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666,262,453B
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635M
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listlengths 1
128
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listlengths 1
3
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231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-14 02:38:35
| filename
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| hash
stringlengths 32
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A384164 | a(n) = Product_{k=0..n-1} (3*n+k). | [
"1",
"3",
"42",
"990",
"32760",
"1395360",
"72681840",
"4475671200",
"318073392000",
"25622035084800",
"2306992893004800",
"229601607198163200",
"25028504609870361600",
"2965681982933429760000",
"379534960108578193920000",
"52170410224819317150720000",
"7666009844358186506465280000",
"1199151678674216896627654656000"
]
| [
"nonn",
"easy"
]
| 32 | 0 | 2 | [
"A000407",
"A061924",
"A124320",
"A352601",
"A384164",
"A384165"
]
| null | Seiichi Manyama, May 21 2025 | 2025-05-24T10:35:29 | oeisdata/seq/A384/A384164.seq | 7468646a648991942b6d054b57906f45 |
A384165 | a(n) = Product_{k=0..n-1} (3*n+2*k). | [
"1",
"3",
"48",
"1287",
"48384",
"2340135",
"138378240",
"9672183675",
"780151357440",
"71322093677835",
"7287813911347200",
"823100991923184975",
"101819334240239616000",
"13690816766440373134575",
"1988199345147516813312000",
"310120801435080997013527875",
"51709528644340997758648320000"
]
| [
"nonn",
"easy"
]
| 23 | 0 | 2 | [
"A384164",
"A384165",
"A384166"
]
| null | Seiichi Manyama, May 21 2025 | 2025-05-22T09:54:29 | oeisdata/seq/A384/A384165.seq | 2a60e52906d7cfe3b98802f7c938af73 |
A384166 | a(n) = Product_{k=0..n-1} (3*n+4*k). | [
"1",
"3",
"60",
"1989",
"92160",
"5486535",
"399072960",
"34298042625",
"3400783626240",
"382128386114475",
"47986411423104000",
"6659996213472126525",
"1012334387351519232000",
"167253493686752981883375",
"29842935065036371998720000",
"5719198821953333723419037625",
"1171620424982972483984424960000"
]
| [
"nonn",
"easy"
]
| 19 | 0 | 2 | [
"A303487",
"A384164",
"A384165",
"A384166"
]
| null | Seiichi Manyama, May 21 2025 | 2025-05-22T16:41:11 | oeisdata/seq/A384/A384166.seq | 481f9606ab27668c09e9bf2eed5b68ce |
A384167 | a(n) = 2^n * n! * binomial(3*n/2,n) * Sum_{k=1..n} 1/(n+2*k). | [
"1",
"10",
"143",
"2736",
"66009",
"1926912",
"66086271",
"2605455360",
"116123049585",
"5774107852800",
"316921177332495",
"19032668386099200",
"1241454631056114825",
"87402945316493721600",
"6606130538582006306175",
"533534147838972474163200",
"45855293972076668267481825",
"4178822478568980876361728000"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A098118",
"A113551",
"A384167",
"A384168",
"A384169"
]
| null | Seiichi Manyama, May 21 2025 | 2025-05-21T06:38:33 | oeisdata/seq/A384/A384167.seq | 9bd9a00f4fb6ab58ffe8d53ef829c12c |
A384168 | a(n) = 3^n * n! * binomial(4*n/3,n) * Sum_{k=1..n} 1/(n+3*k). | [
"1",
"13",
"234",
"5566",
"165944",
"5966136",
"251491120",
"12169996912",
"665146831680",
"40530954643840",
"2724842629685120",
"200361647815660800",
"15997170878205905920",
"1378271357428552115200",
"127459020533529062246400",
"12593128815600367187507200",
"1323895109721239722075136000"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A098118",
"A303486",
"A384167",
"A384168",
"A384169"
]
| null | Seiichi Manyama, May 21 2025 | 2025-05-21T06:39:09 | oeisdata/seq/A384/A384168.seq | 39b8015d004c1957b1bc1dddac74bc96 |
A384169 | a(n) = 4^n * n! * binomial(5*n/4,n) * Sum_{k=1..n} 1/(n+4*k). | [
"1",
"16",
"347",
"9856",
"349269",
"14885760",
"742589175",
"42479124480",
"2742327328905",
"197267905658880",
"15649214440432275",
"1357388618032742400",
"127808331929417605725",
"12983375200126773657600",
"1415428114244995252270575",
"164837363498660501913600000",
"20423530465926352502482292625"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A098118",
"A303487",
"A384167",
"A384168",
"A384169"
]
| null | Seiichi Manyama, May 21 2025 | 2025-05-21T06:39:24 | oeisdata/seq/A384/A384169.seq | 6a89f395cf9b4a35418c8103b6b6b053 |
A384170 | a(n) = 3^n * n! * binomial(5*n/3,n) * Sum_{k=1..n} 1/(2*n+3*k). | [
"1",
"17",
"423",
"14198",
"603194",
"31069980",
"1882538440",
"131223122480",
"10345975290000",
"910393948446560",
"88452245803947200",
"9405081915991747200",
"1086351888729412883200",
"135456246872643979788800",
"18134220756665496528460800",
"2594357788916663689703168000",
"395006034401484168868002560000"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A384136",
"A384170"
]
| null | Seiichi Manyama, May 21 2025 | 2025-05-21T06:39:36 | oeisdata/seq/A384/A384170.seq | 1c771834a4a6f29e55fff92b9b4f78c9 |
A384171 | a(n) = 2^n * n! * binomial(5*n/2,n) * Sum_{k=1..n} 1/(3*n+2*k). | [
"1",
"18",
"503",
"19312",
"946009",
"56419200",
"3967700295",
"321506211840",
"29497821190065",
"3022798062551040",
"342204383046633975",
"42414460290839347200",
"5712600791700063700425",
"830773593435129407078400",
"129744737403826992957167175",
"21657021896289762215460864000",
"3847769544999445159548440534625"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A384137",
"A384171",
"A384172"
]
| null | Seiichi Manyama, May 21 2025 | 2025-05-21T06:39:52 | oeisdata/seq/A384/A384171.seq | 8d8567af62cd8234dcc0383b10405f8a |
A384172 | a(n) = 4^n * n! * binomial(7*n/4,n) * Sum_{k=1..n} 1/(3*n+4*k). | [
"1",
"24",
"851",
"40832",
"2483269",
"183241728",
"15912395295",
"1590131687424",
"179766351690345",
"22685041361848320",
"3161081216499580395",
"482101740659382681600",
"79876921394710650447405",
"14287114673531430042009600",
"2743817201103924825303993975",
"563131793021994402478188134400"
]
| [
"nonn"
]
| 10 | 1 | 2 | [
"A384137",
"A384166",
"A384171",
"A384172"
]
| null | Seiichi Manyama, May 21 2025 | 2025-05-21T06:40:14 | oeisdata/seq/A384/A384172.seq | b5742f8ac07dd9b161cc10e60b934127 |
A384173 | Number of Hamiltonian paths from NW to SW corners in an n X n grid reduced for symmetry, i.e., where reflection about the x-axis is not counted as distinct. | [
"1",
"1",
"1",
"5",
"43",
"897",
"44209",
"4467927",
"1043906917",
"506673590576",
"555799435739334",
"1284472450789974196",
"6625529679919810063544",
"72597408139909172033687226",
"1762085630816152820582838187465",
"91326629994353561722347679614188407"
]
| [
"nonn",
"walk"
]
| 13 | 1 | 4 | [
"A209077",
"A265914",
"A384173"
]
| null | Oliver R. Bellwood, May 21 2025 | 2025-06-06T08:07:11 | oeisdata/seq/A384/A384173.seq | 30e48d8756039921831c3e010cc807b0 |
A384174 | Primes p such that the concatenations of p and 123456789 in both orders are prime. | [
"409",
"653",
"881",
"1091",
"1489",
"1913",
"1993",
"2039",
"2729",
"3677",
"4073",
"5039",
"5507",
"5683",
"5849",
"7349",
"7789",
"7907",
"8419",
"8623",
"8689",
"9973",
"10429",
"11057",
"11617",
"11689",
"11821",
"12527",
"13367",
"14033",
"15259",
"15511",
"15629",
"16139",
"17569",
"17881",
"17911",
"19373",
"19577",
"21187",
"21383",
"23197",
"23399",
"23629",
"24043",
"24317"
]
| [
"nonn",
"base"
]
| 34 | 1 | 1 | [
"A232726",
"A232728",
"A384174",
"A384218"
]
| null | Robert Israel, May 22 2025 | 2025-05-23T10:14:07 | oeisdata/seq/A384/A384174.seq | add6524fab9801776d50c1c902a1dc2d |
A384175 | Number of subsets of {1..n} with all distinct lengths of maximal runs (increasing by 1). | [
"1",
"2",
"4",
"7",
"13",
"24",
"44",
"77",
"135",
"236",
"412",
"713",
"1215",
"2048",
"3434",
"5739",
"9559",
"15850",
"26086",
"42605",
"69133",
"111634",
"179602",
"288069",
"460553",
"733370",
"1162356",
"1833371",
"2878621",
"4501856",
"7016844",
"10905449",
"16904399",
"26132460",
"40279108",
"61885621",
"94766071",
"144637928"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A000009",
"A010027",
"A034839",
"A044813",
"A047993",
"A098859",
"A116674",
"A242882",
"A243815",
"A268193",
"A325325",
"A328592",
"A329739",
"A336866",
"A351202",
"A383013",
"A384175",
"A384176",
"A384177",
"A384178",
"A384879",
"A384880",
"A384884",
"A384886",
"A384889",
"A384890",
"A384891",
"A384892",
"A384893",
"A384905"
]
| null | Gus Wiseman, Jun 16 2025 | 2025-06-18T23:19:55 | oeisdata/seq/A384/A384175.seq | a69e8ac42cb9b73d0ddd6f6994bfd64f |
A384176 | Number of subsets of {1..n} without all distinct lengths of maximal runs (increasing by 1). | [
"0",
"0",
"0",
"1",
"3",
"8",
"20",
"51",
"121",
"276",
"612",
"1335",
"2881",
"6144",
"12950",
"27029",
"55977",
"115222",
"236058",
"481683",
"979443"
]
| [
"nonn",
"more"
]
| 7 | 0 | 5 | [
"A000009",
"A010027",
"A034839",
"A044813",
"A098859",
"A116674",
"A242882",
"A243815",
"A268193",
"A325325",
"A328592",
"A329739",
"A336866",
"A351202",
"A383013",
"A384175",
"A384176",
"A384177",
"A384178",
"A384880",
"A384884",
"A384886",
"A384889",
"A384890",
"A384891",
"A384892",
"A384893",
"A384905"
]
| null | Gus Wiseman, Jun 16 2025 | 2025-06-17T09:18:05 | oeisdata/seq/A384/A384176.seq | 9b89f467185ebb530329d8f641e64256 |
A384177 | Number of subsets of {1..n} with all distinct lengths of maximal anti-runs (increasing by more than 1). | [
"1",
"2",
"3",
"5",
"10",
"19",
"35",
"62",
"109",
"197",
"364",
"677",
"1251",
"2288",
"4143",
"7443",
"13318",
"23837",
"42809",
"77216",
"139751",
"253293",
"458800",
"829237",
"1494169",
"2683316",
"4804083",
"8580293",
"15301324",
"27270061",
"48607667",
"86696300",
"154758265",
"276453311",
"494050894",
"882923051"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A000009",
"A010027",
"A034839",
"A044813",
"A047993",
"A098859",
"A106529",
"A116674",
"A123513",
"A242882",
"A243815",
"A268193",
"A325325",
"A328592",
"A329739",
"A336866",
"A351202",
"A384175",
"A384176",
"A384177",
"A384178",
"A384879",
"A384880",
"A384884",
"A384886",
"A384889",
"A384890",
"A384893",
"A384905"
]
| null | Gus Wiseman, Jun 16 2025 | 2025-06-18T23:18:43 | oeisdata/seq/A384/A384177.seq | 40510fe2095dd35181f2422c52b517d7 |
A384178 | Number of strict integer partitions of n with all distinct lengths of maximal runs (decreasing by 1). | [
"1",
"1",
"1",
"2",
"1",
"2",
"2",
"3",
"3",
"4",
"5",
"6",
"6",
"8",
"8",
"10",
"11",
"13",
"13",
"16",
"15",
"19",
"19",
"23",
"22",
"26",
"28",
"31",
"35",
"39",
"37",
"47",
"51",
"52",
"60",
"65",
"67",
"78",
"85",
"86",
"99",
"108",
"110",
"127",
"136",
"138",
"159",
"170",
"171",
"196",
"209",
"213",
"240",
"257",
"260",
"292",
"306",
"313",
"350",
"371",
"369",
"417",
"441"
]
| [
"nonn"
]
| 9 | 0 | 4 | [
"A000009",
"A000041",
"A008284",
"A044813",
"A047993",
"A098859",
"A239455",
"A242882",
"A325324",
"A325325",
"A329739",
"A336866",
"A351202",
"A351293",
"A351294",
"A351295",
"A381432",
"A381433",
"A384175",
"A384176",
"A384178",
"A384880",
"A384884",
"A384886"
]
| null | Gus Wiseman, Jun 12 2025 | 2025-06-14T23:51:08 | oeisdata/seq/A384/A384178.seq | 32744790f646b0d23af6b08eab13f992 |
A384179 | Number of ways to choose strict integer partitions of each conjugate prime index of n. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"4",
"2",
"1",
"2",
"1",
"3",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"4",
"1",
"1",
"3",
"1",
"2",
"1",
"2",
"1",
"4",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"4",
"4",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"1",
"4",
"2",
"1",
"2",
"1",
"3",
"4",
"1",
"1",
"2",
"1",
"1",
"1"
]
| [
"nonn"
]
| 5 | 1 | 8 | [
"A000009",
"A000041",
"A033942",
"A037143",
"A048767",
"A048768",
"A050361",
"A055396",
"A056239",
"A061395",
"A112798",
"A122111",
"A130091",
"A179009",
"A217605",
"A239455",
"A270995",
"A279375",
"A279790",
"A351293",
"A351294",
"A351295",
"A357982",
"A381432",
"A381433",
"A382913",
"A383706",
"A383707",
"A383710",
"A384005",
"A384010",
"A384011",
"A384179"
]
| null | Gus Wiseman, May 23 2025 | 2025-05-24T11:00:31 | oeisdata/seq/A384/A384179.seq | faa143f7cc27d2611f5270659360da1d |
A384180 | Irregular triangle read by rows where row n lists the Heinz numbers of all uniform (equal multiplicities) and normal (covering an initial interval) multisets of length n. | [
"2",
"4",
"6",
"8",
"30",
"16",
"36",
"210",
"32",
"2310",
"64",
"216",
"900",
"30030",
"128",
"510510",
"256",
"1296",
"44100",
"9699690",
"512",
"27000",
"223092870",
"1024",
"7776",
"5336100",
"6469693230",
"2048",
"200560490130",
"4096",
"46656",
"810000",
"9261000",
"901800900",
"7420738134810",
"8192",
"304250263527210"
]
| [
"nonn",
"tabf"
]
| 5 | 1 | 1 | [
"A000005",
"A000009",
"A001694",
"A002110",
"A047966",
"A048767",
"A048768",
"A056239",
"A098859",
"A100778",
"A106529",
"A112798",
"A116540",
"A122111",
"A130091",
"A217605",
"A258280",
"A322792",
"A324939",
"A325326",
"A325337",
"A381431",
"A383512",
"A384180"
]
| null | Gus Wiseman, May 25 2025 | 2025-05-28T09:19:54 | oeisdata/seq/A384/A384180.seq | aae9164d3dd801d8ed00a0574f947118 |
A384181 | Primes p such that k! + p or |k! - p| is composite for all k >= 0. | [
"2",
"3",
"71",
"97",
"179",
"181",
"211",
"223",
"251",
"283",
"431",
"503",
"577",
"827",
"857",
"971",
"1019",
"1021",
"1109",
"1213",
"1249",
"1259",
"1279",
"1289",
"1373",
"1427",
"1429",
"1483",
"1571",
"1609",
"1619",
"1637",
"1699",
"1709",
"1759",
"1801",
"2053",
"2129",
"2141",
"2213",
"2269",
"2281",
"2293",
"2297",
"2339",
"2381",
"2477",
"2503"
]
| [
"nonn"
]
| 18 | 1 | 1 | [
"A082470",
"A352912",
"A384181"
]
| null | Gonzalo Martínez, May 21 2025 | 2025-06-02T18:11:27 | oeisdata/seq/A384/A384181.seq | 4e0cff7b5e0a863c4dd07b858a1c4b26 |
A384182 | a(n) is the smallest integer k such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = k^4, where 0 < x < y < z < w has exactly n integer solutions. | [
"6",
"9",
"15",
"34",
"20",
"19",
"66",
"28",
"36",
"35",
"26",
"30",
"355",
"97",
"44",
"329",
"151",
"65",
"590",
"89",
"48",
"42",
"129",
"54",
"70",
"99",
"56",
"178",
"580",
"128",
"110",
"392",
"107",
"518",
"63",
"125",
"90",
"887",
"242",
"78",
"100",
"138",
"105",
"96",
"235",
"141",
"281",
"205",
"326",
"1094",
"117",
"108",
"197",
"860"
]
| [
"nonn",
"more"
]
| 14 | 1 | 1 | [
"A383877",
"A384182"
]
| null | Zhining Yang, May 21 2025 | 2025-05-28T16:47:14 | oeisdata/seq/A384/A384182.seq | c1d2a6aba73df8ff226674cc9de2ac89 |
A384183 | a(n) = minimum number of steps required to move n stones from a hole to the next one in an infinite row of holes, where at one step we can move any k stones at once from a hole to the hole at distance k to the left or to the right, and there are n stones overall. | [
"0",
"1",
"2",
"3",
"4",
"5",
"5",
"6",
"7",
"7",
"6",
"7",
"7",
"8",
"7",
"7",
"8",
"9",
"8",
"8",
"9",
"8",
"8",
"9",
"8",
"9",
"8",
"9",
"9",
"10",
"9",
"9",
"10",
"9",
"9",
"9",
"10",
"10",
"9",
"10",
"9",
"10",
"9",
"10",
"10",
"10",
"10",
"10",
"10",
"10",
"10",
"10",
"11",
"11",
"10",
"10",
"10",
"10",
"10",
"11",
"10",
"11",
"10",
"11",
"11",
"10",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"10",
"11",
"11",
"11"
]
| [
"nonn",
"nice"
]
| 57 | 0 | 3 | null | null | Konstantin Knop, May 21 2025 | 2025-06-25T00:26:52 | oeisdata/seq/A384/A384183.seq | 7b3d1f8ff4db71edee6070112582542b |
A384184 | Order of the permutation of {0,...,n-1} formed by successively swapping elements at i and 2*i mod n, for i = 0,...,n-1. | [
"1",
"2",
"1",
"4",
"2",
"2",
"2",
"8",
"3",
"4",
"5",
"4",
"6",
"4",
"6",
"16",
"4",
"6",
"9",
"8",
"4",
"10",
"28",
"8",
"10",
"12",
"9",
"8",
"14",
"12",
"12",
"32",
"5",
"8",
"70",
"12",
"18",
"18",
"24",
"16",
"10",
"8",
"7",
"20",
"210",
"56",
"126",
"16",
"110",
"20",
"60",
"24",
"26",
"18",
"120",
"16",
"9",
"28",
"29",
"24",
"30",
"24",
"60",
"64",
"6",
"10",
"33",
"16"
]
| [
"nonn"
]
| 72 | 1 | 2 | [
"A000027",
"A001122",
"A001133",
"A001134",
"A001135",
"A003418",
"A004626",
"A051732",
"A065119",
"A155072",
"A225759",
"A384184"
]
| null | Mia Boudreau, May 29 2025 | 2025-06-23T22:11:41 | oeisdata/seq/A384/A384184.seq | e1f74de52f9a9ca03703d821f15551fb |
A384185 | Integers in A375491 in order of their first appearance. | [
"1",
"2",
"4",
"6",
"12",
"5",
"8",
"24",
"3",
"7",
"18",
"16",
"30",
"36",
"48",
"10",
"32",
"14",
"72",
"9",
"60",
"96",
"120",
"19",
"64",
"13",
"40",
"144",
"21",
"35",
"56",
"38",
"28",
"90",
"26",
"240",
"15",
"192",
"384",
"44",
"76",
"360",
"88",
"80",
"180",
"168",
"114",
"54",
"288",
"112",
"264",
"25",
"41",
"33",
"256",
"98",
"20",
"55",
"312",
"128"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A375491",
"A384185"
]
| null | Robin Jones, May 21 2025 | 2025-05-26T23:51:35 | oeisdata/seq/A384/A384185.seq | c3d0859e7e8bede53cbed1b828241df0 |
A384186 | Number of permutations of 1, 2,..., n with exactly one rising or falling successon, namely (n-1)n or n(n-1). | [
"0",
"2",
"2",
"2",
"6",
"34",
"214",
"1506",
"11990",
"107234",
"1065846",
"11659426",
"139217494",
"1801784610",
"25124797046",
"375531165794",
"5989287277014",
"101524201538146",
"1822662037112950",
"34548339122512674",
"689469487015534166",
"14450128299126915746"
]
| [
"nonn",
"easy"
]
| 7 | 1 | 2 | [
"A002464",
"A086652",
"A383857",
"A384186"
]
| null | Wolfdieter Lang, May 21 2025 | 2025-05-22T01:27:17 | oeisdata/seq/A384/A384186.seq | ddebe6bb52e4af9b6dc0492ab6e41733 |
A384187 | Primes p such that p + 6, p^2 + 6, p^3 + 6, p^4 + 6 and p^5 + 6 are primes. | [
"1361",
"70216961",
"71317991",
"311153281",
"371383381",
"385230821",
"400675721",
"466490881",
"487757861",
"620258761",
"818694271",
"822486341",
"888942491",
"898259491",
"1102784471",
"1423261241",
"1443957371",
"1623698051",
"1628827091",
"1729743571",
"1831375171",
"1837091231",
"1904579381",
"1978478521",
"2070333781"
]
| [
"nonn"
]
| 12 | 1 | 1 | [
"A023201",
"A243734",
"A384187"
]
| null | Gonzalo Martínez, May 21 2025 | 2025-06-13T15:34:59 | oeisdata/seq/A384/A384187.seq | 85222d857ad89c0b4ae5ff60682036dc |
A384188 | Population of elementary triangular automaton rule 178 at generation n, starting from a lone 1 cell at generation 0. | [
"1",
"4",
"10",
"16",
"16",
"28",
"46",
"52",
"40",
"64",
"76",
"94",
"118",
"142",
"184",
"184",
"166",
"196",
"214",
"232",
"256",
"286",
"334",
"376",
"418",
"454",
"508",
"544",
"604",
"682",
"766",
"748",
"742",
"766",
"784",
"802",
"826",
"856",
"904",
"946",
"988",
"1036",
"1090",
"1168",
"1258",
"1360",
"1480",
"1552",
"1636",
"1672",
"1714",
"1756"
]
| [
"nonn"
]
| 9 | 0 | 2 | null | null | Paul Cousin, May 21 2025 | 2025-05-22T09:38:32 | oeisdata/seq/A384/A384188.seq | dbf9f99dc1497b5406b9ad05004e0c50 |
A384189 | Numbers whose number of zeros in their binary representation is not equal to 1. | [
"1",
"3",
"4",
"7",
"8",
"9",
"10",
"12",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"22",
"24",
"25",
"26",
"28",
"31",
"32",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"40",
"41",
"42",
"43",
"44",
"45",
"46",
"48",
"49",
"50",
"51",
"52",
"53",
"54",
"56",
"57",
"58",
"60",
"63",
"64",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"72",
"73",
"74",
"75",
"76",
"77",
"78",
"79",
"80",
"81",
"82"
]
| [
"nonn",
"base"
]
| 14 | 1 | 2 | [
"A023416",
"A030130",
"A164874",
"A384189"
]
| null | Chai Wah Wu, May 21 2025 | 2025-05-22T05:23:06 | oeisdata/seq/A384/A384189.seq | fbf4e132b5c1de5809e26bd55838c937 |
A384190 | Number of non-isomorphic AG-groupoids of order n. | [
"1",
"3",
"20",
"331",
"31913",
"40104513",
"643460323187"
]
| [
"nonn",
"hard",
"more"
]
| 34 | 1 | 2 | [
"A001329",
"A001426",
"A124506",
"A350874",
"A350875",
"A384190"
]
| null | Elijah Beregovsky, May 21 2025 | 2025-05-26T05:50:12 | oeisdata/seq/A384/A384190.seq | 16ff717e61ec100a3197c4ef3479b6e8 |
A384191 | Unique increasing sequence (a(n)) whose complement, (b(n)), satisfies b(n) = a(a(n))+3. | [
"1",
"2",
"3",
"7",
"8",
"9",
"10",
"11",
"12",
"16",
"17",
"18",
"22",
"23",
"24",
"25",
"26",
"27",
"31",
"32",
"33",
"34",
"35",
"36",
"40",
"41",
"42",
"46",
"47",
"48",
"49",
"50",
"51",
"55",
"56",
"57",
"61",
"62",
"63",
"64",
"65",
"66",
"70",
"71",
"72",
"73",
"74",
"75",
"79",
"80",
"81",
"85",
"86",
"87",
"88",
"89",
"90",
"94",
"95",
"96",
"97",
"98",
"99",
"103",
"104"
]
| [
"nonn"
]
| 8 | 1 | 2 | [
"A000201",
"A137708",
"A384191",
"A384192"
]
| null | Clark Kimberling, May 21 2025 | 2025-05-28T00:53:17 | oeisdata/seq/A384/A384191.seq | 877ebe6ab769b8546fc6cfc40a878c44 |
A384192 | Complement of A384191. | [
"4",
"5",
"6",
"13",
"14",
"15",
"19",
"20",
"21",
"28",
"29",
"30",
"37",
"38",
"39",
"43",
"44",
"45",
"52",
"53",
"54",
"58",
"59",
"60",
"67",
"68",
"69",
"76",
"77",
"78",
"82",
"83",
"84",
"91",
"92",
"93",
"100",
"101",
"102",
"106",
"107",
"108",
"115",
"116",
"117",
"121",
"122",
"123",
"130",
"131",
"132",
"139",
"140",
"141",
"145",
"146",
"147",
"154",
"155"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A137709",
"A384191",
"A384192"
]
| null | Clark Kimberling, May 21 2025 | 2025-05-30T01:09:07 | oeisdata/seq/A384/A384192.seq | 616e8f89fcb0e3ea14505815463d4076 |
A384193 | Slice of elementary triangular automaton rule 210, starting from a lone 1 cell. | [
"1",
"3",
"5",
"13",
"17",
"59",
"81",
"219",
"257",
"899",
"1301",
"3381",
"4357",
"15245",
"20753",
"56123",
"65809",
"230331",
"332049",
"867227",
"1118465",
"3914627",
"5312837",
"14400365",
"16847169",
"58964835",
"85266693",
"221592365",
"285561153",
"999119715",
"1358954837",
"3674219349",
"4312076629",
"15094059861"
]
| [
"nonn"
]
| 20 | 0 | 2 | [
"A372581",
"A374413",
"A384193"
]
| null | Paul Cousin, May 21 2025 | 2025-06-03T01:11:09 | oeisdata/seq/A384/A384193.seq | 785869b818d1e6e4b020385c2bcda1ad |
A384194 | Consecutive states of the linear congruential pseudo-random number generator 259*s mod 2^15 when started at s=1. | [
"1",
"259",
"1545",
"6939",
"27729",
"5619",
"13529",
"30603",
"29089",
"30179",
"17577",
"30459",
"24561",
"4307",
"1401",
"2411",
"1857",
"22211",
"18249",
"7899",
"14225",
"14259",
"23065",
"10059",
"16609",
"9123",
"3561",
"4795",
"29489",
"2707",
"12985",
"20779",
"7809",
"23683",
"6281",
"21147",
"4817",
"2419",
"3929",
"1803",
"8225"
]
| [
"nonn",
"easy"
]
| 19 | 1 | 2 | [
"A096555",
"A384158",
"A384194"
]
| null | Sean A. Irvine, May 21 2025 | 2025-06-15T22:36:22 | oeisdata/seq/A384/A384194.seq | 3ab32ffd62909f2d36752640bcf4387a |
A384195 | a(n) = tau(n+1) - tau(n-1), where tau(n) = A000005(n), the number of divisors of n. | [
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"-1",
"2",
"0",
"-2",
"2",
"1",
"-2",
"1",
"0",
"0",
"2",
"-2",
"-2",
"4",
"1",
"-4",
"1",
"2",
"-2",
"2",
"0",
"-2",
"2",
"-2",
"0",
"5",
"-2",
"-5",
"2",
"4",
"-2",
"0",
"0",
"-2",
"4",
"-2",
"-4",
"6",
"1",
"-4",
"1",
"0",
"-2",
"2",
"2",
"0",
"0",
"-4",
"-2",
"8",
"0",
"-8",
"4",
"3",
"-2",
"1",
"-2",
"-2",
"2",
"2",
"-2",
"4",
"0",
"-8",
"4",
"2",
"-2",
"2",
"-2",
"2",
"3",
"-6",
"-3",
"8",
"2",
"-8"
]
| [
"sign"
]
| 14 | 2 | 10 | [
"A000005",
"A051950",
"A051951",
"A067888",
"A384195"
]
| null | Dan Dart, May 21 2025 | 2025-05-27T19:09:12 | oeisdata/seq/A384/A384195.seq | 6a3b0add9b989dce435f3f82a04eaaeb |
A384196 | Consecutive states of the linear congruential pseudo-random number generator 20403*s mod 2^15 when started at s=1. | [
"1",
"20403",
"30505",
"30891",
"9361",
"20579",
"16953",
"25819",
"6689",
"29715",
"1609",
"27659",
"28849",
"27331",
"21337",
"15931",
"14401",
"25715",
"14697",
"2923",
"209",
"4387",
"18553",
"923",
"23137",
"8403",
"4233",
"22219",
"21745",
"17283",
"8601",
"13563",
"129",
"10547",
"2985",
"20011",
"27921",
"483",
"24249",
"21083"
]
| [
"nonn",
"easy",
"changed"
]
| 17 | 1 | 2 | [
"A096550",
"A096561",
"A384196"
]
| null | Sean A. Irvine, May 21 2025 | 2025-07-06T17:47:49 | oeisdata/seq/A384/A384196.seq | a659ccd9ba2ab9012373d060ab9049cf |
A384197 | The Barret reducer reciprocal mod n. | [
"4",
"8",
"5",
"16",
"12",
"10",
"9",
"32",
"28",
"25",
"23",
"21",
"19",
"18",
"17",
"64",
"60",
"56",
"53",
"51",
"48",
"46",
"44",
"42",
"40",
"39",
"37",
"36",
"35",
"34",
"33",
"128",
"124",
"120",
"117",
"113",
"110",
"107",
"105",
"102",
"99",
"97",
"95",
"93",
"91",
"89",
"87",
"85",
"83",
"81",
"80",
"78",
"77",
"75",
"74",
"73",
"71",
"70",
"69",
"68",
"67",
"66",
"65",
"256"
]
| [
"nonn",
"easy"
]
| 11 | 1 | 1 | [
"A070939",
"A143096",
"A384197"
]
| null | Darío Clavijo, May 21 2025 | 2025-06-06T14:46:18 | oeisdata/seq/A384/A384197.seq | f65da754d79f301cea83f3fc68d22d2e |
A384198 | a(n) = 3^(n-3)*(binomial(n,3) + 3*binomial(n,2) + 9*n + 27). | [
"1",
"4",
"16",
"64",
"255",
"1008",
"3942",
"15228",
"58077",
"218700",
"813564",
"2991816",
"10884699",
"39208536",
"139946130",
"495303012",
"1739406393",
"6064804692",
"21006799848",
"72318491280",
"247561692471",
"843026984064",
"2856838685886",
"9637472084364",
"32374793163285",
"108327417770268",
"361133233980372"
]
| [
"nonn",
"easy",
"changed"
]
| 11 | 0 | 2 | [
"A382618",
"A384198"
]
| null | Enrique Navarrete, May 21 2025 | 2025-06-30T09:05:50 | oeisdata/seq/A384/A384198.seq | 4e6ce2decbd2d5e82bbde1e4897917f0 |
A384199 | Expansion of e.g.f. log(1 + x)/(1 - 3*x). | [
"0",
"1",
"5",
"47",
"558",
"8394",
"150972",
"3171132",
"76102128",
"2054797776",
"61643570400",
"2034241452000",
"73232652355200",
"2856073920854400",
"119955098448864000",
"5397979517377171200",
"259103015526429849600",
"13214253812770712217600",
"713569705533931031654400"
]
| [
"nonn",
"easy"
]
| 18 | 0 | 3 | [
"A024167",
"A069015",
"A383897",
"A384199"
]
| null | Seiichi Manyama, May 22 2025 | 2025-05-23T03:28:59 | oeisdata/seq/A384/A384199.seq | bd1d6a9ea549adc7b733d8cf144066e1 |
A384200 | Expansion of e.g.f. -log(1 - 3*x)/(3 * (1 - x)). | [
"0",
"1",
"5",
"33",
"294",
"3414",
"49644",
"872388",
"18001584",
"426553776",
"11408104800",
"339766164000",
"11148335337600",
"399489448694400",
"15520734764640000",
"649782085752172800",
"29160211264750540800",
"1396381090351116441600",
"71068392067688315596800",
"3830710201119961857331200"
]
| [
"nonn",
"easy"
]
| 15 | 0 | 3 | [
"A126674",
"A384200"
]
| null | Seiichi Manyama, May 22 2025 | 2025-05-22T16:41:58 | oeisdata/seq/A384/A384200.seq | ad64e91d8a2a19e6b9706109b13ffe18 |
A384201 | Expansion of e.g.f. -log(1 - 2*x)/(2 * (1 + x)). | [
"0",
"1",
"0",
"8",
"16",
"304",
"2016",
"31968",
"389376",
"6817536",
"117619200",
"2422080000",
"52684646400",
"1277090150400",
"33132492288000",
"931341738700800",
"27948405871411200",
"896073058285977600",
"30491347526251315200",
"1099008249715585843200",
"41796901408833994752000"
]
| [
"nonn",
"easy"
]
| 9 | 0 | 4 | [
"A384201",
"A384202"
]
| null | Seiichi Manyama, May 22 2025 | 2025-05-22T05:23:34 | oeisdata/seq/A384/A384201.seq | 3f3546c0693c7e5e91bc40eaf3d13bc0 |
A384202 | Expansion of e.g.f. -log(1 - 3*x)/(3 * (1 + x)). | [
"0",
"1",
"1",
"15",
"102",
"1434",
"20556",
"380988",
"7974576",
"192768336",
"5214883680",
"156913290720",
"5188181880960",
"187114724853120",
"7308276334974720",
"307346919257952000",
"13846147184588544000",
"665272996712352000000",
"33958618500545883648000",
"1835197000323512071680000"
]
| [
"nonn",
"easy"
]
| 11 | 0 | 4 | [
"A384201",
"A384202"
]
| null | Seiichi Manyama, May 22 2025 | 2025-05-22T06:56:51 | oeisdata/seq/A384/A384202.seq | 73519382f79aebbdee3ab084fa1c6c33 |
A384203 | Population of elementary triangular automaton rule 250 at generation n, starting from a lone 1 cell at generation 0. | [
"1",
"4",
"10",
"16",
"22",
"34",
"52",
"64",
"70",
"82",
"106",
"142",
"172",
"202",
"244",
"268",
"274",
"286",
"310",
"346",
"382",
"430",
"502",
"574",
"616",
"646",
"706",
"802",
"892",
"976",
"1078",
"1132",
"1138",
"1150",
"1174",
"1210",
"1246",
"1294",
"1366",
"1438",
"1486",
"1534",
"1618",
"1750",
"1894",
"2026",
"2182",
"2326",
"2392",
"2422"
]
| [
"nonn"
]
| 9 | 0 | 2 | null | null | Paul Cousin, May 22 2025 | 2025-05-22T09:38:37 | oeisdata/seq/A384/A384203.seq | 61a1e8516576d54173de0d4ee6bf9866 |
A384205 | a(n) = [x^(2*n)] Product_{k=0..n} 1/(1 - k*x)^2. | [
"1",
"3",
"201",
"40792",
"16904053",
"11861321255",
"12632193171300",
"19003969060842360",
"38387884967440214085",
"100260769162534336491025",
"328834941448280603509191681",
"1323249839691864496146379353852",
"6410573322270839015074278503521740",
"36805304509116365389123823470306765972"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A007820",
"A350376",
"A384205",
"A384206"
]
| null | Vaclav Kotesovec, May 22 2025 | 2025-05-22T17:07:03 | oeisdata/seq/A384/A384205.seq | 45ed9f9f520d845f3fd1475af13dbd4d |
A384206 | a(n) = [x^(3*n)] Product_{k=0..n} 1/(1 - k*x)^2. | [
"1",
"4",
"1291",
"2107596",
"9822847079",
"99559982844000",
"1870441451243408425",
"58630795546429054116336",
"2846132741588198942785663319",
"202389763024999232451527049522000",
"20194222519959431156536932169706390700",
"2731878423936456763814384150978735866605108"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A350376",
"A384206",
"A384207"
]
| null | Vaclav Kotesovec, May 22 2025 | 2025-05-22T17:09:18 | oeisdata/seq/A384/A384206.seq | 578e278a9ea384fa48602c076632acbe |
A384207 | a(n) = [x^(3*n)] Product_{k=0..n} 1/(1 - k*x)^3. | [
"1",
"10",
"6562",
"21157758",
"192817813260",
"3803916720008250",
"138757892706447212551",
"8432782489668636227456524",
"792912489591430219972681508172",
"109146372957847294924041235504625400",
"21071987342698034891951000233099719150440",
"5513873439400596105839885628799257242723984298"
]
| [
"nonn"
]
| 11 | 0 | 2 | [
"A007820",
"A383862",
"A384022",
"A384206",
"A384207"
]
| null | Vaclav Kotesovec, May 22 2025 | 2025-05-22T17:12:46 | oeisdata/seq/A384/A384207.seq | b849396273631f7bfc3294d13289f5d6 |
A384208 | a(n) is the number of ways to partition a square n X n into five rectangles of different dimensions, without any straight cut spanning the entire square. | [
"0",
"0",
"0",
"1",
"4",
"15",
"39",
"88",
"162",
"283",
"450",
"691",
"1005",
"1425",
"1954",
"2626",
"3444",
"4452",
"5652",
"7094",
"8775",
"10755",
"13035",
"15676",
"18679",
"22053",
"25819",
"29967",
"34543",
"39531",
"44976",
"50878",
"57231",
"64026",
"71296",
"79026",
"87243",
"95920",
"105036",
"114590",
"124672",
"135206",
"146231",
"157684",
"169642",
"182051",
"194927",
"208298",
"222125",
"236484"
]
| [
"nonn"
]
| 21 | 1 | 5 | [
"A381847",
"A384208"
]
| null | Janaka Rodrigo, May 22 2025 | 2025-06-04T10:24:24 | oeisdata/seq/A384/A384208.seq | 1d87dc45d32eae310aa4309b767c99a5 |
A384209 | Maximum period for Game of Life on a simple graph with n vertices. | [
"1",
"1",
"1",
"1",
"2",
"4",
"8",
"14",
"27"
]
| [
"nonn",
"more"
]
| 8 | 1 | 5 | [
"A357951",
"A384209"
]
| null | Pontus von Brömssen, May 22 2025 | 2025-05-22T09:53:28 | oeisdata/seq/A384/A384209.seq | c3de30753be04bc418947d793a304723 |
A384210 | Number of numbers <= n of the form p * m^2, where p is a prime and m is an integer >= 1. | [
"0",
"1",
"2",
"2",
"3",
"3",
"4",
"5",
"5",
"5",
"6",
"7",
"8",
"8",
"8",
"8",
"9",
"10",
"11",
"12",
"12",
"12",
"13",
"13",
"13",
"13",
"14",
"15",
"16",
"16",
"17",
"18",
"18",
"18",
"18",
"18",
"19",
"19",
"19",
"19",
"20",
"20",
"21",
"22",
"23",
"23",
"24",
"25",
"25",
"26",
"26",
"27",
"28",
"28",
"28",
"28",
"28",
"28",
"29",
"29",
"30",
"30",
"31",
"31",
"31",
"31",
"32",
"33",
"33",
"33",
"34",
"35",
"36",
"36",
"37"
]
| [
"nonn"
]
| 16 | 1 | 3 | [
"A000720",
"A001221",
"A008836",
"A229125",
"A358769",
"A384210"
]
| null | Ridouane Oudra, May 22 2025 | 2025-06-06T14:48:06 | oeisdata/seq/A384/A384210.seq | 659915eb94c098c44127c962f3adee37 |
A384211 | a(n) is the number of distinct ways of representing n in any integer base >= 2 using only prime digits. | [
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"1",
"2",
"2",
"2",
"1",
"4",
"2",
"3",
"2",
"3",
"1",
"6",
"2",
"3",
"4",
"4",
"1",
"6",
"2",
"5",
"4",
"5",
"2",
"7",
"2",
"7",
"4",
"5",
"3",
"8",
"4",
"9",
"3",
"7",
"3",
"12",
"3",
"6",
"5",
"6",
"4",
"11",
"2",
"9",
"4",
"9",
"6",
"13",
"3",
"11",
"8",
"12",
"3",
"12",
"3",
"13",
"7",
"8",
"5",
"14",
"5",
"13",
"5",
"11",
"4",
"15",
"3",
"13",
"8",
"10",
"7",
"15"
]
| [
"nonn",
"base"
]
| 12 | 0 | 12 | [
"A055240",
"A355034",
"A384211"
]
| null | Felix Huber, May 23 2025 | 2025-05-30T18:11:10 | oeisdata/seq/A384/A384211.seq | 031ccf5bb2fb0a1010cad6b33da19d1f |
A384212 | a(n) is the number of bases >= 2 in which the alternating sum of digits of n is equal to 0. | [
"0",
"0",
"1",
"1",
"1",
"2",
"1",
"2",
"2",
"2",
"1",
"4",
"1",
"2",
"3",
"3",
"1",
"4",
"1",
"3",
"2",
"2",
"1",
"6",
"2",
"2",
"3",
"4",
"1",
"6",
"1",
"4",
"3",
"2",
"2",
"7",
"1",
"2",
"3",
"6",
"1",
"5",
"1",
"4",
"5",
"2",
"1",
"8",
"2",
"3",
"3",
"4",
"1",
"5",
"2",
"6",
"3",
"2",
"1",
"9",
"1",
"2",
"5",
"5",
"3",
"6",
"1",
"4",
"2",
"6",
"1",
"10",
"1",
"2",
"5",
"4",
"2",
"5",
"1",
"8",
"3",
"2",
"1",
"8",
"3",
"2",
"2"
]
| [
"nonn",
"base"
]
| 19 | 1 | 6 | [
"A055240",
"A061845",
"A135499",
"A135551",
"A225693",
"A384211",
"A384212"
]
| null | Felix Huber, May 24 2025 | 2025-06-03T17:49:23 | oeisdata/seq/A384/A384212.seq | a33953b6f3029d83b7b611fcfc3833b3 |
A384213 | Decimal expansion of the volume of an elongated pentagonal rotunda with unit edge. | [
"1",
"4",
"6",
"1",
"1",
"9",
"7",
"1",
"8",
"1",
"1",
"0",
"6",
"2",
"8",
"3",
"5",
"5",
"7",
"6",
"3",
"3",
"8",
"7",
"2",
"2",
"4",
"7",
"0",
"7",
"9",
"4",
"9",
"1",
"5",
"8",
"9",
"3",
"5",
"5",
"7",
"6",
"3",
"1",
"3",
"6",
"8",
"2",
"9",
"4",
"1",
"4",
"2",
"5",
"1",
"0",
"3",
"1",
"4",
"9",
"9",
"5",
"0",
"5",
"6",
"9",
"3",
"5",
"3",
"9",
"6",
"1",
"9",
"9",
"2",
"2",
"4",
"6",
"1",
"7",
"5",
"7",
"0",
"3",
"0",
"6",
"9",
"0",
"4",
"7"
]
| [
"nonn",
"cons",
"easy"
]
| 11 | 2 | 2 | [
"A002163",
"A010476",
"A179637",
"A384138",
"A384140",
"A384144",
"A384213"
]
| null | Paolo Xausa, May 23 2025 | 2025-05-23T10:14:01 | oeisdata/seq/A384/A384213.seq | 9f1b7d3250cdbc3c754daffa838738b7 |
A384214 | Decimal expansion of the volume of a gyroelongated square cupola with unit edge. | [
"6",
"2",
"1",
"0",
"7",
"6",
"5",
"7",
"9",
"2",
"0",
"3",
"9",
"2",
"0",
"0",
"0",
"3",
"6",
"6",
"5",
"8",
"2",
"2",
"8",
"8",
"3",
"3",
"4",
"5",
"9",
"8",
"0",
"7",
"3",
"1",
"6",
"9",
"6",
"0",
"1",
"0",
"0",
"3",
"2",
"0",
"9",
"1",
"3",
"7",
"4",
"5",
"1",
"7",
"8",
"3",
"6",
"4",
"1",
"8",
"1",
"7",
"0",
"5",
"4",
"3",
"7",
"9",
"9",
"6",
"0",
"4",
"6",
"7",
"0",
"8",
"9",
"3",
"8",
"4",
"9",
"5",
"9",
"9",
"9",
"4",
"2",
"7",
"1",
"3"
]
| [
"nonn",
"cons",
"easy"
]
| 10 | 1 | 1 | [
"A002193",
"A010466",
"A179587",
"A179638",
"A384142",
"A384214",
"A384215"
]
| null | Paolo Xausa, May 23 2025 | 2025-05-24T01:56:29 | oeisdata/seq/A384/A384214.seq | 16f5dc075f440e755111ee713a47cd8d |
A384215 | Decimal expansion of the surface area of a gyroelongated square cupola with unit edge. | [
"1",
"8",
"4",
"8",
"8",
"6",
"8",
"1",
"1",
"6",
"2",
"5",
"9",
"0",
"5",
"7",
"6",
"5",
"6",
"5",
"2",
"4",
"0",
"6",
"0",
"9",
"1",
"5",
"5",
"9",
"4",
"8",
"7",
"5",
"7",
"9",
"9",
"1",
"8",
"5",
"3",
"3",
"7",
"0",
"0",
"1",
"9",
"8",
"0",
"5",
"7",
"9",
"9",
"2",
"8",
"6",
"6",
"3",
"2",
"3",
"9",
"4",
"3",
"7",
"3",
"2",
"4",
"1",
"1",
"3",
"0",
"0",
"4",
"1",
"4",
"6",
"8",
"2",
"1",
"4",
"2",
"6",
"3",
"1",
"0",
"6",
"5",
"0",
"6",
"0"
]
| [
"nonn",
"cons",
"easy"
]
| 7 | 2 | 2 | [
"A002194",
"A010466",
"A384214",
"A384215"
]
| null | Paolo Xausa, May 23 2025 | 2025-05-24T01:58:52 | oeisdata/seq/A384/A384215.seq | c227b4651f544b4d6fe84b4c9b008ea6 |
A384216 | Square array A(n,k), n >= 0, k >= 1, read by antidiagonals: A(n,k) = n! * [x^n] (1 + k*x)^(n/k). | [
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"0",
"6",
"1",
"1",
"-2",
"-3",
"24",
"1",
"1",
"-4",
"0",
"0",
"120",
"1",
"1",
"-6",
"15",
"40",
"45",
"720",
"1",
"1",
"-8",
"42",
"0",
"-280",
"0",
"5040",
"1",
"1",
"-10",
"81",
"-264",
"-1155",
"0",
"-1575",
"40320",
"1",
"1",
"-12",
"132",
"-896",
"0",
"20160",
"24640",
"0",
"362880",
"1",
"1",
"-14",
"195",
"-2040",
"8645",
"57456",
"-208845",
"-291200",
"99225",
"3628800"
]
| [
"sign",
"tabl",
"easy"
]
| 21 | 0 | 6 | [
"A282627",
"A303489",
"A383996",
"A383997",
"A384216"
]
| null | Seiichi Manyama, May 22 2025 | 2025-05-24T05:29:37 | oeisdata/seq/A384/A384216.seq | 813e19eefe3e18264e892a9a6ff87874 |
A384217 | Consecutive states of the linear congruential pseudo-random number generator (843314861*s+453816693) mod 2^31 when started at s=1. | [
"1",
"1297131554",
"17103983",
"1426780792",
"2111429773",
"1142766270",
"888797147",
"1081516660",
"1471148505",
"488941338",
"1429379591",
"2081849904",
"166513637",
"1928300854",
"1776832243",
"142642604",
"236172977",
"1916812562",
"182141599",
"551190760",
"1397538365",
"1487855278",
"1455317259"
]
| [
"nonn",
"easy"
]
| 24 | 1 | 2 | [
"A096550",
"A096561",
"A384217",
"A384387"
]
| null | Sean A. Irvine, May 29 2025 | 2025-05-30T03:43:53 | oeisdata/seq/A384/A384217.seq | edfe7c0eba02e6b38745a0430e50a8f9 |
A384218 | Numbers k such that the concatenations of k and 123456789 in both orders are prime. | [
"217",
"409",
"629",
"653",
"779",
"871",
"881",
"1091",
"1463",
"1489",
"1913",
"1993",
"2039",
"2729",
"2881",
"3397",
"3649",
"3677",
"3751",
"3961",
"4073",
"4321",
"4843",
"4961",
"5039",
"5507",
"5609",
"5683",
"5849",
"5941",
"6593",
"6613",
"6713",
"6923",
"7349",
"7571",
"7789",
"7907",
"8413",
"8419",
"8617",
"8623",
"8687",
"8689",
"8797",
"8909",
"9083",
"9589",
"9973",
"10241"
]
| [
"nonn",
"base"
]
| 16 | 1 | 1 | [
"A232725",
"A232727",
"A384174",
"A384218"
]
| null | Robert Israel, May 22 2025 | 2025-05-23T10:13:52 | oeisdata/seq/A384/A384218.seq | 9910abb5ed94251b90213f39e4c7cf2c |
A384219 | Areas of triangles whose three vertices are consecutive ordered pairs of consecutive odd Fibonacci numbers such that an ordered pair’s y-value is the next ordered pair’s x-value. | [
"2",
"6",
"24",
"104",
"442",
"1870",
"7920",
"33552",
"142130",
"602070",
"2550408",
"10803704",
"45765226",
"193864606",
"821223648",
"3478759200",
"14736260450",
"62423800998",
"264431464440",
"1120149658760",
"4745030099482",
"20100270056686",
"85146110326224",
"360684711361584",
"1527884955772562"
]
| [
"nonn",
"easy"
]
| 17 | 1 | 1 | [
"A000045",
"A014437",
"A384219"
]
| null | Angela L. Brobson, May 22 2025 | 2025-05-30T18:47:35 | oeisdata/seq/A384/A384219.seq | 33de3d57125d5d3432f4aa9bc8abc0dc |
A384220 | Consecutive states of the linear congruential pseudo-random number generator for Smalltalk-80 when started at 1. | [
"1",
"41030",
"24167",
"29748",
"11069",
"4562",
"19459",
"53408",
"8761",
"54302",
"60255",
"60364",
"8437",
"29482",
"55419",
"12728",
"9073",
"15094",
"28503",
"52836",
"58797",
"14210",
"52211",
"44496",
"58281",
"13518",
"51791",
"31740",
"22885",
"48858",
"1643",
"42216",
"17121",
"8614",
"56391",
"21652",
"23581",
"26930"
]
| [
"nonn",
"easy"
]
| 14 | 1 | 2 | [
"A096550",
"A096561",
"A383940",
"A384220"
]
| null | Sean A. Irvine, May 22 2025 | 2025-05-28T00:56:38 | oeisdata/seq/A384/A384220.seq | d7afd2afe803fc1b1bc431b63d8259bd |
A384221 | Consecutive states of the linear congruential pseudo-random number generator for the Texas Instruments TI99 when started at 1. | [
"1",
"60062",
"56335",
"54564",
"49133",
"60602",
"58139",
"22240",
"20761",
"56598",
"51559",
"19676",
"40837",
"55218",
"39667",
"29464",
"55089",
"14478",
"41919",
"50580",
"25629",
"39850",
"28619",
"32848",
"62025",
"56582",
"51991",
"8012",
"28085",
"6306",
"49571",
"24200",
"609",
"43646",
"40815",
"14852",
"7245",
"11930"
]
| [
"nonn",
"easy"
]
| 15 | 1 | 2 | [
"A096550",
"A096561",
"A384221"
]
| null | Sean A. Irvine, May 22 2025 | 2025-05-28T16:25:07 | oeisdata/seq/A384/A384221.seq | 3f3c1017d955fc03046077fe5693dd48 |
A384222 | Irregular triangle read by rows: T(n,k) is the length of the k-th sublist of divisors of n whose terms increase by a factor of at most 2, with n >= 1, k >= 1. | [
"1",
"2",
"1",
"1",
"3",
"1",
"1",
"4",
"1",
"1",
"4",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"6",
"1",
"1",
"2",
"2",
"1",
"2",
"1",
"5",
"1",
"1",
"6",
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"6",
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"1",
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"8",
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"2",
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"2",
"2",
"1",
"1",
"1",
"1",
"3",
"3",
"1",
"1",
"8"
]
| [
"nonn",
"tabf",
"changed"
]
| 79 | 1 | 2 | [
"A000005",
"A000203",
"A027750",
"A174973",
"A237270",
"A237271",
"A237591",
"A237593",
"A240062",
"A320537",
"A384149",
"A384222"
]
| null | Omar E. Pol, Jun 03 2025 | 2025-07-08T10:44:20 | oeisdata/seq/A384/A384222.seq | 079a7983825f6a29a43a6ebf87730d54 |
A384223 | Irregular triangle read by rows: T(n,k) is the sum of the k-th odd divisor and the next even divisors that are less than the next odd divisor of n, with n >= 1, k >= 1. | [
"1",
"3",
"1",
"3",
"7",
"1",
"5",
"3",
"9",
"1",
"7",
"15",
"1",
"3",
"9",
"3",
"15",
"1",
"11",
"3",
"25",
"1",
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"1",
"37",
"3",
"57",
"1",
"3",
"13",
"39",
"7",
"83"
]
| [
"nonn",
"tabf",
"easy"
]
| 20 | 1 | 2 | [
"A000079",
"A000203",
"A001227",
"A027750",
"A237270",
"A237271",
"A237593",
"A279387",
"A384149",
"A384223",
"A384224"
]
| null | Omar E. Pol, Jun 03 2025 | 2025-06-16T17:30:34 | oeisdata/seq/A384/A384223.seq | 87e16ff20d24d2bc6c008ac9f6b7196b |
A384224 | Irregular triangle read by rows: T(n,k) is the number of divisors in the k-th sublist of the divisors of n formed by the k-th odd divisor and the next even divisors that are less than the next odd divisor of n, with n >= 1, k >= 1. | [
"1",
"2",
"1",
"1",
"3",
"1",
"1",
"2",
"2",
"1",
"1",
"4",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"4",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"5",
"1",
"1",
"2",
"2",
"2",
"1",
"1",
"3",
"3",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"6",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"3",
"3",
"1",
"1",
"2",
"1",
"3",
"2",
"1",
"1",
"6",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"3",
"4",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"3",
"5",
"1",
"1",
"2",
"2",
"2",
"2",
"1",
"1",
"3",
"3"
]
| [
"nonn",
"tabf",
"easy"
]
| 16 | 1 | 2 | [
"A000005",
"A000079",
"A001227",
"A027750",
"A237270",
"A237271",
"A237593",
"A279387",
"A384222",
"A384223",
"A384224"
]
| null | Omar E. Pol, Jun 04 2025 | 2025-06-16T17:37:41 | oeisdata/seq/A384/A384224.seq | 494904b81108d483e0ad3535b886b419 |
A384225 | Irregular triangle read by rows: T(n,k) is the number of odd divisors in the k-th sublist of divisors of n whose terms increase by a factor of at most 2, with n >= 1, k >= 1. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"3",
"1",
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"1",
"4",
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"1",
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"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"4",
"1",
"1",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"4"
]
| [
"nonn",
"tabf",
"changed"
]
| 26 | 1 | 8 | [
"A001227",
"A237271",
"A237590",
"A237593",
"A279387",
"A280940",
"A384149",
"A384222",
"A384225"
]
| null | Omar E. Pol, Jun 16 2025 | 2025-07-08T10:42:33 | oeisdata/seq/A384/A384225.seq | 6e2a1255865ff1803013378a87bec1d6 |
A384226 | Irregular triangle read by rows: T(n,k) is the sum of odd divisors in the k-th sublist of divisors of n whose terms increase by a factor of at most 2, with n >= 1, k >= 1. | [
"1",
"1",
"1",
"3",
"1",
"1",
"5",
"4",
"1",
"7",
"1",
"1",
"3",
"9",
"1",
"5",
"1",
"11",
"4",
"1",
"13",
"1",
"7",
"1",
"8",
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"17",
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"1",
"41",
"32",
"1",
"43",
"1",
"11",
"1",
"32",
"45",
"1",
"23",
"1",
"47",
"4"
]
| [
"nonn",
"tabf",
"changed"
]
| 22 | 1 | 4 | [
"A000593",
"A237271",
"A237593",
"A384149",
"A384222",
"A384225",
"A384226"
]
| null | Omar E. Pol, Jun 24 2025 | 2025-07-08T10:42:46 | oeisdata/seq/A384/A384226.seq | db2c647affd3824c1d86c0d301ba7f9e |
A384231 | Index of the largest odd noncomposite divisor in the list of divisors of n. | [
"1",
"1",
"2",
"1",
"2",
"3",
"2",
"1",
"2",
"3",
"2",
"3",
"2",
"3",
"3",
"1",
"2",
"3",
"2",
"4",
"3",
"3",
"2",
"3",
"2",
"3",
"2",
"4",
"2",
"4",
"2",
"1",
"3",
"3",
"3",
"3",
"2",
"3",
"3",
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"5",
"2",
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"3",
"2",
"3",
"3",
"4",
"2",
"3",
"3",
"4",
"3",
"3",
"2",
"5",
"2",
"3",
"3",
"1",
"3",
"5",
"2",
"4",
"3",
"4",
"2",
"3",
"2",
"3",
"3",
"4",
"3",
"5",
"2",
"4",
"2",
"3",
"2",
"6",
"3",
"3",
"3",
"5",
"2",
"4",
"3",
"4",
"3",
"3",
"3",
"3",
"2",
"3",
"4",
"4"
]
| [
"nonn",
"easy"
]
| 14 | 1 | 3 | [
"A000079",
"A006005",
"A027750",
"A383401",
"A384231",
"A384232",
"A384233",
"A384234"
]
| null | Omar E. Pol, May 29 2025 | 2025-06-03T00:59:39 | oeisdata/seq/A384/A384231.seq | 6c2d113e686b893f38f224eeb6f1bab6 |
A384232 | Smallest number whose largest odd noncomposite divisor is its n-th divisor. | [
"1",
"3",
"6",
"20",
"42",
"84",
"156",
"312",
"684",
"1020",
"1380",
"1860",
"3480",
"3720",
"4920",
"7320",
"10980",
"14640",
"16920",
"21960",
"26280",
"34920",
"45720",
"59640",
"69840",
"89880",
"106680",
"125160",
"145320",
"177240",
"213360",
"244440",
"269640",
"354480",
"320040",
"375480",
"435960",
"456120",
"531720",
"647640",
"708120"
]
| [
"nonn"
]
| 20 | 1 | 2 | [
"A006005",
"A027750",
"A087134",
"A383402",
"A384232",
"A384233"
]
| null | Omar E. Pol, May 23 2025 | 2025-05-29T00:13:52 | oeisdata/seq/A384/A384232.seq | c212fffee45f1b73bf02f367046464fc |
A384233 | Square array read by upward antidiagonals: T(n,k) is the n-th number whose largest odd noncomposite divisor is its k-th divisor, n >= 1, k >= 1. | [
"1",
"2",
"3",
"4",
"5",
"6",
"8",
"7",
"10",
"20",
"16",
"9",
"12",
"28",
"42",
"32",
"11",
"14",
"30",
"60",
"84",
"64",
"13",
"15",
"40",
"66",
"132",
"156",
"128",
"17",
"18",
"44",
"78",
"168",
"204",
"312",
"256",
"19",
"21",
"52",
"88",
"198",
"228",
"408",
"684",
"512",
"23",
"22",
"56",
"102",
"210",
"264",
"456",
"696",
"1020",
"1024",
"25",
"24",
"68",
"104",
"220",
"276",
"468",
"744",
"1140",
"1380"
]
| [
"nonn",
"tabl"
]
| 17 | 1 | 2 | [
"A000079",
"A006005",
"A027750",
"A061345",
"A065091",
"A087134",
"A383961",
"A384232",
"A384233"
]
| null | Omar E. Pol, May 22 2025 | 2025-05-29T00:12:45 | oeisdata/seq/A384/A384233.seq | ecc4f9b6d55e66c45a7a19c0b79a7079 |
A384234 | Irregular triangle read by rows: T(n,k) is the index of the k-th odd noncomposite divisor in the list of divisors of n, with n >=1, k >= 1. | [
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"3",
"1",
"2",
"3",
"1",
"1",
"2",
"1",
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"1",
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"1",
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"1",
"2",
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"1",
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"1",
"3",
"1",
"2",
"1",
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"1",
"2",
"1",
"3",
"4",
"1",
"2",
"1",
"1",
"2",
"3",
"1",
"3",
"1",
"2",
"3",
"1",
"3",
"1",
"2",
"1",
"3",
"1",
"2",
"3",
"1",
"4",
"1",
"2",
"1",
"3",
"5",
"1",
"2",
"1",
"4",
"1",
"2",
"3",
"1",
"3",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"3"
]
| [
"nonn",
"tabf",
"easy"
]
| 12 | 1 | 4 | [
"A000012",
"A000079",
"A006005",
"A027750",
"A383962",
"A384231",
"A384232",
"A384233",
"A384234"
]
| null | Omar E. Pol, May 29 2025 | 2025-06-03T01:00:09 | oeisdata/seq/A384/A384234.seq | e44aa22a0623a0de8e3d0c7c8a41ea85 |
A384235 | a(n) is the least number that is the concatenation of n consecutive primes, in increasing order, and is the product of n primes, counted with multiplicity. | [
"2",
"35",
"357",
"11131719",
"3571113",
"5711131719",
"463467479487491499503",
"811821823827829839853857",
"103910491051106110631069108710911093",
"1291129713011303130713191321132713611367",
"19011907191319311933194919511973197919871993",
"109091093710939109491095710973109791098710993110031102711047"
]
| [
"nonn",
"base"
]
| 17 | 1 | 1 | [
"A383114",
"A384235"
]
| null | Robert Israel, May 23 2025 | 2025-06-03T02:28:06 | oeisdata/seq/A384/A384235.seq | b5998cab47584b12b40b7fb3b34ea34b |
A384236 | Consecutive states of the linear congruential pseudo-random number generator (9806*s+1) mod (2^17-1) when started at s=1. | [
"1",
"9807",
"92400",
"111649",
"125103",
"66530",
"52814",
"32564",
"33629",
"122410",
"4243",
"57352",
"99123",
"108674",
"50015",
"110480",
"65066",
"114640",
"94945",
"33358",
"86404",
"34681",
"83713",
"123077",
"122366",
"97063",
"93248",
"38593",
"40982",
"5807",
"58629",
"38569",
"67780",
"120711",
"120937",
"108886"
]
| [
"nonn",
"easy"
]
| 13 | 1 | 2 | [
"A096550",
"A096561",
"A384236"
]
| null | Sean A. Irvine, May 22 2025 | 2025-06-17T17:47:10 | oeisdata/seq/A384/A384236.seq | f51546cca521b1006f93c2d24bcf1a26 |
A384237 | The number of divisors d of n such that d^d = d (mod n). | [
"1",
"2",
"2",
"2",
"2",
"3",
"2",
"2",
"2",
"3",
"2",
"4",
"2",
"3",
"3",
"2",
"2",
"3",
"2",
"3",
"3",
"3",
"2",
"3",
"2",
"3",
"2",
"4",
"2",
"6",
"2",
"2",
"3",
"3",
"2",
"4",
"2",
"3",
"3",
"3",
"2",
"4",
"2",
"3",
"3",
"3",
"2",
"3",
"2",
"3",
"3",
"3",
"2",
"3",
"3",
"4",
"3",
"3",
"2",
"4",
"2",
"3",
"3",
"2",
"4",
"5",
"2",
"3",
"3",
"3",
"2",
"3",
"2",
"3",
"3",
"3",
"2",
"4",
"2",
"4",
"2",
"3",
"2",
"6",
"3",
"3",
"3",
"3",
"2",
"5",
"3",
"3",
"3",
"3",
"3",
"2",
"2",
"3",
"2",
"3"
]
| [
"nonn"
]
| 22 | 1 | 2 | [
"A000005",
"A027750",
"A384237"
]
| null | Juri-Stepan Gerasimov, May 22 2025 | 2025-05-31T00:00:43 | oeisdata/seq/A384/A384237.seq | acbb2d3a9a45da48f390fdda67b3c067 |
A384238 | Decimal expansion of sqrt(5) - log(phi) - 1, where phi is the golden ratio. | [
"7",
"5",
"4",
"8",
"5",
"6",
"1",
"5",
"2",
"4",
"4",
"0",
"1",
"8",
"6",
"2",
"4",
"8",
"9",
"1",
"1",
"4",
"1",
"4",
"7",
"5",
"5",
"3",
"0",
"6",
"9",
"0",
"7",
"8",
"1",
"2",
"3",
"0",
"5",
"4",
"3",
"4",
"0",
"2",
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"2",
"2",
"5",
"8",
"6",
"5",
"2",
"0",
"4",
"6",
"0",
"9",
"8",
"7",
"9",
"0",
"7",
"6",
"5",
"7",
"0",
"3",
"5",
"7",
"0",
"5",
"8",
"0",
"2",
"9",
"5",
"8",
"3",
"1",
"2",
"5",
"0",
"0",
"2",
"4",
"0",
"4"
]
| [
"nonn",
"cons"
]
| 24 | 0 | 1 | [
"A002163",
"A002390",
"A384238",
"A384682"
]
| null | Kritsada Moomuang, May 22 2025 | 2025-06-09T10:38:50 | oeisdata/seq/A384/A384238.seq | 173457cd2983d85d593e9ef63a79c6e4 |
A384239 | The number of primes p <= n such that p^p = p (mod n). | [
"0",
"1",
"1",
"1",
"1",
"2",
"1",
"3",
"1",
"1",
"1",
"4",
"2",
"2",
"3",
"3",
"2",
"3",
"2",
"5",
"3",
"1",
"1",
"8",
"1",
"2",
"1",
"3",
"2",
"6",
"1",
"2",
"3",
"2",
"4",
"5",
"1",
"4",
"3",
"8",
"2",
"7",
"3",
"5",
"5",
"1",
"1",
"10",
"4",
"3",
"2",
"4",
"1",
"3",
"3",
"8",
"4",
"3",
"1",
"11",
"3",
"3",
"7",
"3",
"5",
"6",
"2",
"3",
"3",
"7",
"1",
"11",
"2",
"2",
"5",
"5",
"6",
"7",
"1",
"12",
"3",
"4",
"1",
"14",
"2",
"4",
"5",
"8",
"2",
"11"
]
| [
"nonn"
]
| 20 | 1 | 6 | [
"A000720",
"A010051",
"A384239"
]
| null | Juri-Stepan Gerasimov, May 22 2025 | 2025-05-30T16:50:18 | oeisdata/seq/A384/A384239.seq | 9ef3b5ae651e9040964192effbf2cbca |
A384240 | Consecutive states of the linear congruential pseudo-random number generator (2897*s + 1) mod 2^23 when started at s=1. | [
"1",
"2898",
"6899",
"3209188",
"2439973",
"5393846",
"6383767",
"5280968",
"6531913",
"6640922",
"3672891",
"3610284",
"6787181",
"7954814",
"1589983",
"834960",
"2960017",
"2011874",
"6705027",
"4835700",
"47541",
"3508550",
"5665063",
"3570264",
"8289753",
"7218346",
"7137227",
"7016508",
"1226493",
"4769038"
]
| [
"nonn",
"easy"
]
| 13 | 1 | 2 | [
"A096550",
"A096561",
"A384240"
]
| null | Sean A. Irvine, May 22 2025 | 2025-06-19T19:44:06 | oeisdata/seq/A384/A384240.seq | 25df307fc065aff435edf210e77a89ad |
A384241 | a(n) = Product_{k=0..n-1} (3*n-4*k). | [
"1",
"3",
"12",
"45",
"0",
"-3465",
"-60480",
"-626535",
"0",
"204417675",
"6227020800",
"104928949125",
"0",
"-77849405258625",
"-3379030566912000",
"-78792721832199375",
"0",
"104312208642352585875",
"5875458349746585600000",
"174954117301479619228125",
"0",
"-362526128354588965187045625",
"-25100240092118201519308800000"
]
| [
"sign",
"easy"
]
| 11 | 0 | 2 | [
"A064352",
"A343445",
"A383996",
"A384166",
"A384241"
]
| null | Seiichi Manyama, May 22 2025 | 2025-05-23T10:20:55 | oeisdata/seq/A384/A384241.seq | ae5d540ef8499a68e2b6e375e35cbf8a |
A384242 | a(n) = Product_{k=0..n-1} (4*n-5*k). | [
"1",
"4",
"24",
"168",
"1056",
"0",
"-229824",
"-7233408",
"-162860544",
"-2573835264",
"0",
"2333140153344",
"131053381595136",
"4948323499671552",
"124773727026364416",
"0",
"-256422032696998232064",
"-20710128948965418074112",
"-1096668276542495972130816",
"-37948699305215165278715904",
"0"
]
| [
"sign",
"easy"
]
| 13 | 0 | 2 | [
"A061924",
"A343446",
"A383997",
"A384242"
]
| null | Seiichi Manyama, May 22 2025 | 2025-05-26T05:43:00 | oeisdata/seq/A384/A384242.seq | 4c1bc686cab536c01a05bb5735d32862 |
A384243 | a(n) = 2^(n-6)*n*(n^3 - 6*n^2 + 19*n - 14). | [
"0",
"0",
"1",
"6",
"30",
"140",
"600",
"2352",
"8512",
"28800",
"92160",
"281600",
"827904",
"2356224",
"6522880",
"17633280",
"46694400",
"121438208",
"310837248",
"784465920",
"1954938880",
"4816896000",
"11747721216",
"28386000896",
"68010639360",
"161690419200",
"381681664000",
"895098028032",
"2086448136192",
"4836200284160"
]
| [
"nonn",
"easy"
]
| 11 | 0 | 4 | [
"A060354",
"A327319",
"A383778",
"A384243"
]
| null | Enrique Navarrete, May 23 2025 | 2025-05-27T10:10:09 | oeisdata/seq/A384/A384243.seq | b8483bd1f98f9c98c89037283f368380 |
A384244 | Triangle in which the n-th row gives the numbers k from 1 to n such that the greatest common unitary divisor of k and n is 1. | [
"1",
"1",
"1",
"2",
"1",
"2",
"3",
"1",
"2",
"3",
"4",
"1",
"4",
"5",
"1",
"2",
"3",
"4",
"5",
"6",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"1",
"3",
"4",
"7",
"8",
"9",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"1",
"2",
"5",
"7",
"8",
"9",
"10",
"11",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"1",
"3",
"4",
"5",
"8",
"9",
"11",
"12",
"13",
"1",
"2",
"4",
"7",
"8",
"9",
"11",
"13",
"14"
]
| [
"nonn",
"tabf",
"easy"
]
| 9 | 1 | 4 | [
"A038566",
"A064379",
"A077610",
"A089912",
"A116550",
"A165430",
"A200723",
"A225174",
"A384046",
"A384244"
]
| null | Amiram Eldar, May 23 2025 | 2025-05-27T01:17:52 | oeisdata/seq/A384/A384244.seq | 99da3be026595605afb157aa453948b7 |
A384245 | Triangle read by rows: T(n, k) for 1 <= k <= n is the largest divisor of k that is an infinitary divisor of n. | [
"1",
"1",
"2",
"1",
"1",
"3",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"1",
"5",
"1",
"2",
"3",
"2",
"1",
"6",
"1",
"1",
"1",
"1",
"1",
"1",
"7",
"1",
"2",
"1",
"4",
"1",
"2",
"1",
"8",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"9",
"1",
"2",
"1",
"2",
"5",
"2",
"1",
"2",
"1",
"10",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"11",
"1",
"1",
"3",
"4",
"1",
"3",
"1",
"4",
"3",
"1",
"1",
"12",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"13"
]
| [
"nonn",
"tabl",
"easy"
]
| 8 | 1 | 3 | [
"A050873",
"A064379",
"A077609",
"A384047",
"A384245",
"A384246"
]
| null | Amiram Eldar, May 23 2025 | 2025-05-27T01:17:42 | oeisdata/seq/A384/A384245.seq | bca069befca97f028d88ce6f98adb7cc |
A384246 | Triangle in which the n-th row gives the numbers from 1 to n whose largest divisor that is an infinitary divisor of n is 1. | [
"1",
"1",
"1",
"2",
"1",
"2",
"3",
"1",
"2",
"3",
"4",
"1",
"5",
"1",
"2",
"3",
"4",
"5",
"6",
"1",
"3",
"5",
"7",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"1",
"3",
"7",
"9",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"1",
"2",
"5",
"7",
"10",
"11",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"1",
"3",
"5",
"9",
"11",
"13",
"1",
"2",
"4",
"7",
"8",
"11",
"13",
"14",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"15"
]
| [
"nonn",
"tabf",
"easy"
]
| 7 | 1 | 4 | [
"A064379",
"A384046",
"A384245",
"A384246",
"A384247",
"A384248"
]
| null | Amiram Eldar, May 23 2025 | 2025-05-27T01:17:33 | oeisdata/seq/A384/A384246.seq | e20e1842f4f9fc4fe57964a84c88e12d |
A384247 | The number of integers from 1 to n whose largest divisor that is an infinitary divisor of n is 1. | [
"1",
"1",
"2",
"3",
"4",
"2",
"6",
"4",
"8",
"4",
"10",
"6",
"12",
"6",
"8",
"15",
"16",
"8",
"18",
"12",
"12",
"10",
"22",
"8",
"24",
"12",
"18",
"18",
"28",
"8",
"30",
"16",
"20",
"16",
"24",
"24",
"36",
"18",
"24",
"16",
"40",
"12",
"42",
"30",
"32",
"22",
"46",
"30",
"48",
"24",
"32",
"36",
"52",
"18",
"40",
"24",
"36",
"28",
"58",
"24",
"60",
"30",
"48",
"48",
"48",
"20",
"66",
"48",
"44",
"24"
]
| [
"nonn",
"easy",
"mult"
]
| 6 | 1 | 3 | [
"A000010",
"A001146",
"A006519",
"A047994",
"A064380",
"A091732",
"A116550",
"A138302",
"A268335",
"A384246",
"A384247",
"A384248"
]
| null | Amiram Eldar, May 23 2025 | 2025-05-27T01:17:06 | oeisdata/seq/A384/A384247.seq | 0fee8728d3eb341ef7b1e8783f9e9200 |
A384248 | The sum of the integers from 1 to n whose largest divisor that is an infinitary divisor of n is 1. | [
"1",
"1",
"3",
"6",
"10",
"6",
"21",
"16",
"36",
"20",
"55",
"36",
"78",
"42",
"60",
"120",
"136",
"72",
"171",
"120",
"126",
"110",
"253",
"96",
"300",
"156",
"243",
"252",
"406",
"120",
"465",
"256",
"330",
"272",
"420",
"432",
"666",
"342",
"468",
"320",
"820",
"252",
"903",
"660",
"720",
"506",
"1081",
"720",
"1176",
"600",
"816",
"936",
"1378",
"486",
"1100",
"672"
]
| [
"nonn",
"easy"
]
| 6 | 1 | 3 | [
"A023896",
"A138302",
"A200723",
"A268335",
"A333576",
"A384246",
"A384247",
"A384248"
]
| null | Amiram Eldar, May 23 2025 | 2025-05-27T01:17:11 | oeisdata/seq/A384/A384248.seq | 5ee83091e1ff595c8145ba3de242dd1f |
A384249 | The number of integers k from 1 to n such that the greatest divisor of k that is an infinitary divisor of n is squarefree. | [
"1",
"2",
"3",
"3",
"5",
"6",
"7",
"6",
"8",
"10",
"11",
"9",
"13",
"14",
"15",
"15",
"17",
"16",
"19",
"15",
"21",
"22",
"23",
"18",
"24",
"26",
"24",
"21",
"29",
"30",
"31",
"30",
"33",
"34",
"35",
"24",
"37",
"38",
"39",
"30",
"41",
"42",
"43",
"33",
"40",
"46",
"47",
"45",
"48",
"48",
"51",
"39",
"53",
"48",
"55",
"42",
"57",
"58",
"59",
"45",
"61",
"62",
"56",
"48",
"65",
"66",
"67",
"51"
]
| [
"nonn",
"easy",
"mult"
]
| 10 | 1 | 2 | [
"A005117",
"A063659",
"A065176",
"A077609",
"A384048",
"A384247",
"A384249",
"A384250",
"A384251",
"A384252"
]
| null | Amiram Eldar, May 23 2025 | 2025-05-24T00:21:55 | oeisdata/seq/A384/A384249.seq | 1e670e98e8a1546f0e5b7e3d599ec39f |
A384250 | The number of integers k from 1 to n such that the greatest divisor of k that is an infinitary divisor of n is a powerful number. | [
"1",
"1",
"2",
"4",
"4",
"2",
"6",
"6",
"9",
"4",
"10",
"8",
"12",
"6",
"8",
"16",
"16",
"9",
"18",
"16",
"12",
"10",
"22",
"12",
"25",
"12",
"21",
"24",
"28",
"8",
"30",
"18",
"20",
"16",
"24",
"36",
"36",
"18",
"24",
"24",
"40",
"12",
"42",
"40",
"36",
"22",
"46",
"32",
"49",
"25",
"32",
"48",
"52",
"21",
"40",
"36",
"36",
"28",
"58",
"32",
"60",
"30",
"54",
"64",
"48",
"20",
"66",
"64",
"44"
]
| [
"nonn",
"easy",
"mult"
]
| 12 | 1 | 3 | [
"A001694",
"A006519",
"A077609",
"A384039",
"A384050",
"A384247",
"A384249",
"A384250",
"A384251",
"A384252"
]
| null | Amiram Eldar, May 23 2025 | 2025-05-24T00:22:04 | oeisdata/seq/A384/A384250.seq | c12fa0c199be2de1e6fa1dbd2391d2f9 |
A384251 | The number of integers k from 1 to n such that the greatest divisor of k that is an infinitary divisor of n is odd. | [
"1",
"1",
"3",
"3",
"5",
"3",
"7",
"4",
"9",
"5",
"11",
"9",
"13",
"7",
"15",
"15",
"17",
"9",
"19",
"15",
"21",
"11",
"23",
"12",
"25",
"13",
"27",
"21",
"29",
"15",
"31",
"16",
"33",
"17",
"35",
"27",
"37",
"19",
"39",
"20",
"41",
"21",
"43",
"33",
"45",
"23",
"47",
"45",
"49",
"25",
"51",
"39",
"53",
"27",
"55",
"28",
"57",
"29",
"59",
"45",
"61",
"31",
"63",
"48",
"65",
"33",
"67",
"51",
"69"
]
| [
"nonn",
"easy",
"mult"
]
| 14 | 1 | 3 | [
"A006519",
"A026741",
"A048649",
"A077609",
"A384055",
"A384247",
"A384249",
"A384250",
"A384251",
"A384252"
]
| null | Amiram Eldar, May 23 2025 | 2025-05-24T00:21:48 | oeisdata/seq/A384/A384251.seq | 36f4490a7df411fac0ed56cc8d281299 |
A384252 | The number of integers k from 1 to n such that the greatest divisor of k that is an infinitary divisor of n is a power of 2. | [
"1",
"2",
"2",
"4",
"4",
"4",
"6",
"8",
"8",
"8",
"10",
"8",
"12",
"12",
"8",
"16",
"16",
"16",
"18",
"16",
"12",
"20",
"22",
"16",
"24",
"24",
"18",
"24",
"28",
"16",
"30",
"32",
"20",
"32",
"24",
"32",
"36",
"36",
"24",
"32",
"40",
"24",
"42",
"40",
"32",
"44",
"46",
"32",
"48",
"48",
"32",
"48",
"52",
"36",
"40",
"48",
"36",
"56",
"58",
"32",
"60",
"60",
"48",
"64",
"48",
"40",
"66",
"64",
"44"
]
| [
"nonn",
"easy",
"mult"
]
| 15 | 1 | 2 | [
"A000079",
"A006519",
"A062570",
"A077609",
"A384056",
"A384247",
"A384249",
"A384250",
"A384251",
"A384252"
]
| null | Amiram Eldar, May 23 2025 | 2025-05-24T00:21:37 | oeisdata/seq/A384/A384252.seq | 4d30aba513666a9b964e0d9d8eac7fec |
A384253 | a(n) = 1 + ((1+(-1)^(n-1))*(n-1)!)/(n+1). | [
"2",
"1",
"2",
"1",
"9",
"1",
"181",
"1",
"8065",
"1",
"604801",
"1",
"68428801",
"1",
"10897286401",
"1",
"2324754432001",
"1",
"640237370572801",
"1",
"221172909834240001",
"1",
"93666727314800640001",
"1",
"47726800133326110720001",
"1",
"28806532937614688256000001",
"1",
"20325889640780924033433600001",
"1",
"16578303738261941164769280000001"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A060593",
"A384253"
]
| null | Michel Marcus, May 23 2025 | 2025-05-26T05:48:59 | oeisdata/seq/A384/A384253.seq | b01f70f6c82b24302e98a8f83062a60d |
A384254 | Number of connected components of n polyhedra in the rectified cubic honeycomb up to translation, rotation, and reflection of the honeycomb. | [
"1",
"2",
"2",
"9",
"40",
"290",
"2529",
"26629",
"301289",
"3568048",
"43305326",
"534671742",
"6684869463"
]
| [
"nonn",
"more",
"hard"
]
| 17 | 0 | 2 | [
"A038119",
"A038181",
"A343577",
"A343909",
"A384254",
"A384274"
]
| null | Peter Kagey, May 23 2025 | 2025-06-09T14:40:40 | oeisdata/seq/A384/A384254.seq | 2483133088a968471d1277a0ed9908f5 |
A384255 | Integers k such that there exists an integer 0<m<k such that sigma(m)^2 + sigma(k)^2 = 2*(m^2+k^2). | [
"2",
"21",
"27",
"123",
"175",
"2133",
"2187",
"6093",
"340917",
"504309",
"1594323",
"1895841",
"5308415",
"23006577",
"62188641"
]
| [
"nonn",
"hard",
"more",
"changed"
]
| 28 | 1 | 1 | [
"A063990",
"A259180",
"A383484",
"A383714",
"A384255"
]
| null | S. I. Dimitrov, May 23 2025 | 2025-07-10T12:14:43 | oeisdata/seq/A384/A384255.seq | 7805a31a2196378866651bb9a8abb625 |
A384256 | a(n) = Product_{k=0..n-1} (n+3*k+1). | [
"1",
"2",
"18",
"280",
"6160",
"174960",
"6086080",
"250490240",
"11904278400",
"641472832000",
"38645634227200",
"2573895458534400",
"187787322731008000",
"14894027431162880000",
"1275931456704672768000",
"117412145664335441920000",
"11550258696757088788480000",
"1209613643310990696210432000"
]
| [
"nonn",
"easy"
]
| 8 | 0 | 2 | [
"A303486",
"A384256",
"A384257"
]
| null | Seiichi Manyama, May 23 2025 | 2025-05-23T10:15:26 | oeisdata/seq/A384/A384256.seq | e0520a9b57f6fd44e5712fce0712c9b3 |
A384257 | a(n) = Product_{k=0..n-1} (n+3*k+2). | [
"1",
"3",
"28",
"440",
"9720",
"276640",
"9634240",
"396809280",
"18866848000",
"1016990374400",
"61283225203200",
"4082333102848000",
"297880548623257600",
"23628360309345792000",
"2024347339040266240000",
"186294495108985303040000",
"18327479444105919639552000",
"1919453757320555804508160000"
]
| [
"nonn",
"easy"
]
| 8 | 0 | 2 | [
"A303486",
"A384256",
"A384257"
]
| null | Seiichi Manyama, May 23 2025 | 2025-05-23T10:15:21 | oeisdata/seq/A384/A384257.seq | 836f245f4b95ea1476b067c75f18f8e9 |
A384258 | a(n) = Product_{k=0..n-1} (n+4*k+1). | [
"1",
"2",
"21",
"384",
"9945",
"332640",
"13627845",
"660602880",
"36974963025",
"2346549004800",
"166490632833525",
"13059009124761600",
"1122040194333683625",
"104802322548059136000",
"10572978481108199281125",
"1145749403453003661312000",
"132730561036298082383150625",
"16369108295524571830763520000"
]
| [
"nonn",
"easy"
]
| 9 | 0 | 2 | [
"A303487",
"A384258",
"A384259"
]
| null | Seiichi Manyama, May 23 2025 | 2025-05-23T10:15:17 | oeisdata/seq/A384/A384258.seq | 0fd6e8a39d4f357e578512ab131373c4 |
A384259 | a(n) = Product_{k=0..n-1} (n+4*k+3). | [
"1",
"4",
"45",
"840",
"21945",
"737280",
"30282525",
"1470268800",
"82380323025",
"5231974809600",
"371413503586125",
"29144138639616000",
"2504851570980383625",
"234017443515727872000",
"23613335889752371888125",
"2559272716623604101120000",
"296519181502679448839150625",
"36572320958219876869079040000"
]
| [
"nonn",
"easy"
]
| 11 | 0 | 2 | [
"A303487",
"A384258",
"A384259"
]
| null | Seiichi Manyama, May 23 2025 | 2025-05-26T07:15:26 | oeisdata/seq/A384/A384259.seq | 9357d1dba4f9a8c48e073c6480f5f490 |
A384260 | Consecutive internal states of the linear congruential pseudo-random number generator 3373*s mod (2^24-3) when started at s=1. | [
"1",
"3373",
"11377129",
"5569986",
"13861431",
"13291345",
"2993549",
"14135764",
"15869839",
"9657477",
"10099488",
"7830634",
"5395220",
"11578168",
"12586013",
"6272959",
"2625114",
"12918271",
"2905922",
"3782514",
"7737842",
"11174851",
"11152025",
"1268779",
"1402252",
"15399143",
"15835104",
"9936813"
]
| [
"nonn",
"easy"
]
| 12 | 1 | 2 | [
"A096550",
"A096561",
"A384260"
]
| null | Sean A. Irvine, May 23 2025 | 2025-06-19T19:45:11 | oeisdata/seq/A384/A384260.seq | 70253c4735570e5e48f1759770f9945f |
A384261 | a(n) = Product_{k=0..n-1} (2*n+k-1). | [
"1",
"1",
"12",
"210",
"5040",
"154440",
"5765760",
"253955520",
"12893126400",
"741354768000",
"47621141568000",
"3379847863392000",
"262662462526464000",
"22183557976419840000",
"2023140487449489408000",
"198155371076302768128000",
"20744817468539834621952000",
"2311708772421640603275264000"
]
| [
"nonn",
"easy"
]
| 13 | 0 | 3 | [
"A064352",
"A090816",
"A117671",
"A352601",
"A384261"
]
| null | Seiichi Manyama, May 23 2025 | 2025-05-26T05:19:53 | oeisdata/seq/A384/A384261.seq | ab4d8e19535d6ba3cff7c5b56912fea0 |
A384262 | a(n) = Product_{k=0..n-1} (3*n+k-2). | [
"1",
"1",
"20",
"504",
"17160",
"742560",
"39070080",
"2422728000",
"173059286400",
"13995229248000",
"1264020397516800",
"126115611484262400",
"13776096431889792000",
"1635195634511530291200",
"209574860127295703040000",
"28844656968251942737920000",
"4243193364951971128258560000",
"664387519844376163893657600000"
]
| [
"nonn",
"easy"
]
| 15 | 0 | 3 | [
"A061924",
"A335647",
"A384164",
"A384262",
"A384263"
]
| null | Seiichi Manyama, May 23 2025 | 2025-05-26T07:57:24 | oeisdata/seq/A384/A384262.seq | 84bb6ed5b115fc56e9a88c50070e024b |
A384263 | a(n) = Product_{k=0..n-1} (3*n+k-1). | [
"1",
"2",
"30",
"720",
"24024",
"1028160",
"53721360",
"3315312000",
"235989936000",
"19033511777280",
"1715456253772800",
"170866312333516800",
"18638248113733248000",
"2209723830420986880000",
"282926061171849199104000",
"38906746608339829739520000",
"5719086709283091520696320000",
"894889312443445445244518400000"
]
| [
"nonn",
"easy"
]
| 11 | 0 | 2 | [
"A061924",
"A384164",
"A384262",
"A384263"
]
| null | Seiichi Manyama, May 23 2025 | 2025-05-24T10:35:41 | oeisdata/seq/A384/A384263.seq | b1832e26b47f5a44d808d6c0914a99e5 |
A384264 | G.f. A(x) satisfies a(n) = [x^n] ( A(x)^(n-1) - 2*A(x)^n + A(x)^(n+1) ) for n > 1, with a(0) = a(1) = 1. | [
"1",
"1",
"1",
"4",
"21",
"138",
"1049",
"8878",
"81802",
"808584",
"8487493",
"93916298",
"1089508229",
"13195281850",
"166288822167",
"2174706541532",
"29449251073640",
"412174159048920",
"5952977488264644",
"88601062941267432",
"1357279730956877595",
"21377432888018361996",
"345837371025600620202",
"5741547579102846093378",
"97738792064478739075798"
]
| [
"nonn"
]
| 7 | 0 | 4 | null | null | Paul D. Hanna, May 23 2025 | 2025-05-24T02:23:34 | oeisdata/seq/A384/A384264.seq | f0f59d65312aa37099ef9ecb44e7267c |
A384265 | G.f. A(x) satisfies A( x/A(x)^2 + x^2 ) = 1 + x*A(x)^2. | [
"1",
"1",
"3",
"16",
"119",
"1087",
"11408",
"132468",
"1663047",
"22234598",
"313303201",
"4618133168",
"70815362628",
"1124901511837",
"18450127411436",
"311636597558992",
"5409374008212747",
"96326565666389514",
"1757212245656330130",
"32798907320986196010",
"625759879697614204041",
"12192353855092076824051",
"242419156191210763668352"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A145347",
"A182954",
"A383563",
"A384265"
]
| null | Paul D. Hanna, May 30 2025 | 2025-05-31T14:38:08 | oeisdata/seq/A384/A384265.seq | 01a06f5817176cd7d91dc31d1ad596da |
A384266 | G.f. A(x) = (3*sqrt(1 - 8*x) - (1 - 4*x)) / (2*(1 - 8*x - 2*x^2)). | [
"1",
"4",
"22",
"136",
"892",
"6064",
"42232",
"299296",
"2149360",
"15596992",
"114138592",
"841108096",
"6234779584",
"46448349952",
"347541337984",
"2610319254016",
"19671552622336",
"148689857920000",
"1126905157115392",
"8561360256526336",
"65185363066289152",
"497307750242234368",
"3800975843189291008",
"29100188150365757440"
]
| [
"nonn"
]
| 27 | 0 | 2 | [
"A179587",
"A384266"
]
| null | Paul D. Hanna, Jun 06 2025 | 2025-06-08T03:32:47 | oeisdata/seq/A384/A384266.seq | 99c2d9c4f4184113850152c8bfc66b94 |
A384267 | G.f. A(x) satisfies A(x) = 1 + abs( x/A(x)^2 ). | [
"1",
"1",
"2",
"1",
"6",
"13",
"4",
"80",
"242",
"109",
"1702",
"5177",
"2208",
"40348",
"128560",
"56864",
"1052102",
"3406333",
"1509862",
"28900645",
"94971462",
"42420281",
"825816148",
"2740269448",
"1228678588",
"24277298940",
"81183221736",
"36526643608",
"729682028652",
"2454721201940",
"1107304048024",
"22319301025880",
"75450489469554"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A006013",
"A380708",
"A380710",
"A384267"
]
| null | Paul D. Hanna, Jun 19 2025 | 2025-06-20T10:46:39 | oeisdata/seq/A384/A384267.seq | 76aa53c9081cc8caf30394079922d05f |
A384268 | E.g.f. A(x) satisfies 1 = Sum_{n>=0} (A(x) - x^n)^n / n!. | [
"1",
"-1",
"8",
"-54",
"484",
"-5220",
"69978",
"-1123584",
"20636208",
"-427048560",
"9855043560",
"-251178602400",
"6999042156456",
"-211667930623968",
"6906285876838320",
"-241834002452380800",
"9045871629011352960",
"-359980905120027776640",
"15186181445703977599296",
"-676969958167108542074880",
"31797743045658537121856640"
]
| [
"sign"
]
| 10 | 1 | 3 | null | null | Paul D. Hanna, Jun 05 2025 | 2025-06-06T08:57:57 | oeisdata/seq/A384/A384268.seq | aa7a19d44e9a7c9ad9cd9f7dd4df6c37 |
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