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2.35k
| offset_a
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666,262,453B
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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
2025-07-14 02:38:35
| filename
stringlengths 29
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| hash
stringlengths 32
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A362801 | Numbers whose set of divisors can be partitioned into disjoint parts, all of length > 1 and having integer harmonic mean. | [
"6",
"12",
"18",
"24",
"28",
"30",
"40",
"42",
"45",
"48",
"54",
"56",
"60",
"66",
"72",
"78",
"84",
"90",
"96",
"102",
"108",
"112",
"114",
"120",
"126",
"132",
"135",
"138",
"140",
"144",
"150",
"156",
"162",
"168",
"174",
"180",
"186",
"192",
"196",
"198",
"200",
"204",
"210",
"216",
"220",
"222",
"224",
"225",
"228",
"234",
"240",
"246",
"252",
"258",
"264",
"270",
"276"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A001599",
"A348715",
"A362801",
"A362802",
"A362803"
]
| null | Amiram Eldar, May 04 2023 | 2023-05-05T01:40:09 | oeisdata/seq/A362/A362801.seq | a7711853f1e5644227e44b601e976a3a |
A362802 | a(n) is the number of ways in which the set of divisors of n can be partitioned into disjoint parts, all of length > 1 and with integer harmonic mean. | [
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"4",
"0",
"0",
"0",
"1",
"0",
"3",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"15",
"0",
"0",
"0",
"0",
"0",
"3",
"0",
"1",
"0",
"0",
"0",
"175",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"78",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"188",
"0"
]
| [
"nonn"
]
| 9 | 1 | 24 | [
"A339453",
"A339665",
"A362801",
"A362802",
"A362803"
]
| null | Amiram Eldar, May 04 2023 | 2023-05-05T01:41:30 | oeisdata/seq/A362/A362802.seq | d0cb4fa71eac8158b20ccb15f32c48cf |
A362803 | Indices of records in A362802. | [
"1",
"6",
"24",
"48",
"60",
"84"
]
| [
"nonn",
"hard",
"more"
]
| 6 | 1 | 2 | [
"A348716",
"A349179",
"A362801",
"A362802",
"A362803"
]
| null | Amiram Eldar, May 04 2023 | 2023-05-05T01:41:47 | oeisdata/seq/A362/A362803.seq | a3dfc940a176d1204f94b4acce86c6d6 |
A362804 | Numbers k such that the set of divisors {d | k, BitOr(k, d) = k} has an integer harmonic mean. | [
"1",
"2",
"4",
"6",
"8",
"12",
"16",
"24",
"28",
"30",
"32",
"45",
"48",
"56",
"60",
"64",
"90",
"96",
"112",
"120",
"128",
"180",
"192",
"224",
"240",
"256",
"360",
"384",
"448",
"480",
"496",
"512",
"720",
"768",
"896",
"960",
"992",
"1024",
"1440",
"1536",
"1792",
"1920",
"1984",
"2048",
"2880",
"3072",
"3584",
"3840",
"3968",
"4096",
"5760",
"6144",
"7168",
"7680"
]
| [
"nonn",
"base"
]
| 9 | 1 | 2 | [
"A000043",
"A000079",
"A000396",
"A001599",
"A005009",
"A006086",
"A007283",
"A063947",
"A110286",
"A246600",
"A246601",
"A286325",
"A319745",
"A362804",
"A362805"
]
| null | Amiram Eldar, May 04 2023 | 2023-05-04T14:57:57 | oeisdata/seq/A362/A362804.seq | b29b3f4828ac35dca94df33c6dd54558 |
A362805 | Primitive terms of A362804: terms k of A362804 such that k/2 is not a term of A362804. | [
"1",
"6",
"28",
"30",
"45",
"496",
"8128",
"16380",
"57720",
"65472",
"235246",
"683520",
"33550336",
"50426880",
"60945408",
"105553910",
"131297280",
"3052879872",
"8589869056"
]
| [
"nonn",
"base",
"more"
]
| 5 | 1 | 2 | [
"A000396",
"A362804",
"A362805"
]
| null | Amiram Eldar, May 04 2023 | 2023-05-05T01:41:58 | oeisdata/seq/A362/A362805.seq | 6b32284ee3b40e08a399f6fdde6c7191 |
A362806 | Number of numbers k, 1 <= k <= n, such that mu(k) = mu(n-k+1). | [
"1",
"0",
"1",
"2",
"1",
"4",
"3",
"2",
"3",
"2",
"5",
"4",
"3",
"4",
"11",
"2",
"5",
"2",
"11",
"6",
"9",
"2",
"13",
"6",
"7",
"6",
"13",
"6",
"9",
"6",
"17",
"8",
"13",
"8",
"27",
"8",
"5",
"8",
"21",
"10",
"11",
"12",
"23",
"14",
"9",
"12",
"29",
"18",
"13",
"2",
"27",
"16",
"21",
"10",
"27",
"12",
"17",
"14",
"35",
"24",
"11",
"12",
"29",
"16",
"23",
"14",
"33",
"16",
"23",
"16",
"53",
"26",
"19",
"16",
"35",
"24",
"25",
"22"
]
| [
"nonn",
"easy"
]
| 6 | 1 | 4 | [
"A008683",
"A362806"
]
| null | Wesley Ivan Hurt, May 04 2023 | 2023-05-12T15:22:54 | oeisdata/seq/A362/A362806.seq | 85a5797772b2def21d8a7ea0ef97f95c |
A362807 | Number of (non-null) connected induced subgraphs in the n-flower graph. | [
"12",
"100",
"1588",
"15978",
"179972",
"1809558",
"18324824",
"181378366",
"1782805552",
"17363990448",
"168057761164",
"1617180377184",
"15486675862236",
"147673946969116",
"1402890497740544",
"13283057055815430",
"125395241075209800",
"1180599951439852770",
"11088548750458808244",
"103918533147459728842"
]
| [
"nonn",
"easy"
]
| 16 | 1 | 1 | [
"A362793",
"A362807"
]
| null | Eric W. Weisstein, May 04 2023 | 2025-05-24T19:00:56 | oeisdata/seq/A362/A362807.seq | fd6694af28a7610d885366413dd9ec85 |
A362808 | Number of minimal vertex cuts in the n X n torus grid graph. | [
"18",
"260",
"8060"
]
| [
"nonn",
"bref",
"more"
]
| 5 | 3 | 1 | null | null | Eric W. Weisstein, May 04 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A362/A362808.seq | d42bb1ab3b6d451d7ccd388e8a3dfbf8 |
A362809 | Numbers k for which the area of the first part of the symmetric representation of sigma(k) equals sigma(k)/3 and its width is 1. | [
"15",
"207",
"1023",
"2975",
"5950",
"19359",
"147455",
"294910",
"1207359",
"5017599",
"2170814463"
]
| [
"nonn",
"hard",
"more"
]
| 44 | 1 | 1 | [
"A063906",
"A068156",
"A235791",
"A237048",
"A237591",
"A237593",
"A249223",
"A251820",
"A362809"
]
| null | Hartmut F. W. Hoft, May 04 2023 | 2024-03-21T21:12:00 | oeisdata/seq/A362/A362809.seq | 4213e619a51f829c63a530659836d307 |
A362810 | Define G(n, k) to be the n-th derivative of Gamma(x) at k. a(n)=floor(min(G(2n, x))), where min(f) is the local minimum of f in [0,oo). | [
"0",
"0",
"1",
"6",
"30",
"173",
"1138",
"8386",
"67951",
"596745",
"5618916",
"56249658",
"594648335",
"6602123630",
"76631632344",
"926329705808",
"11623455427764",
"150970962492188",
"2024773236657401",
"27980260971851306",
"397645587914766071",
"5801999753304428181",
"86784442260270596447",
"1328924296505789704631",
"20807559990139289975657",
"332753116291423840918784"
]
| [
"nonn"
]
| 19 | 0 | 4 | [
"A030171",
"A362810"
]
| null | Jodi Spitz, May 04 2023 | 2023-11-18T03:18:36 | oeisdata/seq/A362/A362810.seq | bb5b6ba921162ec7dae8dea15df68db3 |
A362811 | Sphenic numbers (product of 3 distinct primes) sandwiched between two semiprimes (product of 2 primes). | [
"186",
"266",
"290",
"322",
"470",
"518",
"534",
"582",
"590",
"670",
"754",
"790",
"814",
"894",
"994",
"1146",
"1158",
"1166",
"1338",
"1370",
"1390",
"1562",
"1686",
"1798",
"1842",
"1958",
"2118",
"2158",
"2230",
"2318",
"2454",
"2482",
"2514",
"2570",
"2630",
"2758",
"2786",
"2810",
"2922",
"2930",
"2994",
"3154",
"3206",
"3262",
"3278",
"3378",
"3454",
"3522",
"3562"
]
| [
"nonn",
"easy"
]
| 21 | 1 | 1 | [
"A001358",
"A007304",
"A171179",
"A362811"
]
| null | Alexandru Petrescu, May 04 2023 | 2023-06-15T10:35:53 | oeisdata/seq/A362/A362811.seq | 098ab9ae48911c786c07a718695679c7 |
A362812 | Number of minimal total dominating sets in the n-double cone graph. | [
"15",
"24",
"35",
"93",
"63",
"32",
"162",
"645",
"506",
"649",
"1547",
"2429",
"4654",
"10032",
"14195",
"20772",
"43719",
"83561",
"134731",
"234300",
"414782",
"707329",
"1276950",
"2313493",
"3932343",
"6765257",
"12110458",
"21381436",
"37295511",
"65610064",
"114854155",
"200533989",
"353703319",
"623201368"
]
| [
"nonn"
]
| 9 | 3 | 1 | [
"A300738",
"A362750",
"A362812"
]
| null | Eric W. Weisstein, May 04 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A362/A362812.seq | 95bfabb736d14d3da0a3192e4c3c9bf7 |
A362813 | Number of numbers that occur more than once in column n of McGarvey's array (A007062). | [
"0",
"2",
"3",
"4",
"6",
"6",
"7",
"9",
"11",
"12",
"14",
"13",
"14",
"16",
"15",
"17",
"21",
"20",
"22",
"25",
"24",
"25",
"29",
"26",
"26",
"31",
"29",
"31",
"36",
"33",
"33",
"40",
"37",
"36",
"44",
"41",
"39",
"48",
"42",
"44",
"50",
"44",
"48",
"53",
"49",
"49",
"56",
"54",
"53",
"62",
"55",
"56",
"69",
"61",
"59",
"66",
"61",
"66",
"73",
"65",
"64",
"75",
"71",
"70",
"80",
"72",
"71"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A007062",
"A309977",
"A362813"
]
| null | Clark Kimberling, May 04 2023 | 2023-05-20T15:48:37 | oeisdata/seq/A362/A362813.seq | c2720acdb86e48e10965b0b27c452ce7 |
A362814 | Rectangular array read by descending antidiagonals; row n shows the numbers whose prime factorization p(1)^e(1)*p(2)^e(2)*... has n = max{e(k)}. | [
"2",
"3",
"4",
"5",
"9",
"8",
"6",
"12",
"24",
"16",
"7",
"18",
"27",
"48",
"32",
"10",
"20",
"40",
"80",
"96",
"64",
"11",
"25",
"54",
"81",
"160",
"192",
"128",
"13",
"28",
"56",
"112",
"224",
"320",
"384",
"256",
"14",
"36",
"72",
"144",
"243",
"448",
"640",
"768",
"512",
"15",
"44",
"88",
"162",
"288",
"576",
"896",
"1280",
"1536",
"1024",
"17",
"45",
"104",
"176",
"352"
]
| [
"nonn",
"tabl"
]
| 8 | 1 | 1 | [
"A000040",
"A005117",
"A051903",
"A362814"
]
| null | Clark Kimberling, May 04 2023 | 2023-05-20T15:48:52 | oeisdata/seq/A362/A362814.seq | 508db44b8d5c87e2d0fd123eb66d9734 |
A362815 | Start with 2. Then, numbers are added to the sequence if they do not form any arithmetic progression p with numbers in the sequence such that length(p) > min(p). | [
"2",
"3",
"5",
"6",
"7",
"11",
"13",
"14",
"16",
"17",
"18",
"19",
"21",
"22",
"23",
"25",
"28",
"29",
"31",
"37",
"38",
"39",
"41",
"43",
"46",
"47",
"50",
"51",
"52",
"53",
"55",
"58",
"59",
"61",
"62",
"64",
"66",
"67",
"68",
"70",
"71",
"73",
"75",
"77",
"79",
"82",
"83",
"85",
"86",
"88",
"89",
"93",
"94",
"96",
"97",
"99",
"101",
"103",
"106",
"107",
"109",
"110",
"113",
"115"
]
| [
"nonn"
]
| 21 | 1 | 1 | [
"A362815",
"A362816",
"A363011"
]
| null | Samuel Harkness, May 04 2023 | 2024-09-28T07:39:17 | oeisdata/seq/A362/A362815.seq | aa7d611d857c6482f693538a4c9bf69e |
A362816 | Lexicographically earliest sequence such that nowhere is a term a(n) contained in an arithmetic progression of length greater than a(n). | [
"2",
"2",
"3",
"2",
"2",
"3",
"3",
"3",
"5",
"2",
"2",
"3",
"2",
"2",
"3",
"3",
"3",
"5",
"3",
"5",
"5",
"5",
"3",
"3",
"3",
"5",
"5",
"2",
"2",
"3",
"2",
"2",
"5",
"5",
"3",
"3",
"2",
"2",
"3",
"2",
"2",
"5",
"3",
"3",
"5",
"3",
"5",
"5",
"3",
"3",
"5",
"5",
"3",
"5",
"5",
"5",
"6",
"5",
"3",
"5",
"5",
"6",
"5",
"3",
"3",
"3",
"5",
"3",
"5",
"5",
"5",
"3",
"3",
"3",
"5",
"5",
"5",
"6",
"5",
"5",
"3",
"2",
"2",
"5",
"2",
"2",
"6"
]
| [
"nonn"
]
| 34 | 1 | 1 | [
"A003278",
"A090822",
"A281579",
"A362815",
"A362816",
"A363011"
]
| null | Samuel Harkness, May 04 2023 | 2024-09-28T07:39:13 | oeisdata/seq/A362/A362816.seq | 882815937668be670358fb2ebd11ca4e |
A362817 | Irregular triangle read by rows: T(n,k) (n>=1, k>=1) is the number of edges of the k-th polygon (or part), from left to right, of the symmetric representation of sigma(n). | [
"4",
"6",
"4",
"4",
"10",
"4",
"4",
"12",
"4",
"4",
"14",
"4",
"6",
"4",
"8",
"8",
"4",
"4",
"18",
"4",
"4",
"8",
"8",
"4",
"12",
"4",
"22",
"4",
"4",
"22",
"4",
"4",
"22",
"4",
"8",
"8",
"4",
"8",
"8",
"4",
"4",
"26",
"4",
"10",
"4",
"8",
"8",
"4",
"8",
"8",
"4",
"28",
"4",
"4",
"30",
"4",
"4",
"30"
]
| [
"nonn",
"tabf",
"more"
]
| 41 | 1 | 1 | [
"A000079",
"A000203",
"A000396",
"A003056",
"A065091",
"A174973",
"A196020",
"A235791",
"A236104",
"A237270",
"A237271",
"A237591",
"A237593",
"A238443",
"A244363",
"A245092",
"A262626",
"A274919",
"A348705",
"A362817",
"A362818"
]
| null | Omar E. Pol, May 04 2023 | 2023-08-02T14:34:08 | oeisdata/seq/A362/A362817.seq | 60f887797e77ae696455a06a29300706 |
A362818 | Total number of edges of all polygons (or parts) of the symmetric representation of sigma(n). | [
"4",
"6",
"8",
"10",
"8",
"12",
"8",
"14",
"14",
"16",
"8",
"18",
"8",
"16",
"20",
"22",
"8",
"22",
"8",
"22",
"24",
"16",
"8",
"26",
"18",
"16",
"24",
"28",
"8",
"30",
"8",
"30"
]
| [
"nonn",
"more"
]
| 29 | 1 | 1 | [
"A000079",
"A000203",
"A000396",
"A003056",
"A065091",
"A174973",
"A196020",
"A235791",
"A236104",
"A237270",
"A237271",
"A237591",
"A237593",
"A238443",
"A244363",
"A245092",
"A262626",
"A274919",
"A348705",
"A362817",
"A362818"
]
| null | Omar E. Pol, May 04 2023 | 2023-08-02T14:34:27 | oeisdata/seq/A362/A362818.seq | d47ee92f0f7bdf8e0d960d5ef8bb9c22 |
A362819 | Number of ordered pairs of involutions on [n] that commute. | [
"1",
"1",
"4",
"10",
"52",
"196",
"1216",
"5944",
"42400",
"250912",
"2008576",
"13815616",
"122074624",
"950640640",
"9158267392",
"79258479616",
"824644235776",
"7823203807744",
"87245790791680",
"897748312609792",
"10665239974537216",
"118040852776093696",
"1486172381689544704",
"17572063073426206720",
"233446797379437248512"
]
| [
"nonn"
]
| 15 | 0 | 3 | [
"A000085",
"A000898",
"A053529",
"A181162",
"A362819",
"A362820",
"A362824",
"A362825"
]
| null | Andrew Howroyd, May 05 2023 | 2023-05-08T15:33:17 | oeisdata/seq/A362/A362819.seq | 7d73034acdd57ad8f1434f5d270ffed6 |
A362820 | Number of ordered pairs of derangements on [n] that commute. | [
"1",
"0",
"1",
"4",
"33",
"136",
"1825",
"10956",
"163009",
"1575568",
"23894721",
"280090900",
"5410068961",
"73066199064",
"1483125027553",
"25872759745756",
"561027082980225",
"10796395534986016",
"266457543316023169",
"5743345672152317988",
"152031229968147150241",
"3717043193920429157800",
"104377807879737865769121"
]
| [
"nonn"
]
| 12 | 0 | 4 | [
"A000166",
"A053529",
"A362819",
"A362820"
]
| null | Andrew Howroyd, May 05 2023 | 2023-05-28T22:20:58 | oeisdata/seq/A362/A362820.seq | 6e5b16a4198830304fb3e34acf2c64c5 |
A362821 | Number of labeled right involutory Płonka magmas with n elements. | [
"1",
"1",
"2",
"10",
"70",
"916",
"16636",
"494824",
"20486432",
"1320568624",
"119526633136",
"16466317431136",
"3210471529800448",
"940911157770908416",
"392559353168479443584",
"244017910517578226511616",
"216775189886094655708439296",
"284778404550532041821957456896",
"536018349047631899870416803595264"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A361720",
"A362643",
"A362821",
"A362822",
"A362824"
]
| null | Andrew Howroyd, May 08 2023 | 2025-05-08T19:41:11 | oeisdata/seq/A362/A362821.seq | 3c2c09a0505fed555ceb14d3e27bcc48 |
A362822 | Number of nonisomorphic magmas with n elements satisfying the identities (xy)y = x and (xy)z = (xz)y. | [
"1",
"1",
"3",
"6",
"68",
"254",
"14310",
"112762",
"43419892"
]
| [
"nonn",
"more"
]
| 6 | 0 | 3 | [
"A001329",
"A361720",
"A362382",
"A362642",
"A362822",
"A362823"
]
| null | Andrew Howroyd, May 06 2023 | 2023-05-08T15:39:50 | oeisdata/seq/A362/A362822.seq | 70438a9817f42a4f3b5143dcb044b080 |
A362823 | Number of labeled magmas with n elements satisfying the identities (xy)y = x and (xy)z = (xz)y. | [
"1",
"1",
"4",
"22",
"976",
"19376",
"7680016",
"430723168",
"1489656111616",
"214815786486400",
"6364561150037368576",
"2241692646969785651456",
"566719960584895502028138496",
"471612192582034433034750951424",
"1008512943343839231897776246546624512",
"1936475539456937172034340659334701398016"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A362383",
"A362643",
"A362821",
"A362822",
"A362823",
"A362824"
]
| null | Andrew Howroyd, May 06 2023 | 2023-05-08T15:33:32 | oeisdata/seq/A362/A362823.seq | 1f4eb761e03340d25d176a2537b5c74a |
A362824 | Array read by antidiagonals: T(n,k) is the number of k-tuples of involutions on [n] that pairwise commute. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"4",
"4",
"1",
"1",
"1",
"8",
"10",
"10",
"1",
"1",
"1",
"16",
"22",
"52",
"26",
"1",
"1",
"1",
"32",
"46",
"232",
"196",
"76",
"1",
"1",
"1",
"64",
"94",
"976",
"1016",
"1216",
"232",
"1",
"1",
"1",
"128",
"190",
"4000",
"4576",
"12496",
"5944",
"764",
"1",
"1",
"1",
"256",
"382",
"16192",
"19376",
"111376",
"73648",
"42400",
"2620",
"1"
]
| [
"nonn",
"tabl"
]
| 8 | 0 | 9 | [
"A000012",
"A000079",
"A000085",
"A022166",
"A033484",
"A362648",
"A362819",
"A362823",
"A362824",
"A362825"
]
| null | Andrew Howroyd, May 06 2023 | 2023-05-08T15:32:28 | oeisdata/seq/A362/A362824.seq | 4b2b3587e8711cb145e728cf50865117 |
A362825 | Number of ordered triples of involutions on [n] that pairwise commute. | [
"1",
"1",
"8",
"22",
"232",
"1016",
"12496",
"73648",
"1032032",
"7586272",
"118141696",
"1033672256",
"17668427008",
"178649596672",
"3313667912192",
"37898019913216",
"756948065453056",
"9640771045925888",
"205935949714235392",
"2885307792776353792",
"65568056040976818176"
]
| [
"nonn"
]
| 7 | 0 | 3 | [
"A362819",
"A362824",
"A362825"
]
| null | Andrew Howroyd, May 06 2023 | 2023-05-08T15:33:02 | oeisdata/seq/A362/A362825.seq | 485eb6c01525736566a9cd6708f8c17c |
A362826 | Array read by antidiagonals: T(n,k) is the number of k-tuples of permutations of [n] which commute, divided by n!, n >= 0, k >= 1. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"4",
"3",
"1",
"1",
"1",
"8",
"8",
"5",
"1",
"1",
"1",
"16",
"21",
"21",
"7",
"1",
"1",
"1",
"32",
"56",
"84",
"39",
"11",
"1",
"1",
"1",
"64",
"153",
"331",
"206",
"92",
"15",
"1",
"1",
"1",
"128",
"428",
"1300",
"1087",
"717",
"170",
"22",
"1",
"1",
"1",
"256",
"1221",
"5111",
"5832",
"5512",
"1810",
"360",
"30",
"1"
]
| [
"nonn",
"tabl"
]
| 13 | 0 | 9 | [
"A000012",
"A000041",
"A061256",
"A160870",
"A226313",
"A362826",
"A362827",
"A362903"
]
| null | Andrew Howroyd, May 09 2023 | 2023-05-30T14:10:38 | oeisdata/seq/A362/A362826.seq | b62e458953b76418172c0ede73711e23 |
A362827 | Array read by antidiagonals: T(n,k) is the number of k-tuples of permutations of [n] that pairwise commute. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"4",
"6",
"1",
"1",
"1",
"8",
"18",
"24",
"1",
"1",
"1",
"16",
"48",
"120",
"120",
"1",
"1",
"1",
"32",
"126",
"504",
"840",
"720",
"1",
"1",
"1",
"64",
"336",
"2016",
"4680",
"7920",
"5040",
"1",
"1",
"1",
"128",
"918",
"7944",
"24720",
"66240",
"75600",
"40320",
"1",
"1",
"1",
"256",
"2568",
"31200",
"130440",
"516240",
"856800",
"887040",
"362880",
"1"
]
| [
"nonn",
"tabl"
]
| 11 | 0 | 9 | [
"A000012",
"A000142",
"A053529",
"A072169",
"A362824",
"A362826",
"A362827",
"A362828"
]
| null | Andrew Howroyd, May 08 2023 | 2023-05-09T15:36:28 | oeisdata/seq/A362/A362827.seq | 5f9c2a27bf5484497de33db734e27a66 |
A362828 | Number of n-tuples of permutations of [n] that pairwise commute. | [
"1",
"1",
"4",
"48",
"2016",
"130440",
"30672720",
"11608682400",
"12055770800640",
"24154259257215360",
"117792549941415955200",
"1161512734993746635808000",
"25629823970496421449477580800",
"1215203193235691517749414518195200",
"123585796012441765074167804498857267200"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A362823",
"A362827",
"A362828"
]
| null | Andrew Howroyd, May 08 2023 | 2023-05-09T15:36:32 | oeisdata/seq/A362/A362828.seq | 348ba60437fcd854a84a1be2aea37279 |
A362829 | Positions in lexicographic order of odd partitions of sufficiently large numbers. | [
"1",
"3",
"7",
"10",
"15",
"20",
"27",
"30",
"39",
"41",
"51",
"56",
"69",
"72",
"75",
"93",
"95",
"101",
"123",
"128",
"132",
"134",
"160",
"163",
"166",
"172",
"176",
"212",
"214",
"220",
"227",
"229",
"273",
"278",
"282",
"284",
"291",
"297",
"353",
"356",
"359",
"365",
"369",
"379",
"382",
"384",
"453",
"455",
"461",
"468",
"470",
"481",
"483",
"490",
"579",
"584"
]
| [
"nonn"
]
| 61 | 1 | 2 | [
"A000009",
"A000041",
"A087897",
"A362829"
]
| null | Richard Peterson, Aug 01 2023 | 2023-09-18T06:18:08 | oeisdata/seq/A362/A362829.seq | ebf9b78cd69bab5c1ca4af327a2415db |
A362830 | Number of bases b with 2 <= b < n such that n written in base b is a strictly increasing sequence of digits. | [
"0",
"0",
"0",
"0",
"1",
"1",
"2",
"2",
"3",
"3",
"5",
"4",
"6",
"6",
"7",
"7",
"9",
"8",
"11",
"10",
"11",
"12",
"14",
"12",
"15",
"15",
"17",
"16",
"19",
"17",
"20",
"19",
"21",
"22",
"23",
"21",
"25",
"26",
"27",
"25",
"29",
"27",
"30",
"30",
"30",
"32",
"34",
"31",
"35",
"34",
"37",
"37",
"40",
"37",
"40",
"39",
"41",
"43",
"45",
"40",
"46",
"46",
"46",
"46",
"49",
"48",
"52",
"51",
"54",
"51"
]
| [
"nonn",
"base"
]
| 26 | 1 | 7 | null | null | Matthew R. Maas, May 04 2023 | 2023-08-02T09:18:55 | oeisdata/seq/A362/A362830.seq | 26939d92f846eddada9ad192dd0b2871 |
A362831 | Number of partitions of n into two distinct parts (s,t) such that pi(s) = pi(t). | [
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"2",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"2",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"2",
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"2",
"2",
"3",
"2",
"2",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"2",
"2",
"3",
"2",
"2",
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"2",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"2",
"1"
]
| [
"nonn",
"easy"
]
| 16 | 1 | 17 | [
"A000720",
"A362721",
"A362831"
]
| null | Wesley Ivan Hurt, May 04 2023 | 2023-05-15T19:19:31 | oeisdata/seq/A362/A362831.seq | 3343e559847e46ad16e352463fa6b839 |
A362832 | Number of partitions of n into two distinct parts (s,t) such that phi(s) = phi(t). | [
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"0",
"0",
"2",
"1",
"1",
"0",
"0",
"1",
"1",
"2",
"1",
"0",
"3",
"1",
"1",
"0",
"0",
"2",
"1",
"0",
"3",
"1",
"0",
"0",
"0",
"1",
"1",
"1",
"2",
"1",
"0",
"1",
"2",
"1",
"0",
"1",
"1",
"2",
"1",
"0",
"2",
"1",
"0",
"2",
"1",
"1",
"1",
"1",
"0",
"0",
"2",
"1",
"0",
"0",
"3"
]
| [
"nonn",
"easy"
]
| 15 | 1 | 39 | [
"A000010",
"A362719",
"A362832"
]
| null | Wesley Ivan Hurt, May 04 2023 | 2023-05-15T19:20:19 | oeisdata/seq/A362/A362832.seq | 3894f4f12ea2ca7c81711b93c795e157 |
A362833 | Number of partitions of n into two distinct parts (s,t) such that mu(s) = mu(t). | [
"0",
"0",
"0",
"0",
"1",
"0",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"2",
"5",
"1",
"2",
"1",
"5",
"3",
"4",
"1",
"6",
"3",
"3",
"3",
"6",
"3",
"4",
"3",
"8",
"4",
"6",
"4",
"13",
"4",
"2",
"4",
"10",
"5",
"5",
"6",
"11",
"7",
"4",
"6",
"14",
"9",
"6",
"1",
"13",
"8",
"10",
"5",
"13",
"6",
"8",
"7",
"17",
"12",
"5",
"6",
"14",
"8",
"11",
"7",
"16",
"8",
"11",
"8",
"26",
"13",
"9",
"8",
"17",
"12",
"12",
"11",
"18",
"11",
"7",
"13"
]
| [
"nonn",
"easy"
]
| 13 | 1 | 7 | [
"A008683",
"A362806",
"A362833"
]
| null | Wesley Ivan Hurt, May 04 2023 | 2023-05-15T19:20:54 | oeisdata/seq/A362/A362833.seq | 2b9d77a63ea72b3b458ad516c6bf66d1 |
A362834 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = (-1)^n * n! * Sum_{j=0..floor(n/2)} k^j * Stirling1(n-j,j)/(n-j)!. | [
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"2",
"0",
"1",
"0",
"4",
"3",
"0",
"1",
"0",
"6",
"6",
"20",
"0",
"1",
"0",
"8",
"9",
"64",
"90",
"0",
"1",
"0",
"10",
"12",
"132",
"300",
"594",
"0",
"1",
"0",
"12",
"15",
"224",
"630",
"2568",
"4200",
"0",
"1",
"0",
"14",
"18",
"340",
"1080",
"6642",
"20160",
"34544",
"0",
"1",
"0",
"16",
"21",
"480",
"1650",
"13536",
"55440",
"193856",
"316008",
"0"
]
| [
"nonn",
"tabl"
]
| 21 | 0 | 9 | [
"A000007",
"A053489",
"A053490",
"A066166",
"A318615",
"A361652",
"A362834"
]
| null | Seiichi Manyama, May 05 2023 | 2023-05-05T12:24:37 | oeisdata/seq/A362/A362834.seq | 1756100ac3f0794b137cd0c05483c5d1 |
A362835 | Expansion of e.g.f. 1/(1 + LambertW(x * log(1-x))). | [
"1",
"0",
"2",
"3",
"56",
"270",
"4704",
"43260",
"814736",
"11356632",
"240848640",
"4492204200",
"108396245088",
"2513538490320",
"68878522931568",
"1896787592514360",
"58622475066067200",
"1860520458522196800",
"64297710768900261888",
"2303738717704104464640"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A318615",
"A362835",
"A362836"
]
| null | Seiichi Manyama, May 05 2023 | 2023-05-05T12:25:53 | oeisdata/seq/A362/A362835.seq | 1d40ebf1361c7528a36f0e07c155baee |
A362836 | Expansion of e.g.f. 1/(1 + LambertW(-x * (exp(x) - 1))). | [
"1",
"0",
"2",
"3",
"52",
"245",
"4086",
"36547",
"663832",
"8984313",
"184262770",
"3334315391",
"77900601780",
"1751855308645",
"46508427942718",
"1241853335819475",
"37195023972070576",
"1144511291020453361",
"38337497638919397738",
"1331709923436162817447"
]
| [
"nonn"
]
| 14 | 0 | 3 | [
"A290158",
"A362835",
"A362836"
]
| null | Seiichi Manyama, May 05 2023 | 2025-05-19T05:06:36 | oeisdata/seq/A362/A362836.seq | 9c3cb46dc09a3ee32898c32b17f44d07 |
A362837 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = (-1)^n * n! * Sum_{j=0..floor(n/2)} k^(n-j) * Stirling1(n-j,j)/(n-j)!. | [
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"2",
"0",
"1",
"0",
"4",
"3",
"0",
"1",
"0",
"6",
"12",
"20",
"0",
"1",
"0",
"8",
"27",
"112",
"90",
"0",
"1",
"0",
"10",
"48",
"324",
"960",
"594",
"0",
"1",
"0",
"12",
"75",
"704",
"4050",
"10848",
"4200",
"0",
"1",
"0",
"14",
"108",
"1300",
"11520",
"64962",
"141120",
"34544",
"0",
"1",
"0",
"16",
"147",
"2160",
"26250",
"239616",
"1224720",
"2122496",
"316008",
"0"
]
| [
"nonn",
"tabl"
]
| 17 | 0 | 9 | [
"A000007",
"A053491",
"A066166",
"A351735",
"A362834",
"A362837",
"A362838"
]
| null | Seiichi Manyama, May 05 2023 | 2023-05-05T12:23:54 | oeisdata/seq/A362/A362837.seq | 00babdbe7543e2a22517ac82539ee1a7 |
A362838 | a(n) = (-1)^n * n! * Sum_{k=0..floor(n/2)} n^(n-k) * Stirling1(n-k,k)/(n-k)!. | [
"1",
"0",
"4",
"27",
"704",
"26250",
"1573344",
"137145120",
"16494166016",
"2622125642472",
"532936224000000",
"134858889573071400",
"41584752648545107968",
"15351240982641183631440",
"6684412762278362097401856",
"3390180844777789569609375000",
"1981175610959755697378851553280"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A362837",
"A362838"
]
| null | Seiichi Manyama, May 05 2023 | 2023-05-05T12:23:39 | oeisdata/seq/A362/A362838.seq | bf190bf92cf766562c55d9fd6c25ca21 |
A362839 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/2)} k^(n-j) * Stirling2(n-j,j)/(n-j)!. | [
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"2",
"0",
"1",
"0",
"4",
"3",
"0",
"1",
"0",
"6",
"12",
"16",
"0",
"1",
"0",
"8",
"27",
"80",
"65",
"0",
"1",
"0",
"10",
"48",
"216",
"560",
"336",
"0",
"1",
"0",
"12",
"75",
"448",
"2025",
"4512",
"1897",
"0",
"1",
"0",
"14",
"108",
"800",
"5120",
"21708",
"40768",
"11824",
"0",
"1",
"0",
"16",
"147",
"1296",
"10625",
"67584",
"260253",
"407808",
"80145",
"0"
]
| [
"nonn",
"tabl"
]
| 17 | 0 | 9 | [
"A000007",
"A052506",
"A351736",
"A351737",
"A356806",
"A362652",
"A362839"
]
| null | Seiichi Manyama, May 05 2023 | 2023-05-05T12:23:18 | oeisdata/seq/A362/A362839.seq | e19ec775b5554d551ee1c6b04f0e2c3f |
A362840 | a(n) is the smallest number x between 1 and n-1 for which the number 1/x achieves the longest cycle of repeating digits in its expansion in base n. | [
"2",
"3",
"3",
"5",
"5",
"5",
"7",
"7",
"9",
"7",
"11",
"9",
"13",
"11",
"11",
"11",
"13",
"17",
"19",
"19",
"17",
"17",
"23",
"23",
"25",
"23",
"19",
"23",
"29",
"29",
"23",
"31",
"29",
"23",
"29",
"23",
"37",
"29",
"19",
"37",
"31",
"31",
"17",
"43",
"41",
"43",
"47",
"37",
"47",
"47",
"41",
"49",
"53",
"53",
"47",
"53",
"49",
"47",
"59",
"47",
"61",
"59",
"59",
"47",
"61",
"61",
"67",
"59",
"61",
"59"
]
| [
"nonn",
"base"
]
| 38 | 3 | 1 | [
"A051626",
"A362840",
"A362865"
]
| null | Itamar Zamir, May 05 2023 | 2023-05-12T12:21:12 | oeisdata/seq/A362/A362840.seq | fd161ed3aab45a85b9f8cf9be85d4289 |
A362841 | Numbers with at least one 5 in their prime signature. | [
"32",
"96",
"160",
"224",
"243",
"288",
"352",
"416",
"480",
"486",
"544",
"608",
"672",
"736",
"800",
"864",
"928",
"972",
"992",
"1056",
"1120",
"1184",
"1215",
"1248",
"1312",
"1376",
"1440",
"1504",
"1568",
"1632",
"1696",
"1701",
"1760",
"1824",
"1888",
"1944",
"1952",
"2016",
"2080",
"2144",
"2208",
"2272",
"2336",
"2400",
"2430",
"2464",
"2528",
"2592",
"2656",
"2673",
"2720",
"2784",
"2848",
"2912",
"2976"
]
| [
"nonn"
]
| 18 | 1 | 1 | [
"A038109",
"A050997",
"A174312",
"A176297",
"A178740",
"A179646",
"A179667",
"A179671",
"A362841"
]
| null | R. J. Mathar, May 05 2023 | 2023-05-05T12:19:35 | oeisdata/seq/A362/A362841.seq | 38a134c04f82f7378c2bc1eea5f34e51 |
A362842 | a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that shares a factor with a(n-1) when both a(n-1) and a(n) are read as numbers in bases from one more than the maximum digit in a(n-1) and a(n), up to base 10. | [
"1",
"2",
"4",
"6",
"3",
"9",
"12",
"24",
"8",
"20",
"10",
"30",
"33",
"11",
"22",
"26",
"13",
"39",
"15",
"48",
"28",
"14",
"49",
"7",
"70",
"16",
"38",
"19",
"57",
"69",
"18",
"56",
"76",
"36",
"60",
"40",
"42",
"21",
"63",
"66",
"44",
"46",
"23",
"92",
"32",
"64",
"62",
"31",
"93",
"27",
"90",
"5",
"50",
"55",
"77",
"84",
"35",
"80",
"68",
"17",
"119",
"34",
"94",
"47",
"329",
"91",
"52",
"96",
"45",
"95",
"25",
"190",
"54",
"98",
"58",
"29"
]
| [
"nonn",
"base"
]
| 16 | 1 | 2 | [
"A004053",
"A064413",
"A337687",
"A348086",
"A352763",
"A354087",
"A362842"
]
| null | Scott R. Shannon, May 05 2023 | 2023-05-07T08:29:56 | oeisdata/seq/A362/A362842.seq | aa0ad99ca39370a14699c2d90266b9bc |
A362843 | Numbers that are equal to the sum of their digits raised to consecutive odd numbered powers (1,3,5,7,...). | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"463",
"3943",
"371915027434113"
]
| [
"nonn",
"base",
"more"
]
| 34 | 1 | 3 | [
"A032799",
"A154160",
"A208130",
"A362843"
]
| null | Wolfe Padawer, May 05 2023 | 2025-05-23T10:19:19 | oeisdata/seq/A362/A362843.seq | 33207b3d69cb4e678c0fbb7c6c5becad |
A362844 | a(n) is the largest k < A360768(n) such that rad(k) = rad(A360768(n)) and n mod k != 0, where rad(n) = A007947(n). | [
"12",
"18",
"24",
"36",
"40",
"48",
"54",
"45",
"50",
"60",
"72",
"56",
"80",
"96",
"98",
"90",
"84",
"75",
"108",
"63",
"120",
"100",
"144",
"126",
"150",
"147",
"162",
"112",
"132",
"160",
"192",
"196",
"135",
"156",
"180",
"176",
"175",
"200",
"168",
"198",
"240",
"216",
"252",
"270",
"204",
"234",
"250",
"288",
"294",
"208",
"228",
"280",
"242",
"300",
"297",
"225",
"336",
"324",
"224",
"264",
"320",
"375",
"306",
"276"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A007947",
"A126706",
"A360768",
"A362041",
"A362844"
]
| null | Michael De Vlieger, May 19 2023 | 2023-05-20T15:05:09 | oeisdata/seq/A362/A362844.seq | 79a03ecfba73fbaadd25dbec63e41352 |
A362845 | Number of divisors of 7*n-2 of form 7*k+1. | [
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"3",
"1",
"1",
"3",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"3",
"1",
"1",
"1",
"2",
"2",
"3",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"2",
"1",
"2",
"2",
"1",
"1",
"1",
"5",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"1"
]
| [
"nonn"
]
| 33 | 1 | 6 | [
"A279061",
"A362845",
"A363807"
]
| null | Seiichi Manyama, Jun 24 2023 | 2023-06-25T10:39:33 | oeisdata/seq/A362/A362845.seq | 709a29f8812dc60e94af4921bf050e0b |
A362846 | a(n) = Sum_{k=0..n-1} Gamma(n + k) / Gamma(n - k) for n > 0, a(0) = 1. Row sums of A362787. | [
"1",
"1",
"3",
"31",
"853",
"45741",
"4012711",
"520795003",
"93651619881",
"22275111534553",
"6768744159489931",
"2557808459478878871",
"1176328664895760953853",
"646871036386631296664581",
"419117251302784557222893103",
"315981471063390925577186307571",
"274248897723749542494288034278481"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A362787",
"A362846"
]
| null | Peter Luschny, May 05 2023 | 2023-05-05T07:47:08 | oeisdata/seq/A362/A362846.seq | 10c32945cb5b2533b5f9769ef639556c |
A362847 | Triangle read by rows, T(n, k) = 4^k * Gamma(n + k + 1/2) / Gamma(n - k + 1/2). | [
"1",
"1",
"3",
"1",
"15",
"105",
"1",
"35",
"945",
"10395",
"1",
"63",
"3465",
"135135",
"2027025",
"1",
"99",
"9009",
"675675",
"34459425",
"654729075",
"1",
"143",
"19305",
"2297295",
"218243025",
"13749310575",
"316234143225",
"1",
"195",
"36465",
"6235515",
"916620705",
"105411381075",
"7905853580625",
"213458046676875"
]
| [
"nonn",
"tabl"
]
| 13 | 0 | 3 | [
"A000466",
"A101485",
"A362847",
"A362848"
]
| null | Peter Luschny, May 05 2023 | 2023-10-09T14:30:10 | oeisdata/seq/A362/A362847.seq | 0d4f40b78e6f0e0d8e4638f853fe59e6 |
A362848 | a(n) = Sum_{k=0..n} 4^k * Gamma(n + k + 1/2) / Gamma(n - k + 1/2). Row sums of A362847. | [
"1",
"4",
"121",
"11376",
"2165689",
"689873284",
"330204013569",
"221470234531456",
"198160750081637521",
"228040136335670652324",
"328106086348844570538409",
"577082259304437657893671984",
"1218130815379359944856599793801",
"3039062974890293661892991548863076"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A362847",
"A362848"
]
| null | Peter Luschny, May 05 2023 | 2023-10-09T14:30:14 | oeisdata/seq/A362/A362848.seq | 02a6a9dd8b54731ea7c64b3fa72c641a |
A362849 | Triangle read by rows, T(n, k) = A243664(n) * binomial(n, k). | [
"1",
"1",
"1",
"21",
"42",
"21",
"1849",
"5547",
"5547",
"1849",
"426405",
"1705620",
"2558430",
"1705620",
"426405",
"203374081",
"1016870405",
"2033740810",
"2033740810",
"1016870405",
"203374081",
"173959321557",
"1043755929342",
"2609389823355",
"3479186431140",
"2609389823355",
"1043755929342",
"173959321557"
]
| [
"nonn",
"tabl"
]
| 6 | 0 | 4 | [
"A055372",
"A243664",
"A278073",
"A362585",
"A362586",
"A362849"
]
| null | Peter Luschny, May 05 2023 | 2023-05-10T11:50:15 | oeisdata/seq/A362/A362849.seq | 130f502d305decfd5eaa624123f49d02 |
A362850 | Positions of records in A194943. | [
"2",
"3",
"5",
"7",
"11",
"13",
"19",
"31",
"47",
"61",
"127",
"139",
"193",
"229",
"283",
"337",
"409",
"461",
"1531",
"1847",
"2129",
"2861",
"4177",
"6037",
"7577",
"8207",
"8941",
"12311",
"22133",
"32647",
"38231",
"40247",
"40951",
"47903",
"52153",
"63031",
"84229",
"93241",
"97259",
"116729",
"124183",
"132331"
]
| [
"nonn",
"more"
]
| 12 | 1 | 1 | [
"A194943",
"A362850",
"A362851"
]
| null | R. J. Mathar, May 05 2023 | 2023-05-19T04:12:55 | oeisdata/seq/A362/A362850.seq | 0dee3e3ec87330da8c5185c88f009453 |
A362851 | Records in A194943. | [
"1",
"2",
"3",
"4",
"6",
"7",
"10",
"18",
"20",
"24",
"29",
"34",
"36",
"40",
"46",
"51",
"58",
"81",
"87",
"89",
"103",
"107",
"120",
"121",
"135",
"136",
"150",
"174",
"181",
"189",
"193",
"196",
"203",
"204",
"208",
"210",
"225",
"230",
"233",
"240",
"244",
"268"
]
| [
"nonn",
"more"
]
| 11 | 1 | 2 | [
"A194943",
"A362850",
"A362851"
]
| null | R. J. Mathar, May 05 2023 | 2023-05-19T04:13:04 | oeisdata/seq/A362/A362851.seq | 730cc5231b84a13a38249bb3be2ab7e0 |
A362852 | The number of divisors of n that are both bi-unitary and exponential. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1"
]
| [
"nonn",
"mult"
]
| 10 | 1 | 8 | [
"A000005",
"A004709",
"A049419",
"A061704",
"A188999",
"A222266",
"A286324",
"A304327",
"A307428",
"A322791",
"A359411",
"A362852",
"A362853",
"A362854"
]
| null | Amiram Eldar, May 05 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A362/A362852.seq | 57de33fa833b4f171c7a36710f43edfe |
A362853 | Numbers with a record number of divisors that are both bi-unitary and exponential. | [
"1",
"8",
"64",
"216",
"1728",
"27000",
"46656",
"110592",
"216000",
"2985984",
"5832000",
"13824000",
"74088000",
"373248000",
"2000376000",
"4741632000",
"46656000000",
"98611128000",
"128024064000",
"2662500456000",
"6311112192000",
"16003008000000",
"93329542656000",
"170400029184000",
"5489031744000000"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A025487",
"A293185",
"A318278",
"A362852",
"A362853"
]
| null | Amiram Eldar, May 05 2023 | 2025-04-22T21:55:47 | oeisdata/seq/A362/A362853.seq | 41a842cc23e41cc54f43aedac738ac2d |
A362854 | The sum of the divisors of n that are both bi-unitary and exponential. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"10",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"18",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"30",
"25",
"26",
"30",
"28",
"29",
"30",
"31",
"34",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"50",
"41",
"42",
"43",
"44",
"45",
"46",
"47",
"54",
"49",
"50",
"51",
"52",
"53",
"60",
"55",
"70",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"70",
"65",
"66",
"67",
"68"
]
| [
"nonn",
"mult"
]
| 7 | 1 | 2 | [
"A002110",
"A004709",
"A051377",
"A082020",
"A115964",
"A188999",
"A222266",
"A322791",
"A361810",
"A362852",
"A362854"
]
| null | Amiram Eldar, May 05 2023 | 2023-05-05T12:54:13 | oeisdata/seq/A362/A362854.seq | 4f7d780588f6e1d8aa7dd80c8c6e2376 |
A362855 | a(n) = n for n <= 3; for n > 3, a(n) is the least novel multiple of k, the product of all distinct prime factors of a(n-2) that do not divide a(n-1). | [
"1",
"2",
"3",
"4",
"6",
"5",
"12",
"10",
"9",
"20",
"15",
"8",
"30",
"7",
"60",
"14",
"45",
"28",
"75",
"42",
"25",
"84",
"35",
"18",
"70",
"21",
"40",
"63",
"50",
"105",
"16",
"210",
"11",
"420",
"22",
"315",
"44",
"525",
"66",
"140",
"33",
"280",
"99",
"350",
"132",
"175",
"198",
"245",
"264",
"385",
"24",
"770",
"27",
"1540",
"36",
"1155",
"26",
"2310",
"13",
"4620",
"39",
"3080",
"78",
"1925",
"156",
"2695",
"234",
"3465",
"52",
"5775"
]
| [
"nonn"
]
| 22 | 1 | 2 | [
"A002110",
"A007947",
"A280866",
"A306237",
"A362631",
"A362855",
"A368133",
"A369825"
]
| null | Michael De Vlieger and David James Sycamore, May 06 2023 | 2025-06-21T00:41:33 | oeisdata/seq/A362/A362855.seq | be09eba09ec0bc92ccb9a8b31f37cb2f |
A362856 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (-k)^(n-j) * j^j * binomial(n,j). | [
"1",
"1",
"1",
"1",
"0",
"4",
"1",
"-1",
"3",
"27",
"1",
"-2",
"4",
"17",
"256",
"1",
"-3",
"7",
"7",
"169",
"3125",
"1",
"-4",
"12",
"-9",
"120",
"2079",
"46656",
"1",
"-5",
"19",
"-37",
"121",
"1373",
"31261",
"823543",
"1",
"-6",
"28",
"-83",
"208",
"797",
"21028",
"554483",
"16777216",
"1",
"-7",
"39",
"-153",
"441",
"21",
"14517",
"373931",
"11336753",
"387420489"
]
| [
"sign",
"tabl"
]
| 17 | 0 | 6 | [
"A000312",
"A069856",
"A290158",
"A362019",
"A362856",
"A362857",
"A362858"
]
| null | Seiichi Manyama, May 05 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A362/A362856.seq | e0393dfe905e148fa95ff87fc20d1e2c |
A362857 | Expansion of e.g.f. exp(-2*x) / (1 + LambertW(-x)). | [
"1",
"-1",
"4",
"7",
"120",
"1373",
"21028",
"373931",
"7670736",
"178064281",
"4615519884",
"132139421423",
"4141235867992",
"141016013784917",
"5184372688776180",
"204668397165154867",
"8635388122600110240",
"387787185320578895537",
"18467131524896950511644"
]
| [
"sign"
]
| 16 | 0 | 3 | [
"A362856",
"A362857",
"A362859"
]
| null | Seiichi Manyama, May 05 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A362/A362857.seq | e651a4873c36d7297076dc75d944f47c |
A362858 | Expansion of e.g.f. exp(-3*x) / (1 + LambertW(-x)). | [
"1",
"-2",
"7",
"-9",
"121",
"797",
"14517",
"251521",
"5199313",
"120881133",
"3139282909",
"90010844657",
"2824532243001",
"96284834673349",
"3543187673495269",
"139992580020525993",
"5910844405813258273",
"265606657711863337181",
"12655895981349401656749"
]
| [
"sign"
]
| 12 | 0 | 2 | [
"A362856",
"A362858",
"A362860"
]
| null | Seiichi Manyama, May 05 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A362/A362858.seq | 5f49b9a52b89e9df0b1ca3ce082c6d70 |
A362859 | Expansion of e.g.f. exp(-x) / (1 + LambertW(-2*x)). | [
"1",
"1",
"13",
"173",
"3321",
"81529",
"2443333",
"86475493",
"3529941873",
"163260749681",
"8437633695741",
"481912844592541",
"30142773978386281",
"2049173019206244073",
"150443505029536707381",
"11862692305729094644949",
"999864950902004743707873",
"89709634016056661732903137"
]
| [
"nonn",
"easy"
]
| 14 | 0 | 3 | [
"A062971",
"A362019",
"A362857",
"A362859"
]
| null | Seiichi Manyama, May 05 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A362/A362859.seq | b090c7dbcd73d05facd90644e8e8b952 |
A362860 | Expansion of e.g.f. exp(-x) / (1 + LambertW(-3*x)). | [
"1",
"2",
"31",
"629",
"18025",
"662639",
"29752957",
"1578248867",
"96577834801",
"6696994946543",
"518978239136341",
"44448540938239811",
"4169223860364566857",
"425060509005908328071",
"46801425208023247277965",
"5534686715620432932442619",
"699654866766940182167273185"
]
| [
"nonn",
"easy"
]
| 13 | 0 | 2 | [
"A091482",
"A362019",
"A362858",
"A362860"
]
| null | Seiichi Manyama, May 05 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A362/A362860.seq | 10dcc5c86e1cf393a19e08a58c0f1835 |
A362861 | Positive integers n such that 2*n cannot be written as a sum of distinct elements of the set {5^a + 5^b: a,b = 0,1,2,...}. | [
"2",
"7",
"10",
"11",
"12",
"27",
"35",
"50",
"51",
"52",
"55",
"60",
"135",
"255"
]
| [
"nonn",
"more"
]
| 12 | 1 | 1 | [
"A055235",
"A055237",
"A226809",
"A226816",
"A362743",
"A362861"
]
| null | Zhi-Wei Sun, May 05 2023 | 2023-05-16T16:12:38 | oeisdata/seq/A362/A362861.seq | 75fa643de50f7bf60fc1fa2a508baa71 |
A362862 | a(n) = (-1)^n * Sum_{k=0..n} (-n*k)^k * binomial(n,k). | [
"1",
"0",
"13",
"629",
"58993",
"8998399",
"2035844461",
"640881617123",
"267995012680641",
"143734541641235567",
"96200314049944377901",
"78599287990433271805699",
"76993408916168689318057201",
"89072357257840197226050646151"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A290158",
"A362019",
"A362862"
]
| null | Seiichi Manyama, May 06 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A362/A362862.seq | 9082795b8898ea0baa8e6523affaff5a |
A362863 | Centered hecatonicosachoral numbers. | [
"1",
"1441",
"11521",
"44641",
"122401",
"273601",
"534241",
"947521",
"1563841",
"2440801",
"3643201",
"5243041",
"7319521",
"9959041",
"13255201",
"17308801",
"22227841",
"28127521",
"35130241",
"43365601",
"52970401",
"64088641",
"76871521",
"91477441",
"108072001",
"126828001",
"147925441",
"171551521",
"197900641"
]
| [
"nonn",
"easy"
]
| 31 | 1 | 2 | [
"A005891",
"A005904",
"A006322",
"A151989",
"A362863"
]
| null | Léo Cymrot Cymbalista, May 06 2023 | 2023-08-06T17:48:46 | oeisdata/seq/A362/A362863.seq | 30aa3a60a977d59b0823d151c3326cac |
A362864 | Numbers k that divide Sum_{i=1..k} (i - d(i)), where d(n) is the number of divisors of n (A000005). | [
"1",
"2",
"5",
"8",
"15",
"24",
"26",
"47",
"121",
"204",
"347",
"562",
"4204",
"6937",
"6947",
"31108",
"379097",
"379131",
"379133",
"2801205",
"12554202",
"20698345",
"56264197",
"13767391064",
"37423648626",
"37423648726",
"61701166395",
"276525443156",
"276525443176",
"455913379395",
"455913379831",
"751674084802"
]
| [
"nonn"
]
| 46 | 1 | 2 | [
"A000005",
"A000217",
"A006218",
"A049820",
"A050226",
"A161664",
"A362864"
]
| null | Ctibor O. Zizka, May 06 2023 | 2023-05-28T11:17:26 | oeisdata/seq/A362/A362864.seq | 7195e35629568853eff89a8e6dce26f0 |
A362865 | a(n) is the length of the longest possible cycle of repeating digits in the digits expansion of 1/x, in base n, among all numbers x between 1 and n-1. | [
"1",
"1",
"2",
"1",
"4",
"4",
"3",
"6",
"6",
"6",
"10",
"6",
"12",
"5",
"10",
"10",
"12",
"16",
"18",
"18",
"16",
"16",
"11",
"11",
"20",
"22",
"18",
"22",
"28",
"28",
"22",
"30",
"14",
"11",
"28",
"22",
"36",
"28",
"18",
"36",
"30",
"30",
"16",
"42",
"40",
"42",
"23",
"36",
"23",
"46",
"40",
"42",
"52",
"52",
"46",
"52",
"42",
"46",
"58",
"46",
"60",
"29",
"58",
"46",
"60",
"60",
"66",
"58",
"60"
]
| [
"nonn",
"base"
]
| 29 | 3 | 3 | [
"A051626",
"A362840",
"A362865"
]
| null | Itamar Zamir, May 06 2023 | 2023-05-12T12:21:07 | oeisdata/seq/A362/A362865.seq | 68f45dbc6dbbfc9088317648e2a5e733 |
A362866 | Numbers k with the property that the parts of the symmetric representation of sigma(k) are two octagons. | [
"10",
"14",
"22",
"26",
"34",
"38",
"46",
"58",
"62",
"74",
"82",
"86",
"94",
"106",
"118",
"122",
"134",
"142",
"146",
"158",
"166",
"178",
"194",
"202",
"206",
"214",
"218",
"226",
"254",
"262",
"274",
"278",
"298",
"302",
"314",
"326",
"334",
"346",
"358",
"362",
"382",
"386",
"394",
"398",
"422",
"446",
"454",
"458",
"466",
"478",
"482",
"502",
"514",
"526"
]
| [
"nonn"
]
| 79 | 1 | 1 | [
"A000203",
"A001747",
"A063221",
"A065091",
"A091999",
"A100484",
"A196020",
"A235791",
"A236104",
"A237048",
"A237270",
"A237271",
"A237591",
"A237593",
"A239929",
"A241008",
"A245092",
"A246955",
"A249223",
"A249351",
"A262626",
"A362866",
"A364414",
"A364639",
"A365081"
]
| null | Omar E. Pol, May 06 2023 | 2023-09-03T10:52:20 | oeisdata/seq/A362/A362866.seq | fffec24a1c781f1e60173863c264b79b |
A362867 | Irregular triangle read by rows; the n-th row is the n-th permutation of 0 to infinity, in reversed colexicographic ordering, terminating when the rest of the row equals k. | [
"0",
"1",
"0",
"0",
"2",
"1",
"2",
"0",
"1",
"1",
"2",
"0",
"2",
"1",
"0",
"0",
"1",
"3",
"2",
"1",
"0",
"3",
"2",
"0",
"3",
"1",
"2",
"3",
"0",
"1",
"2",
"1",
"3",
"0",
"2",
"3",
"1",
"0",
"2",
"0",
"2",
"3",
"1",
"2",
"0",
"3",
"1",
"0",
"3",
"2",
"1",
"3",
"0",
"2",
"1",
"2",
"3",
"0",
"1",
"3",
"2",
"0",
"1",
"1",
"2",
"3",
"0",
"2",
"1",
"3",
"0",
"1",
"3",
"2",
"0",
"3",
"1",
"2",
"0",
"2",
"3",
"1",
"0",
"3",
"2",
"1",
"0"
]
| [
"nonn",
"tabf"
]
| 26 | 0 | 5 | [
"A055089",
"A084558",
"A353962",
"A362867"
]
| null | Davis Smith, May 06 2023 | 2023-07-15T06:09:32 | oeisdata/seq/A362/A362867.seq | 04b81c5f121454ea2e8bf254cdc6f47a |
A362868 | Triangle read by rows: T(n,k) is the number of connected simple graphs G of order n with the property that k is the order of the largest quotient graph G/~ that is a complete graph. 1 <= k <= n. | [
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"1",
"4",
"1",
"0",
"1",
"12",
"7",
"1",
"0",
"1",
"23",
"75",
"12",
"1",
"0",
"1",
"24",
"481",
"329",
"17",
"1"
]
| [
"nonn",
"tabl",
"hard",
"more"
]
| 19 | 1 | 9 | [
"A001349",
"A362868"
]
| null | Peter Kagey, May 06 2023 | 2024-04-02T14:34:53 | oeisdata/seq/A362/A362868.seq | 211ef7f2f56326bb149833c966c90f2a |
A362869 | a(n) is equal to the number of cells in one octant of the octagon of unit squares with side equal n. | [
"1",
"2",
"8",
"11",
"22",
"27",
"43",
"50",
"71",
"80",
"106",
"117",
"148",
"161",
"197",
"212",
"253",
"270",
"316",
"335",
"386",
"407",
"463",
"486",
"547",
"572",
"638",
"665",
"736",
"765",
"841",
"872",
"953",
"986",
"1072",
"1107",
"1198",
"1235",
"1331",
"1370",
"1471",
"1512",
"1618",
"1661",
"1772",
"1817",
"1933",
"1980",
"2101",
"2150",
"2276"
]
| [
"nonn",
"easy"
]
| 59 | 1 | 2 | [
"A000217",
"A002620",
"A362869"
]
| null | Anatoliy A. Abramov, May 07 2023 | 2023-10-16T06:08:17 | oeisdata/seq/A362/A362869.seq | 40a2d3c2e2ec1eedbcf5c0fc279e4e53 |
A362870 | a(n) = sigma_29(n), the sum of the 29th powers of the divisors of n. | [
"1",
"536870913",
"68630377364884",
"288230376688582657",
"186264514923095703126",
"36845653355419807219092",
"3219905755813179726837608",
"154742505198902911050973185",
"4710128697246313465298968573",
"100000000186264514923632574038",
"1586309297171491574414436704892"
]
| [
"nonn",
"easy",
"mult"
]
| 45 | 1 | 2 | [
"A000203",
"A001160",
"A013957",
"A013961",
"A013965",
"A013969",
"A016825",
"A075180",
"A082771",
"A281959",
"A358625",
"A362870"
]
| null | Vaclav Kotesovec, May 07 2023 | 2025-01-15T03:00:17 | oeisdata/seq/A362/A362870.seq | c1cbb4752cf3024289143b465e111af2 |
A362871 | Leading digit of 6^n. | [
"1",
"6",
"3",
"2",
"1",
"7",
"4",
"2",
"1",
"1",
"6",
"3",
"2",
"1",
"7",
"4",
"2",
"1",
"1",
"6",
"3",
"2",
"1",
"7",
"4",
"2",
"1",
"1",
"6",
"3",
"2",
"1",
"7",
"4",
"2",
"1",
"1",
"6",
"3",
"2",
"1",
"8",
"4",
"2",
"1",
"1",
"6",
"3",
"2",
"1",
"8",
"4",
"2",
"1",
"1",
"6",
"3",
"2",
"1",
"8",
"4",
"2",
"1",
"1",
"6",
"3",
"2",
"1",
"8",
"4",
"2",
"1",
"1",
"6",
"3",
"2",
"1",
"8",
"4",
"2",
"1",
"1",
"6",
"3",
"2",
"1",
"8",
"5",
"3",
"1",
"1",
"6",
"3",
"2",
"1",
"8",
"5",
"3",
"1",
"1",
"6"
]
| [
"nonn",
"base",
"easy"
]
| 34 | 0 | 2 | [
"A000030",
"A000400",
"A008567",
"A008952",
"A060956",
"A111395",
"A362871",
"A363093",
"A363249",
"A364185"
]
| null | Seiichi Manyama, Jul 15 2023 | 2023-07-15T14:02:38 | oeisdata/seq/A362/A362871.seq | 5b4bc7e347058800c022da2decf35604 |
A362872 | Length of the "fractional part" of the phi-representation of n. | [
"0",
"0",
"2",
"2",
"2",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"10",
"10",
"10",
"10",
"10",
"10",
"10"
]
| [
"nonn"
]
| 7 | 0 | 3 | [
"A341722",
"A362692",
"A362872"
]
| null | Jeffrey Shallit, May 07 2023 | 2025-01-05T19:51:42 | oeisdata/seq/A362/A362872.seq | 3508b8b806bb997bd9cb136952a750ad |
A362873 | a(n) is the number of points with integer coordinates that are inside an equilateral triangle inscribed in a circle of radius n, the location of the triangle in the Oxy coordinate plane is described in the comments. | [
"1",
"4",
"12",
"17",
"33",
"42",
"64",
"77",
"105",
"122",
"158",
"177",
"219",
"242",
"292",
"319",
"375",
"406",
"470",
"503",
"573",
"610",
"688",
"729",
"813",
"856",
"948",
"995",
"1093",
"1144",
"1248",
"1303",
"1415",
"1472",
"1592",
"1653",
"1779",
"1844",
"1976",
"2045",
"2185",
"2256",
"2402",
"2477",
"2631",
"2710",
"2870",
"2951",
"3119",
"3204",
"3378",
"3467",
"3649"
]
| [
"nonn"
]
| 23 | 1 | 2 | [
"A183143",
"A194106",
"A362873"
]
| null | Nicolay Avilov, May 07 2023 | 2023-07-15T06:30:51 | oeisdata/seq/A362/A362873.seq | ecdf36dbed64787b54499b2b718369d9 |
A362874 | Number of strongly magic quad squares that can be formed using cards from Quads-2^n deck. | [
"322560",
"19998720",
"839946240",
"30478049280",
"1036253675520",
"34162943754240",
"1109482268590080",
"35765515020533760",
"1148704188306554880",
"36825972627862978560",
"1179511064637886955520",
"37761640503165258301440",
"1208649138156256509296640",
"38681199166714368680263680"
]
| [
"nonn",
"easy"
]
| 31 | 4 | 1 | [
"A308436",
"A361495",
"A361613",
"A362874",
"A362963",
"A362964"
]
| null | Tanya Khovanova and MIT PRIMES STEP senior group, May 07 2023 | 2023-08-09T17:28:54 | oeisdata/seq/A362/A362874.seq | 85bc1325aa36dad3662832e0ae3d5016 |
A362875 | Theta series of 15-dimensional lattice Kappa_15. | [
"1",
"0",
"1746",
"21456",
"147150",
"607536",
"2036334",
"5410800",
"13282866",
"27563184",
"56679732",
"102040272",
"184563384",
"302221728",
"504866340",
"763016400",
"1202127174",
"1728479808",
"2575653198",
"3561176016",
"5127122304",
"6797385072",
"9531403128",
"12329627616",
"16701654486",
"21199654080"
]
| [
"nonn"
]
| 21 | 0 | 3 | [
"A029897",
"A047628",
"A362875",
"A362876",
"A362877",
"A362878",
"A362879",
"A362880"
]
| null | Andy Huchala, May 07 2023 | 2023-05-13T01:58:00 | oeisdata/seq/A362/A362875.seq | 9564bfa155ed0eb026e3175642b3abd9 |
A362876 | Theta series of 16-dimensional lattice Kappa_16. | [
"1",
"0",
"2772",
"42624",
"335052",
"1545984",
"5698860",
"16297344",
"42785244",
"94440960",
"204094296",
"385391232",
"730053060",
"1240934400",
"2151268128",
"3374469504",
"5476016700",
"8115545088",
"12477938100",
"17677480320",
"26111897640",
"35570481408",
"50909418000",
"67336722432",
"93433877268"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A029897",
"A047628",
"A362875",
"A362876",
"A362877",
"A362878",
"A362879",
"A362880"
]
| null | Andy Huchala, May 07 2023 | 2023-05-10T05:19:04 | oeisdata/seq/A362/A362876.seq | b1d2d5d15c2dfa7e218839054274816c |
A362877 | Theta series of 17-dimensional lattice Kappa_17. | [
"1",
"0",
"4266",
"81792",
"737862",
"3809280",
"15406210",
"47505792",
"133390290",
"312588288",
"711232812",
"1408787328",
"2789963820",
"4931371008",
"8870944884",
"14417119872",
"24144502662",
"36878456832",
"58393537998",
"84926534016"
]
| [
"nonn"
]
| 15 | 0 | 3 | [
"A029897",
"A047628",
"A362875",
"A362876",
"A362877",
"A362878",
"A362879",
"A362880"
]
| null | Andy Huchala, May 07 2023 | 2023-05-10T05:19:38 | oeisdata/seq/A362/A362877.seq | 8fc90b98f1eafede6663aa07dece65d2 |
A362878 | Theta series of 18-dimensional lattice Kappa_18. | [
"1",
"0",
"6480",
"157680",
"1596510",
"9488016",
"40681440",
"140492880",
"406046520",
"1047312720",
"2426695200",
"5208293520",
"10421250750",
"19873356480",
"35716191840",
"62355291696",
"104234541390",
"169488573120",
"267064691760",
"413777075760",
"619573504896",
"920235334320",
"1331744781600"
]
| [
"nonn"
]
| 16 | 0 | 3 | [
"A029897",
"A047628",
"A362875",
"A362876",
"A362877",
"A362878",
"A362879",
"A362880"
]
| null | Andy Huchala, May 08 2023 | 2023-05-13T01:57:14 | oeisdata/seq/A362/A362878.seq | 8fac384229d0fac55929763b200121de |
A362879 | Theta series of 19-dimensional lattice Kappa_19. | [
"1",
"0",
"9396",
"284528",
"3309660",
"21996036",
"103632480",
"384538752",
"1195104618",
"3253783500",
"7971340896",
"17905302720",
"37530681590",
"74139276672",
"139067432280",
"250102136592",
"433070833500",
"724358442744",
"1178016364548",
"1866143480400",
"2883345017508",
"4367172766500"
]
| [
"nonn"
]
| 24 | 0 | 3 | [
"A029897",
"A047628",
"A362875",
"A362876",
"A362877",
"A362878",
"A362879",
"A362880"
]
| null | Andy Huchala, May 08 2023 | 2023-05-13T01:57:04 | oeisdata/seq/A362/A362879.seq | 83c3e29bb9fd280dafd90bfe3d40d54f |
A362880 | Theta series of 20-dimensional lattice Kappa_20. | [
"1",
"0",
"15390",
"575160",
"7712820",
"57281580",
"296150580",
"1184012640",
"3944197800",
"11364334080",
"29395745478",
"69157229760",
"151652810580",
"311116423500",
"607158951120",
"1127694969072",
"2020055770530",
"3478103852940",
"5829999042420",
"9467119804680",
"15046034533560"
]
| [
"nonn"
]
| 15 | 0 | 3 | [
"A029897",
"A047628",
"A362875",
"A362876",
"A362877",
"A362878",
"A362879",
"A362880"
]
| null | Andy Huchala, May 08 2023 | 2023-05-13T01:56:41 | oeisdata/seq/A362/A362880.seq | 7eca6d674d40f1f24a202eceed877ea7 |
A362881 | a(n) is the length of the longest arithmetic progression ending at a(n-1); a(1)=1. | [
"1",
"1",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
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"4",
"4",
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"2",
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"3",
"6",
"3",
"6",
"4",
"3",
"5",
"3",
"5",
"3",
"4",
"3"
]
| [
"nonn"
]
| 43 | 1 | 3 | [
"A308638",
"A362881",
"A362909"
]
| null | Samuel Harkness, May 07 2023 | 2024-01-06T10:19:16 | oeisdata/seq/A362/A362881.seq | 156a1a35d1dd523de3ddc98d347d7c3a |
A362882 | Number of even numbers generated by adding two distinct odd primes <= prime(n+1). | [
"0",
"1",
"3",
"6",
"8",
"11",
"14",
"17",
"20",
"25",
"28",
"33",
"37",
"40",
"44",
"47",
"53",
"57",
"62",
"66",
"70",
"75",
"79",
"85",
"89",
"93",
"98",
"102",
"106",
"113",
"117",
"122",
"129",
"134",
"140",
"145",
"150",
"157",
"161",
"166",
"172",
"176",
"181",
"186",
"191",
"196",
"202",
"210",
"214",
"221",
"225",
"230",
"236",
"241",
"245",
"248",
"256",
"264"
]
| [
"nonn"
]
| 28 | 1 | 3 | [
"A083060",
"A362882"
]
| null | Kshitij Thakkar and Gargee Girdhari, May 07 2023 | 2023-05-15T21:50:10 | oeisdata/seq/A362/A362882.seq | 5431012a224ae5042f598c0b10b5fdc4 |
A362883 | a(n) = A055498(n) - A055500(n). | [
"-1",
"0",
"0",
"0",
"0",
"4",
"6",
"12",
"24",
"42",
"68",
"122",
"208",
"336",
"552",
"904",
"1464",
"2378",
"3848",
"6232",
"10090",
"16338",
"26446",
"42802",
"69252",
"112072",
"181332",
"293412",
"474762",
"768190",
"1242960",
"2011162",
"3254150",
"5265324",
"8519478",
"13784866",
"22304378",
"36089262",
"58393658",
"94482964",
"152876664"
]
| [
"sign"
]
| 46 | 0 | 6 | [
"A001622",
"A055498",
"A055500",
"A362883"
]
| null | Philip Baciaz, May 07 2023 | 2024-05-19T02:33:22 | oeisdata/seq/A362/A362883.seq | 2eccd28991dd87519b5fffbc8de76a61 |
A362884 | a(n) = (a(n-1)*a(n-2)*a(n-3)+64)/(4*a(n-4)) with a(0) = a(2) = a(3) = 2 and a(1) = 16. | [
"2",
"16",
"2",
"2",
"16",
"2",
"16",
"72",
"37",
"5336",
"222112",
"152263946",
"1219335473828432",
"1932041718420459629645062",
"403742785702569426305018937234491996105486",
"1561663327784579146423924791055619905538560428937482474084426146608982032"
]
| [
"nonn"
]
| 17 | 0 | 1 | [
"A276175",
"A362884"
]
| null | Max Alekseyev, May 07 2023 | 2025-03-27T05:43:36 | oeisdata/seq/A362/A362884.seq | efd7df0cb46af3ca4db342c28cfa1b64 |
A362885 | Array read by ascending antidiagonals: A(n, k) = (1 + 2*n)*k^n. | [
"1",
"0",
"1",
"0",
"3",
"1",
"0",
"5",
"6",
"1",
"0",
"7",
"20",
"9",
"1",
"0",
"9",
"56",
"45",
"12",
"1",
"0",
"11",
"144",
"189",
"80",
"15",
"1",
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"13",
"352",
"729",
"448",
"125",
"18",
"1",
"0",
"15",
"832",
"2673",
"2304",
"875",
"180",
"21",
"1",
"0",
"17",
"1920",
"9477",
"11264",
"5625",
"1512",
"245",
"24",
"1",
"0",
"19",
"4352",
"32805",
"53248",
"34375",
"11664",
"2401",
"320",
"27",
"1"
]
| [
"nonn",
"tabl"
]
| 8 | 0 | 5 | [
"A000007",
"A000012",
"A004248",
"A005408",
"A008585",
"A014480",
"A033429",
"A058962",
"A124647",
"A155988",
"A171220",
"A176043",
"A199299",
"A199300",
"A199301",
"A244727",
"A362885",
"A362886"
]
| null | Stefano Spezia, May 08 2023 | 2023-05-20T16:08:42 | oeisdata/seq/A362/A362885.seq | 2873aee90c5aee7f2e1ba0ee7a83f8c5 |
A362886 | Antidiagonal sums of A362885. | [
"1",
"1",
"4",
"12",
"37",
"123",
"440",
"1686",
"6901",
"30085",
"139212",
"681336",
"3515397",
"19064135",
"108370384",
"644142962",
"3994439189",
"25789465377",
"173033812804",
"1204425693988",
"8683782562597",
"64757730613875",
"498827437211176",
"3964154812486062",
"32463601480302005",
"273670283527555869"
]
| [
"nonn"
]
| 4 | 0 | 3 | [
"A362885",
"A362886"
]
| null | Stefano Spezia, May 08 2023 | 2023-05-20T16:08:55 | oeisdata/seq/A362/A362886.seq | aa47319edb7e23770452b61dfaa221cc |
A362887 | a(0) = 0; for n>=1, a(n) is the smallest number whose Hamming distance from a(n-1) is prime(n). | [
"0",
"3",
"4",
"27",
"100",
"1947",
"6244",
"124827",
"399460",
"7989147",
"528881764",
"1618601883",
"135820351588",
"2063202903963",
"6732890118244",
"134004598237083",
"8873194656503908",
"567587557646919579",
"1738255451566774372",
"145835697138109638555",
"2215347544296712968292"
]
| [
"nonn",
"base"
]
| 15 | 0 | 2 | [
"A000040",
"A000975",
"A362887"
]
| null | Zachary G. Graham, May 08 2023 | 2023-05-23T11:35:16 | oeisdata/seq/A362/A362887.seq | e57ffa7cdc6d436a2688fdd55a5dcb15 |
A362888 | a(1) = 1, a(n) = (3*k + 1)*(6*k + 1)*(8*k + 1), where k = Product_{i=1..n-1} a(i). | [
"1",
"252",
"2310152797",
"28410981127871160285705816883937448685"
]
| [
"nonn"
]
| 6 | 1 | 2 | [
"A002412",
"A360826",
"A362888"
]
| null | Ivan N. Ianakiev, May 08 2023 | 2023-05-20T16:09:38 | oeisdata/seq/A362/A362888.seq | 9e3bab7106414c03ef9451de1545f33c |
A362889 | a(n) = n for n <= 2. Let i = a(n-2), j = a(n-1), q = gpd(i*j) = prime(s), and k = product of all distinct primes < q which do not divide i*j. For n > 2 a(n) is the least novel multiple of either k (if k is not the empty product), or of prime(s+1) if it is. | [
"1",
"2",
"3",
"5",
"4",
"6",
"10",
"7",
"9",
"20",
"14",
"12",
"15",
"21",
"8",
"25",
"18",
"28",
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"50",
"91",
"132",
"75",
"98",
"121",
"90",
"112",
"143",
"120"
]
| [
"nonn"
]
| 12 | 1 | 2 | [
"A002110",
"A007947",
"A362889"
]
| null | David James Sycamore, May 08 2023 | 2023-06-23T07:51:11 | oeisdata/seq/A362/A362889.seq | a0e1f3079d5a478c3924066668c793e8 |
A362890 | a(1)=a(2)=1. For n>2, a(n) is the number of times that a(n-1) and a(n-2) are adjacent in the sequence thus far (in any order). | [
"1",
"1",
"1",
"2",
"1",
"2",
"3",
"1",
"1",
"3",
"2",
"2",
"1",
"4",
"1",
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"1",
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"9",
"1",
"1",
"6",
"6",
"1",
"7",
"4",
"1"
]
| [
"nonn"
]
| 21 | 1 | 4 | [
"A362746",
"A362890"
]
| null | Neal Gersh Tolunsky, May 08 2023 | 2023-05-10T22:39:08 | oeisdata/seq/A362/A362890.seq | d42a9d18f9e23426701fae4acc3f25bf |
A362891 | Expansion of e.g.f. 1/(1 + LambertW(x^2 * log(1-x))). | [
"1",
"0",
"0",
"6",
"12",
"40",
"1620",
"11088",
"80640",
"2289600",
"30471840",
"374663520",
"9819817920",
"195106129920",
"3507260492736",
"95860364846400",
"2466492401318400",
"58909563259223040",
"1775000008437557760",
"54856736708999339520",
"1629826915777548364800"
]
| [
"nonn"
]
| 11 | 0 | 4 | [
"A305981",
"A353228",
"A362835",
"A362891",
"A362892"
]
| null | Seiichi Manyama, May 08 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A362/A362891.seq | fa28cebdc9475bbb73864e89b6777f81 |
A362892 | Expansion of e.g.f. 1/(1 + LambertW(-x^2 * (exp(x) - 1))). | [
"1",
"0",
"0",
"6",
"12",
"20",
"1470",
"10122",
"47096",
"1814472",
"25119450",
"226527950",
"6732015972",
"142901684796",
"2071229736758",
"57596022404130",
"1589579741044080",
"32832196825559312",
"951335638952843826",
"31043287459520549910",
"838738470701197009820"
]
| [
"nonn"
]
| 14 | 0 | 4 | [
"A240989",
"A282190",
"A362836",
"A362891",
"A362892"
]
| null | Seiichi Manyama, May 08 2023 | 2025-05-19T03:07:19 | oeisdata/seq/A362/A362892.seq | 80f0d3ea62f5be385a4713074e57e3aa |
A362893 | Number of partitions of [n] whose blocks can be ordered such that the i-th block has at least i elements and no block j > i has an element smaller than the i-th smallest element of block i. | [
"1",
"1",
"1",
"2",
"5",
"12",
"28",
"69",
"193",
"614",
"2103",
"7359",
"25660",
"88914",
"309502",
"1102146",
"4092840",
"16046224",
"66410789",
"286905421",
"1273646720",
"5729762139",
"25881820352",
"116872997038",
"527375160184",
"2384407416357",
"10856086444051",
"50097994816979",
"235937202788389"
]
| [
"nonn"
]
| 13 | 0 | 4 | [
"A000110",
"A362549",
"A362635",
"A362893"
]
| null | Alois P. Heinz, May 08 2023 | 2023-05-09T20:16:06 | oeisdata/seq/A362/A362893.seq | f5ea8fbc367a354b092f1ee0e82d201d |
A362894 | Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes having Hadwiger number k, 1 <= k <= n. | [
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"2",
"3",
"1",
"0",
"3",
"12",
"5",
"1",
"0",
"6",
"50",
"47",
"8",
"1",
"0",
"11",
"230",
"448",
"152",
"11",
"1"
]
| [
"nonn",
"tabl",
"hard",
"more"
]
| 27 | 1 | 8 | [
"A000055",
"A001349",
"A024206",
"A032766",
"A084269",
"A353212",
"A362894"
]
| null | Peter Kagey, May 08 2023 | 2025-06-18T23:17:59 | oeisdata/seq/A362/A362894.seq | 75f7c67ed8e1ebf797cc286fc16a9b35 |
A362895 | a(n) is the length of the smallest orbit of the n-th natural downset | [
"1",
"1",
"1",
"1",
"1",
"3",
"3",
"1",
"1",
"4",
"12",
"12",
"6",
"6",
"4",
"1",
"1",
"5",
"20",
"30",
"30",
"60",
"60",
"20",
"10",
"10",
"30",
"30",
"10",
"10",
"5",
"1",
"1",
"6",
"30",
"60",
"60",
"180",
"180",
"60",
"60",
"120",
"360",
"360",
"180",
"180",
"120",
"30",
"15",
"15",
"60",
"90",
"90",
"180",
"180",
"60",
"20",
"20",
"60",
"60",
"15",
"15",
"6",
"1",
"1",
"7"
]
| [
"nonn",
"easy"
]
| 33 | 0 | 6 | [
"A000372",
"A132581",
"A362895"
]
| null | Bruno L. O. Andreotti, May 09 2023 | 2023-05-20T14:43:04 | oeisdata/seq/A362/A362895.seq | 6a8521c1824032a0392b9884036139cc |
A362896 | a(0)=2. For n>0, let d = n-th digit in the sequence thus far. a(n) = a(n-1) + d if d is even. Otherwise, a(n) = a(n-1) - d. | [
"2",
"4",
"8",
"16",
"15",
"21",
"20",
"15",
"17",
"16",
"18",
"18",
"17",
"12",
"11",
"4",
"3",
"9",
"8",
"16",
"15",
"23",
"22",
"15",
"14",
"16",
"15",
"14",
"18",
"15",
"6",
"14",
"13",
"19",
"18",
"13",
"15",
"12",
"14",
"16",
"15",
"10",
"9",
"13",
"12",
"18",
"17",
"12",
"11",
"15",
"14",
"22",
"21",
"16",
"22",
"21",
"25",
"24",
"21",
"20",
"11",
"10",
"18",
"17",
"14",
"13",
"8",
"7"
]
| [
"sign",
"easy",
"base"
]
| 25 | 0 | 1 | [
"A362371",
"A362551",
"A362896"
]
| null | Gavin Lupo, May 09 2023 | 2023-05-17T20:45:19 | oeisdata/seq/A362/A362896.seq | 459a74b69d6eaeeed43c2013ed696137 |
A362897 | Array read by antidiagonals: T(n,k) is the number of nonisomorphic multisets of endofunctions on an n-set with k endofunctions. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"7",
"7",
"1",
"1",
"1",
"13",
"74",
"19",
"1",
"1",
"1",
"22",
"638",
"1474",
"47",
"1",
"1",
"1",
"34",
"4663",
"118949",
"41876",
"130",
"1",
"1",
"1",
"50",
"28529",
"7643021",
"42483668",
"1540696",
"343",
"1",
"1",
"1",
"70",
"151600",
"396979499",
"33179970333",
"23524514635",
"68343112",
"951",
"1"
]
| [
"nonn",
"tabl"
]
| 7 | 0 | 9 | [
"A000012",
"A001372",
"A002623",
"A054745",
"A277839",
"A362644",
"A362897",
"A362898"
]
| null | Andrew Howroyd, May 10 2023 | 2023-05-10T22:39:21 | oeisdata/seq/A362/A362897.seq | 07d0218611ef6686676a6022e31ee3d9 |
A362898 | Number of nonisomorphic unordered triples of endofunctions on an n-set. | [
"1",
"1",
"13",
"638",
"118949",
"42483668",
"23524514635",
"18477841853059",
"19526400231564564",
"26714255854638149145",
"45938634690184528585855",
"96990967579564469350287613",
"246664446832722382952639028437",
"743740463651636548809953508690270",
"2623456914417867939801667337352637825"
]
| [
"nonn"
]
| 6 | 0 | 3 | [
"A001372",
"A054745",
"A362897",
"A362898"
]
| null | Andrew Howroyd, May 10 2023 | 2023-05-10T22:39:17 | oeisdata/seq/A362/A362898.seq | 0807cd451eaf544204010e272d80d537 |
A362899 | Array read by antidiagonals: T(n,k) is the number of nonisomorphic multisets of fixed-point-free endofunctions on an n-set with k endofunctions. | [
"1",
"1",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"2",
"1",
"1",
"0",
"1",
"9",
"6",
"1",
"1",
"0",
"1",
"22",
"162",
"13",
"1",
"1",
"0",
"1",
"63",
"3935",
"4527",
"40",
"1",
"1",
"0",
"1",
"136",
"81015",
"1497568",
"172335",
"100",
"1",
"1",
"0",
"1",
"302",
"1369101",
"384069023",
"883538845",
"7861940",
"291",
"1",
"1",
"0",
"1",
"580",
"19601383",
"78954264778",
"3450709120355",
"725601878962",
"416446379",
"797",
"1"
]
| [
"nonn",
"tabl"
]
| 8 | 0 | 14 | [
"A000012",
"A001373",
"A362644",
"A362759",
"A362897",
"A362899",
"A362900",
"A362901",
"A362902"
]
| null | Andrew Howroyd, May 10 2023 | 2023-05-10T22:39:01 | oeisdata/seq/A362/A362899.seq | e43bafe06f6a7963c7b192c487fc6c75 |
A362900 | Number of nonisomorphic unordered pairs of fixed-point-free endofunctions on an n-set. | [
"1",
"0",
"1",
"9",
"162",
"4527",
"172335",
"7861940",
"416446379",
"25076668511",
"1692214417496",
"126525497074469",
"10384653020019554",
"928348695659951013",
"89797089935616345473",
"9344984104905250973209",
"1041167026926648579218267",
"123655975822561996200923033",
"15595901625395079379351443550"
]
| [
"nonn"
]
| 8 | 0 | 4 | [
"A054745",
"A362899",
"A362900"
]
| null | Andrew Howroyd, May 10 2023 | 2023-05-10T22:38:53 | oeisdata/seq/A362/A362900.seq | ffefbd7258653293fc2be8c5880eb94f |
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