
"A112934",
"A126151",
"A126156",
"A258837",
"A303943",
"A305532",
"A305533",
"A317302",
"A365672",
"A365673",
"A365674",
"A366137",
"A366138",
"A366149",
"A366150"
] | null |
Peter Luschny, Sep 30 2023
| 2023-11-27T06:22:40 |
oeisdata/seq/A365/A365673.seq
|
2b28d9ffa96b3b88de52028e21ad0549
|
A365674
|
Triangle read by rows. T(n, k) = ((n - k + 1)*(n - k + 2)/2) * T(n, k - 1) + T(n - 1, k) for 0 < k < n, T(n, 0) = 1 and T(n, n) = T(n, n - 1) for n > 0.
|
[
"1",
"1",
"1",
"1",
"4",
"4",
"1",
"10",
"34",
"34",
"1",
"20",
"154",
"496",
"496",
"1",
"35",
"504",
"3520",
"11056",
"11056",
"1",
"56",
"1344",
"16960",
"112816",
"349504",
"349504",
"1",
"84",
"3108",
"63580",
"748616",
"4841200",
"14873104",
"14873104",
"1",
"120",
"6468",
"199408",
"3739736",
"42238560",
"268304464",
"819786496",
"819786496"
] |
[
"nonn",
"tabl"
] | 7 | 0 | 5 |
[
"A000217",
"A002105",
"A365673",
"A365674"
] | null |
Peter Luschny, Sep 30 2023
| 2023-09-30T20:58:06 |
oeisdata/seq/A365/A365674.seq
|
e4ae489e97c206a1f3fba4c30706116d
|
A365675
|
a(n) = Sum_{k=0..n} p(k) where the p(k) are the partial sums of row n of A365676.
|
[
"1",
"1",
"4",
"8",
"18",
"30",
"58",
"90",
"153",
"233",
"365",
"533",
"806",
"1142",
"1652",
"2308",
"3243",
"4431",
"6103",
"8203",
"11080",
"14710",
"19540",
"25612",
"33612",
"43570",
"56476",
"72548",
"93080",
"118490",
"150699",
"190315",
"240046",
"301042",
"376887",
"469515",
"583993",
"723073",
"893815",
"1100615",
"1352888"
] |
[
"nonn"
] | 8 | 0 | 3 |
[
"A000070",
"A365675",
"A365676"
] | null |
Peter Luschny, Sep 16 2023
| 2023-09-17T02:02:48 |
oeisdata/seq/A365/A365675.seq
|
cdf378867627938ca970183c28655b47
|
A365676
|
Triangle read by rows: T(n, k) is the number of partitions of n having exactly k distinct part sizes, for 0 <= k <= n.
|
[
"1",
"0",
"1",
"0",
"2",
"0",
"0",
"2",
"1",
"0",
"0",
"3",
"2",
"0",
"0",
"0",
"2",
"5",
"0",
"0",
"0",
"0",
"4",
"6",
"1",
"0",
"0",
"0",
"0",
"2",
"11",
"2",
"0",
"0",
"0",
"0",
"0",
"4",
"13",
"5",
"0",
"0",
"0",
"0",
"0",
"0",
"3",
"17",
"10",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"4",
"22",
"15",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"2",
"27",
"25",
"2",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"6",
"29",
"37",
"5",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0"
] |
[
"nonn",
"tabl"
] | 37 | 0 | 5 |
[
"A000005",
"A000041",
"A002133",
"A002134",
"A060177",
"A116608",
"A365630",
"A365631",
"A365676"
] | null |
Peter Luschny, Sep 15 2023
| 2025-03-28T02:10:45 |
oeisdata/seq/A365/A365676.seq
|
dcdd89b388c730fc19210a6aa352b1d8
|
A365677
|
Number of increasing geometric progressions in {1,2,3,...,n} with rational ratio and length >= 3.
|
[
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"3",
"5",
"5",
"5",
"6",
"6",
"6",
"6",
"11",
"11",
"13",
"13",
"14",
"14",
"14",
"14",
"16",
"20",
"20",
"24",
"25",
"25",
"25",
"25",
"31",
"31",
"31",
"31",
"36",
"36",
"36",
"36",
"38",
"38",
"38",
"38",
"39",
"41",
"41",
"41",
"46",
"52",
"56",
"56",
"57",
"57",
"61",
"61",
"63",
"63",
"63",
"63",
"64",
"64",
"64",
"66",
"79",
"79",
"79",
"79",
"80",
"80",
"80",
"80",
"86",
"86",
"86",
"90",
"91",
"91"
] |
[
"nonn"
] | 60 | 1 | 8 |
[
"A051336",
"A078651",
"A365677",
"A366471"
] | null |
Scott R. Shannon and N. J. A. Sloane, Oct 23 2023
| 2023-10-24T12:57:09 |
oeisdata/seq/A365/A365677.seq
|
1c99b110797b9aaceda1da037fe666ff
|
A365678
|
Primes p whose index has a submultiset of their decimal digits.
|
[
"17",
"367",
"491",
"1327",
"1823",
"2039",
"2131",
"2143",
"2153",
"2693",
"4621",
"5417",
"5701",
"6481",
"6883",
"7459",
"7691",
"10723",
"11483",
"11593",
"12491",
"12497",
"12853",
"14723",
"15287",
"17093",
"24781",
"25849",
"26951",
"27091",
"27179",
"33569",
"33967",
"34367",
"35171",
"35809",
"39451",
"40283",
"41263",
"41543",
"41983",
"42437",
"45971"
] |
[
"base",
"nonn"
] | 20 | 1 | 1 |
[
"A000040",
"A355418",
"A365678"
] | null |
Robert G. Wilson v, Sep 15 2023
| 2023-09-18T18:42:24 |
oeisdata/seq/A365/A365678.seq
|
fa610bc0efb2a9afefa793b25155984f
|
A365679
|
a(n) is the number of exterior top arches (no covering arch) for semi-meanders in generation n+1 that are generated by semi-meanders with n top arches and floor((n+2)/2) exterior top arches using the exterior arch splitting algorithm.
|
[
"4",
"10",
"14",
"32",
"40",
"88",
"104",
"224",
"256",
"544",
"608",
"1280",
"1408",
"2944",
"3200",
"6656",
"7168",
"14848",
"15872",
"32768",
"34816",
"71680",
"75776",
"155648",
"163840",
"335872",
"352256",
"720896",
"753664",
"1540096",
"1605632",
"3276800",
"3407872",
"6946816",
"7208960",
"14680064"
] |
[
"nonn"
] | 22 | 2 | 1 |
[
"A259689",
"A365679"
] | null |
Roger Ford, Sep 15 2023
| 2024-07-28T09:20:00 |
oeisdata/seq/A365/A365679.seq
|
fc32d8ccb8b2d34cc6952217e16326b7
|
A365680
|
The number of exponentially squarefree divisors of n.
|
[
"1",
"2",
"2",
"3",
"2",
"4",
"2",
"4",
"3",
"4",
"2",
"6",
"2",
"4",
"4",
"4",
"2",
"6",
"2",
"6",
"4",
"4",
"2",
"8",
"3",
"4",
"4",
"6",
"2",
"8",
"2",
"5",
"4",
"4",
"4",
"9",
"2",
"4",
"4",
"8",
"2",
"8",
"2",
"6",
"6",
"4",
"2",
"8",
"3",
"6",
"4",
"6",
"2",
"8",
"4",
"8",
"4",
"4",
"2",
"12",
"2",
"4",
"6",
"6",
"4",
"8",
"2",
"6",
"4",
"8",
"2",
"12",
"2",
"4",
"6",
"6",
"4",
"8",
"2",
"8",
"4",
"4",
"2",
"12",
"4",
"4"
] |
[
"nonn",
"easy",
"mult"
] | 12 | 1 | 2 |
[
"A000005",
"A013928",
"A046100",
"A209061",
"A252505",
"A325837",
"A353898",
"A365680",
"A365682",
"A365683"
] | null |
Amiram Eldar, Sep 15 2023
| 2023-09-16T02:21:29 |
oeisdata/seq/A365/A365680.seq
|
ff9a2dc82696a60387a1df9f525eea55
|
A365681
|
Numbers with a record number of exponentially squarefree divisors.
|
[
"1",
"2",
"4",
"6",
"12",
"24",
"36",
"60",
"120",
"180",
"360",
"840",
"1260",
"2520",
"6300",
"7560",
"12600",
"27720",
"69300",
"83160",
"138600",
"332640",
"360360",
"900900",
"1081080",
"1801800",
"4324320",
"5405400",
"12612600",
"17297280",
"18378360",
"30630600",
"73513440",
"86486400",
"91891800",
"214414200",
"294053760"
] |
[
"nonn"
] | 8 | 1 | 2 |
[
"A025487",
"A306736",
"A307845",
"A318278",
"A365680",
"A365681"
] | null |
Amiram Eldar, Sep 15 2023
| 2023-09-15T16:25:07 |
oeisdata/seq/A365/A365681.seq
|
4f9963ba31f17e2c0ffa0d2b02a0bcf7
|
A365682
|
The sum of exponentially squarefree divisors of n.
|
[
"1",
"3",
"4",
"7",
"6",
"12",
"8",
"15",
"13",
"18",
"12",
"28",
"14",
"24",
"24",
"15",
"18",
"39",
"20",
"42",
"32",
"36",
"24",
"60",
"31",
"42",
"40",
"56",
"30",
"72",
"32",
"47",
"48",
"54",
"48",
"91",
"38",
"60",
"56",
"90",
"42",
"96",
"44",
"84",
"78",
"72",
"48",
"60",
"57",
"93",
"72",
"98",
"54",
"120",
"72",
"120",
"80",
"90",
"60",
"168",
"62",
"96",
"104",
"111",
"84",
"144"
] |
[
"nonn",
"easy",
"mult"
] | 9 | 1 | 2 |
[
"A000203",
"A046100",
"A209061",
"A365680",
"A365682",
"A365683"
] | null |
Amiram Eldar, Sep 15 2023
| 2023-09-16T02:21:42 |
oeisdata/seq/A365/A365682.seq
|
0dc9d5b632d60b1a49ddb3ba4b6f1518
|
A365683
|
The largest exponentially squarefree divisor of n.
|
[
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"8",
"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",
"46",
"47",
"24",
"49",
"50",
"51",
"52",
"53",
"54",
"55",
"56",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"64",
"65",
"66",
"67",
"68"
] |
[
"nonn",
"easy",
"mult",
"changed"
] | 11 | 1 | 2 |
[
"A070321",
"A209061",
"A365680",
"A365682",
"A365683"
] | null |
Amiram Eldar, Sep 15 2023
| 2025-07-07T04:06:02 |
oeisdata/seq/A365/A365683.seq
|
fa48d84590bdef7e6dfb7c05cc072318
|
A365684
|
a(n) is the smallest multiple of n that is an exponentially squarefree number (A209061).
|
[
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"32",
"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",
"46",
"47",
"96",
"49",
"50",
"51",
"52",
"53",
"54",
"55",
"56",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"64",
"65",
"66",
"67",
"68"
] |
[
"nonn",
"easy",
"mult"
] | 11 | 1 | 2 |
[
"A067535",
"A209061",
"A365684",
"A365685"
] | null |
Amiram Eldar, Sep 15 2023
| 2023-09-16T02:21:58 |
oeisdata/seq/A365/A365684.seq
|
db1c897604ab9a03ec0574cc23838624
|
A365685
|
a(n) is the smallest number k such that k*n is an exponentially squarefree number (A209061).
|
[
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"1",
"1",
"1"
] |
[
"nonn",
"easy",
"mult"
] | 10 | 1 | 16 |
[
"A081221",
"A209061",
"A365684",
"A365685"
] | null |
Amiram Eldar, Sep 15 2023
| 2023-09-16T02:23:00 |
oeisdata/seq/A365/A365685.seq
|
ddca0ecacec178a3164626856f512d4b
|
A365686
|
Numbers k such that there exists a pair of integers (m,h) where 1 <= m < floor(sqrt(k)/2) <= h that satisfy Sum_{j=0..m} (k-j)^2 = Sum_{i=1..m} (h+i)^2.
|
[
"4",
"12",
"21",
"24",
"40",
"60",
"84",
"110",
"112",
"120",
"144",
"180",
"220",
"264",
"312",
"315",
"364",
"420",
"480",
"544",
"612",
"684",
"697",
"760",
"820",
"840",
"924",
"1012",
"1080",
"1104",
"1200",
"1265",
"1300",
"1404",
"1512",
"1624",
"1740",
"1860",
"1984",
"2106",
"2112",
"2244",
"2380",
"2520",
"2664",
"2812",
"2964",
"3120",
"3255"
] |
[
"nonn"
] | 85 | 1 | 1 |
[
"A000290",
"A002378",
"A046092",
"A233035",
"A365686"
] | null |
Darío Clavijo, Sep 15 2023
| 2025-03-02T16:04:04 |
oeisdata/seq/A365/A365686.seq
|
bd67ed077f3e3c43ad489323d2388871
|
A365687
|
a(n) = number of fractions m/n, 0 <= m < n, gcd(m,n) = 1 whose partial fraction decomposition has integer part 0.
|
[
"1",
"1",
"2",
"2",
"4",
"1",
"6",
"4",
"6",
"2",
"10",
"2",
"12",
"3",
"4",
"8",
"16",
"3",
"18",
"4",
"6",
"5",
"22",
"4",
"20",
"6",
"18",
"6",
"28",
"0",
"30",
"16",
"10",
"8",
"12",
"6",
"36",
"9",
"12",
"8",
"40",
"1",
"42",
"10",
"12",
"11",
"46",
"8",
"42",
"10",
"16",
"12",
"52",
"9",
"20",
"12",
"18",
"14",
"58",
"2",
"60",
"15",
"18",
"32",
"24",
"1",
"66",
"16",
"22",
"2",
"70",
"12",
"72",
"18",
"20"
] |
[
"nonn"
] | 21 | 1 | 3 |
[
"A028236",
"A070306",
"A181629",
"A365687"
] | null |
William P. Orrick, Sep 15 2023
| 2023-11-30T12:38:18 |
oeisdata/seq/A365/A365687.seq
|
6fbc05b84c5cae03576b560c761074b8
|
A365688
|
Primitive solutions k to k^2 = u^4 + v^4 + w^4, with u, v, w > 0.
|
[
"481",
"24961",
"28721",
"65441",
"69121",
"113241",
"345761",
"362401",
"384161",
"530881",
"620321",
"854401",
"882889",
"909321",
"1094481",
"1163249",
"1305281",
"1697761",
"1855841",
"2074281",
"2294681",
"2423601",
"2568369",
"2576641",
"2619281",
"2665721",
"2696161",
"2751489",
"2997761",
"3151281"
] |
[
"nonn"
] | 39 | 1 | 1 |
[
"A003828",
"A365657",
"A365688"
] | null |
Jud McCranie, Sep 16 2023
| 2023-09-29T08:26:19 |
oeisdata/seq/A365/A365688.seq
|
9834ba0c2de5ef2890d74cbd9a14421f
|
A365689
|
Final decimal digit of n^((n+1)^(n+2)) = A030198(n).
|
[
"0",
"1",
"2",
"1",
"4",
"5",
"6",
"1",
"8",
"1",
"0",
"1",
"2",
"1",
"4",
"5",
"6",
"1",
"8",
"1",
"0",
"1",
"2",
"1",
"4",
"5",
"6",
"1",
"8",
"1",
"0",
"1",
"2",
"1",
"4",
"5",
"6",
"1",
"8",
"1",
"0",
"1",
"2",
"1",
"4",
"5",
"6",
"1",
"8",
"1",
"0",
"1",
"2",
"1",
"4",
"5",
"6",
"1",
"8",
"1",
"0",
"1",
"2",
"1",
"4",
"5",
"6",
"1",
"8",
"1",
"0",
"1",
"2",
"1",
"4",
"5",
"6",
"1",
"8",
"1",
"0",
"1",
"2",
"1",
"4",
"5",
"6"
] |
[
"nonn",
"base",
"easy"
] | 42 | 0 | 3 |
[
"A030198",
"A103562",
"A120962",
"A365689"
] | null |
Marco Ripà, Sep 16 2023
| 2025-04-18T14:54:54 |
oeisdata/seq/A365/A365689.seq
|
10c6cbd5e108e8d4f4ce374c187c7787
|
A365690
|
G.f. satisfies A(x) = 1 + x^2*A(x)^4 / (1 - x*A(x)).
|
[
"1",
"0",
"1",
"1",
"5",
"10",
"38",
"101",
"353",
"1070",
"3659",
"11843",
"40505",
"135873",
"468104",
"1604375",
"5576315",
"19386656",
"67950717",
"238676813",
"842797959",
"2983745508",
"10603445402",
"37777263153",
"134985354179",
"483438728094",
"1735527037388",
"6243193190117",
"22503637842423"
] |
[
"nonn"
] | 10 | 0 | 5 |
[
"A004148",
"A005043",
"A025246",
"A046736",
"A365690",
"A365691",
"A365692"
] | null |
Seiichi Manyama, Sep 16 2023
| 2023-09-16T10:41:27 |
oeisdata/seq/A365/A365690.seq
|
d12811d4b4b3d3931f70316cc7e228e2
|
A365691
|
G.f. satisfies A(x) = 1 + x^2*A(x)^5 / (1 - x*A(x)).
|
[
"1",
"0",
"1",
"1",
"6",
"12",
"54",
"147",
"593",
"1886",
"7292",
"25204",
"96153",
"348304",
"1327716",
"4946471",
"18936366",
"71827598",
"276612103",
"1062220253",
"4115807184",
"15947902376",
"62148513732",
"242485933208",
"949828266722",
"3726623622402",
"14663689944397",
"57798199213989"
] |
[
"nonn"
] | 10 | 0 | 5 |
[
"A004148",
"A005043",
"A025246",
"A046736",
"A365690",
"A365691",
"A365693"
] | null |
Seiichi Manyama, Sep 16 2023
| 2023-09-16T10:41:47 |
oeisdata/seq/A365/A365691.seq
|
74d9b72fb5d01f4dbd9d934c4b749491
|
A365692
|
G.f. satisfies A(x) = 1 + x*A(x) / (1 - x^2*A(x)^4).
|
[
"1",
"1",
"1",
"2",
"7",
"23",
"72",
"238",
"831",
"2959",
"10645",
"38824",
"143492",
"535700",
"2016020",
"7641574",
"29152015",
"111841263",
"431209723",
"1669945778",
"6493144143",
"25338440143",
"99204579648",
"389570145288",
"1534026813892",
"6055885764548",
"23962654178012",
"95023123291680"
] |
[
"nonn"
] | 11 | 0 | 4 |
[
"A101785",
"A365244",
"A365690",
"A365692",
"A365693"
] | null |
Seiichi Manyama, Sep 16 2023
| 2023-09-16T10:42:00 |
oeisdata/seq/A365/A365692.seq
|
409fffe7546d594d7ecc85d52271a7c1
|
A365693
|
G.f. satisfies A(x) = 1 + x*A(x) / (1 - x^2*A(x)^5).
|
[
"1",
"1",
"1",
"2",
"8",
"30",
"103",
"368",
"1407",
"5531",
"21905",
"87689",
"355929",
"1461022",
"6046160",
"25194331",
"105661615",
"445692621",
"1889454880",
"8045796200",
"34398989998",
"147606568810",
"635481458969",
"2744158752772",
"11882687400375",
"51584960268914",
"224465280616995",
"978851595046223"
] |
[
"nonn"
] | 9 | 0 | 4 |
[
"A101785",
"A365244",
"A365691",
"A365692",
"A365693"
] | null |
Seiichi Manyama, Sep 16 2023
| 2023-09-16T10:42:10 |
oeisdata/seq/A365/A365693.seq
|
1c4accce5f0546aa7ef89c18ccdefa75
|
A365694
|
G.f. satisfies A(x) = 1 + x^3*A(x)^2 / (1 - x*A(x)).
|
[
"1",
"0",
"0",
"1",
"1",
"1",
"3",
"6",
"10",
"20",
"42",
"84",
"170",
"354",
"740",
"1549",
"3269",
"6945",
"14811",
"31711",
"68177",
"147091",
"318313",
"690837",
"1503351",
"3279445",
"7169907",
"15708485",
"34482475",
"75830981",
"167042763",
"368548926",
"814341362",
"1801867812",
"3992172298",
"8855912464",
"19668236110"
] |
[
"nonn"
] | 17 | 0 | 7 |
[
"A023426",
"A023432",
"A054514",
"A114997",
"A365243",
"A365694",
"A365695"
] | null |
Seiichi Manyama, Sep 16 2023
| 2023-09-16T10:42:31 |
oeisdata/seq/A365/A365694.seq
|
411560109503f727e44cfa9b64a85be1
|
A365695
|
G.f. satisfies A(x) = 1 + x^3*A(x)^5 / (1 - x*A(x)).
|
[
"1",
"0",
"0",
"1",
"1",
"1",
"6",
"12",
"19",
"62",
"156",
"318",
"852",
"2254",
"5262",
"13441",
"35543",
"88772",
"226880",
"596937",
"1539188",
"3980364",
"10468270",
"27410289",
"71702956",
"189169352",
"499529048",
"1318355542",
"3493861461",
"9278408639",
"24647900618",
"65620808508",
"175037591303",
"467277998136"
] |
[
"nonn"
] | 10 | 0 | 7 |
[
"A023426",
"A023432",
"A054514",
"A114997",
"A365694",
"A365695"
] | null |
Seiichi Manyama, Sep 16 2023
| 2023-09-16T10:42:48 |
oeisdata/seq/A365/A365695.seq
|
e4e38de534b91c00b7c88cd4a550450a
|
A365696
|
G.f. satisfies A(x) = 1 + x^4*A(x)^2 / (1 - x*A(x)).
|
[
"1",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"3",
"6",
"10",
"15",
"26",
"49",
"92",
"165",
"294",
"535",
"994",
"1852",
"3437",
"6379",
"11905",
"22344",
"42058",
"79260",
"149601",
"283038",
"536806",
"1020066",
"1941317",
"3699922",
"7062308",
"13500402",
"25842489",
"49528164",
"95031920",
"182545222",
"351023451",
"675678911",
"1301838177"
] |
[
"nonn"
] | 11 | 0 | 9 |
[
"A023427",
"A112805",
"A215341",
"A215342",
"A357308",
"A365696",
"A365697"
] | null |
Seiichi Manyama, Sep 16 2023
| 2023-09-26T05:27:46 |
oeisdata/seq/A365/A365696.seq
|
800fcf960b9dea127092dd2514cb8071
|
A365697
|
G.f. satisfies A(x) = 1 + x^4*A(x)^3 / (1 - x*A(x)).
|
[
"1",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"4",
"8",
"13",
"19",
"38",
"79",
"153",
"273",
"509",
"999",
"1979",
"3818",
"7331",
"14279",
"28189",
"55599",
"109275",
"215165",
"426093",
"846638",
"1683215",
"3348212",
"6673679",
"13333171",
"26679522",
"53437369",
"107151335",
"215154204",
"432586412",
"870678377",
"1754094266"
] |
[
"nonn"
] | 9 | 0 | 9 |
[
"A023427",
"A215341",
"A215342",
"A357308",
"A365245",
"A365696",
"A365697"
] | null |
Seiichi Manyama, Sep 16 2023
| 2023-09-16T10:40:50 |
oeisdata/seq/A365/A365697.seq
|
774813828afb8396f0f926a44a4e4d83
|
A365698
|
G.f. satisfies A(x) = 1 + x^5 / (1 - x*A(x)).
|
[
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"4",
"7",
"11",
"16",
"22",
"31",
"47",
"76",
"126",
"207",
"331",
"517",
"801",
"1251",
"1987",
"3206",
"5212",
"8465",
"13677",
"21997",
"35341",
"56937",
"92169",
"149860",
"244274",
"398383",
"649379",
"1058055",
"1724575",
"2814475",
"4600923",
"7533150",
"12347908",
"20252837",
"33230545"
] |
[
"nonn"
] | 14 | 0 | 12 |
[
"A001006",
"A023426",
"A025246",
"A212364",
"A357308",
"A365698",
"A365699",
"A365700",
"A365701",
"A365702"
] | null |
Seiichi Manyama, Sep 16 2023
| 2023-09-16T12:02:22 |
oeisdata/seq/A365/A365698.seq
|
f8a435748c191d01127ce1d362a8584b
|
A365699
|
G.f. satisfies A(x) = 1 + x^5*A(x)^2 / (1 - x*A(x)).
|
[
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"3",
"6",
"10",
"15",
"21",
"33",
"57",
"101",
"175",
"291",
"477",
"791",
"1341",
"2310",
"3986",
"6839",
"11681",
"19966",
"34300",
"59245",
"102647",
"177963",
"308483",
"534973",
"929147",
"1616981",
"2818967",
"4920299",
"8594665",
"15023561",
"26283971",
"46030771",
"80695333",
"141593087"
] |
[
"nonn"
] | 9 | 0 | 11 |
[
"A212364",
"A365698",
"A365699",
"A365700",
"A365701",
"A365702"
] | null |
Seiichi Manyama, Sep 16 2023
| 2023-09-16T10:43:12 |
oeisdata/seq/A365/A365699.seq
|
49b98756c90a62bfc86389c48273f6aa
|
A365700
|
G.f. satisfies A(x) = 1 + x^5*A(x)^3 / (1 - x*A(x)).
|
[
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"4",
"8",
"13",
"19",
"26",
"46",
"88",
"163",
"284",
"466",
"781",
"1369",
"2468",
"4449",
"7856",
"13724",
"24084",
"42788",
"76759",
"137785",
"246418",
"439757",
"786132",
"1411148",
"2541368",
"4581906",
"8259500",
"14889781",
"26871106",
"48573823",
"87934175",
"159333544",
"288857216"
] |
[
"nonn"
] | 14 | 0 | 11 |
[
"A212364",
"A365698",
"A365699",
"A365700",
"A365701",
"A365702"
] | null |
Seiichi Manyama, Sep 16 2023
| 2025-05-29T11:29:11 |
oeisdata/seq/A365/A365700.seq
|
a2b0ce89fe9ee38940cf7cc00575048b
|
A365701
|
G.f. satisfies A(x) = 1 + x^5*A(x)^4 / (1 - x*A(x)).
|
[
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"5",
"10",
"16",
"23",
"31",
"62",
"128",
"243",
"423",
"686",
"1192",
"2223",
"4223",
"7843",
"13991",
"24856",
"45108",
"83673",
"156223",
"288535",
"527971",
"966803",
"1784663",
"3319988",
"6183424",
"11483613",
"21284475",
"39499855",
"73558147",
"137347615",
"256616567",
"479231240"
] |
[
"nonn"
] | 9 | 0 | 11 |
[
"A212364",
"A365698",
"A365699",
"A365700",
"A365701",
"A365702"
] | null |
Seiichi Manyama, Sep 16 2023
| 2023-09-16T10:43:36 |
oeisdata/seq/A365/A365701.seq
|
0654a3c7f9c0f79f97bffd30987fb9c4
|
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