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2.35k
| offset_a
int64 -14,827
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
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stringlengths 29
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A363201 | Number of free linear polycubes of size n, identifying rotations but not reflections. | [
"1",
"1",
"2",
"5",
"16",
"54",
"212",
"827",
"3369",
"13653",
"56052",
"229004",
"939935",
"3843859",
"15753903",
"64380796",
"263475472",
"1075780425",
"4397161320",
"17939394036",
"73251877235",
"298646347226",
"1218453344740"
]
| [
"nonn",
"more"
]
| 12 | 1 | 3 | [
"A363199",
"A363201"
]
| null | Joerg Arndt and Márk Péter Légrádi, May 21 2023 | 2023-06-07T11:44:49 | oeisdata/seq/A363/A363201.seq | 5f6954506c27f8bcbcdbcf79e6f20e98 |
A363202 | Number of free linear polycubes of size n, identifying rotations and reflections. | [
"1",
"1",
"2",
"4",
"12",
"34",
"125",
"450",
"1780",
"7021",
"28521",
"115553",
"472578",
"1927634",
"7890893",
"32221475",
"131812746",
"538059836",
"2198986587",
"8970624060",
"36628143111",
"149328243327",
"609238673619"
]
| [
"nonn",
"more"
]
| 22 | 1 | 3 | [
"A304196",
"A363202",
"A363208",
"A363209",
"A363210"
]
| null | Joerg Arndt and Márk Péter Légrádi, May 21 2023 | 2023-08-12T00:30:39 | oeisdata/seq/A363/A363202.seq | 543a3d0116d843b681240f5dc772a3f6 |
A363203 | Number of free linear polycubes of size n, identifying rotations and reflections and avoiding neighbors at [0,0,+-2], [0,+-2,0], and [+-2,0,0]. | [
"1",
"1",
"1",
"2",
"4",
"9",
"20",
"51",
"128",
"338",
"882",
"2350",
"6238",
"16693",
"44561",
"119339",
"319104",
"854420",
"2285357"
]
| [
"nonn",
"more"
]
| 9 | 1 | 4 | [
"A363203",
"A363204"
]
| null | Joerg Arndt and Márk Péter Légrádi, May 21 2023 | 2023-05-21T12:56:39 | oeisdata/seq/A363/A363203.seq | 4856916777b92c080ff9ad78e446cfc6 |
A363204 | Number of free linear polycubes of size n, identifying rotations and reflections and avoiding the eight corner-connected neighbors. | [
"1",
"1",
"2",
"3",
"8",
"16",
"44",
"106",
"297",
"793",
"2259",
"6322",
"18212",
"52240",
"151818",
"440855",
"1288842",
"3767952",
"11058157",
"32452285",
"95467258"
]
| [
"nonn",
"more"
]
| 14 | 1 | 3 | [
"A363203",
"A363204"
]
| null | Joerg Arndt and Márk Péter Légrádi, May 21 2023 | 2023-12-09T02:18:02 | oeisdata/seq/A363/A363204.seq | 05baf989b83d6d167cc2684580b34afb |
A363205 | Number of polycubes with n cells, allowing face connections as well as corner connections, identifying mirror images. | [
"1",
"2",
"7",
"56",
"567",
"8251",
"135380",
"2390974",
"43659169"
]
| [
"nonn",
"hard",
"more"
]
| 17 | 1 | 2 | [
"A038119",
"A268666",
"A272368",
"A363205",
"A363206",
"A366766"
]
| null | Joerg Arndt and Márk Péter Légrádi, May 21 2023 | 2023-11-04T13:53:00 | oeisdata/seq/A363/A363205.seq | 517c59efee5238e6fd3270478c938536 |
A363206 | Number of polycubes with n cells, allowing edge connections as well as corner connections, identifying mirror images. | [
"1",
"2",
"10",
"113",
"1772",
"37390",
"857772",
"20629656"
]
| [
"nonn",
"hard",
"more"
]
| 12 | 1 | 2 | [
"A038119",
"A268666",
"A272368",
"A363205",
"A363206",
"A366766"
]
| null | Joerg Arndt and Márk Péter Légrádi, May 21 2023 | 2023-11-04T13:50:26 | oeisdata/seq/A363/A363206.seq | de96538c33586813077be503f06cb6a0 |
A363207 | Number of polycubes avoiding corner connections. | [
"1",
"1",
"2",
"6",
"15",
"47",
"170",
"654",
"2699",
"11539",
"50919",
"229529",
"1054374",
"4915265"
]
| [
"nonn",
"hard",
"more"
]
| 7 | 1 | 3 | [
"A363200",
"A363207"
]
| null | Joerg Arndt and Márk Péter Légrádi, May 22 2023 | 2023-05-22T06:37:41 | oeisdata/seq/A363/A363207.seq | 23dfcb6fb09daf9fe42f05a808df9747 |
A363208 | Number of linear connected animals formed from n 6-gon connected truncated octahedra. | [
"1",
"1",
"3",
"7",
"29",
"114",
"578",
"2890",
"15431",
"82091",
"442702",
"2377819",
"12820705"
]
| [
"nonn",
"hard",
"more"
]
| 9 | 1 | 3 | [
"A363208",
"A363210"
]
| null | Joerg Arndt and Márk Péter Légrádi, May 22 2023 | 2023-05-22T06:38:51 | oeisdata/seq/A363/A363208.seq | 0b692c659aeee455ec23c51dfc64f709 |
A363209 | Number of linear connected animals formed from n rhombic dodecahedra. | [
"1",
"1",
"3",
"10",
"52",
"288",
"1826",
"11702",
"76586",
"501429",
"3289245",
"21554198"
]
| [
"nonn",
"hard",
"more"
]
| 10 | 1 | 3 | [
"A363209",
"A363210"
]
| null | Joerg Arndt and Márk Péter Légrádi, May 22 2023 | 2023-05-22T06:39:06 | oeisdata/seq/A363/A363209.seq | 69d7997e439bd89671caccbf9c3a3333 |
A363210 | Number of linear connected animals formed from n 4-gon or 6-gon connected truncated octahedra. | [
"1",
"2",
"5",
"19",
"95",
"598",
"4190",
"30809",
"230104",
"1728305",
"12993821"
]
| [
"nonn",
"hard",
"more"
]
| 9 | 1 | 2 | null | null | Joerg Arndt and Márk Péter Légrádi, May 22 2023 | 2023-05-22T06:39:38 | oeisdata/seq/A363/A363210.seq | d27140dc16085185c99cdd3794ff9b82 |
A363211 | Number of partitions of n such that 3*(least part) <= greatest part. | [
"0",
"0",
"0",
"1",
"2",
"4",
"7",
"12",
"18",
"27",
"39",
"56",
"78",
"106",
"143",
"193",
"254",
"333",
"432",
"560",
"717",
"914",
"1157",
"1461",
"1833",
"2292",
"2849",
"3536",
"4362",
"5372",
"6587",
"8062",
"9825",
"11951",
"14487",
"17533",
"21150",
"25469",
"30583",
"36670",
"43850",
"52357",
"62366",
"74184",
"88048",
"104359",
"123442",
"145826",
"171946",
"202487"
]
| [
"nonn"
]
| 14 | 1 | 5 | [
"A237821",
"A237825",
"A363075",
"A363211",
"A363276"
]
| null | Seiichi Manyama, May 27 2023 | 2023-05-27T10:33:09 | oeisdata/seq/A363/A363211.seq | c323008e4744dc315fbfebb5989433f4 |
A363212 | Sums of distinct factorials that are of the form x^2 - 1. | [
"0",
"3",
"8",
"24",
"120",
"728",
"840",
"5040",
"45368",
"46224",
"363608",
"403224",
"3674888",
"1401602635448"
]
| [
"nonn",
"more"
]
| 21 | 1 | 2 | [
"A005563",
"A014597",
"A059590",
"A363212"
]
| null | Robert Israel, May 30 2023 | 2023-06-26T08:46:43 | oeisdata/seq/A363/A363212.seq | 1ad1896cd84e22242635622a40243ba8 |
A363213 | Number of partitions of n with rank 4 (the rank of a partition is the largest part minus the number of parts). | [
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"1",
"2",
"2",
"4",
"4",
"6",
"7",
"11",
"12",
"18",
"20",
"28",
"33",
"44",
"51",
"68",
"80",
"103",
"122",
"154",
"182",
"229",
"270",
"334",
"396",
"485",
"572",
"698",
"822",
"993",
"1169",
"1404",
"1649",
"1971",
"2310",
"2745",
"3214",
"3803",
"4439",
"5235",
"6099",
"7162",
"8331",
"9750",
"11315",
"13205",
"15294",
"17794",
"20574",
"23872"
]
| [
"nonn"
]
| 14 | 1 | 9 | [
"A000041",
"A063995",
"A105806",
"A363213"
]
| null | Seiichi Manyama, May 21 2023 | 2023-05-22T08:10:16 | oeisdata/seq/A363/A363213.seq | 45cad08688bbf2abb8d01136e947a67d |
A363214 | Number of partitions of n with rank 5 (the rank of a partition is the largest part minus the number of parts). | [
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"1",
"2",
"2",
"4",
"4",
"7",
"7",
"11",
"13",
"19",
"21",
"30",
"35",
"47",
"55",
"73",
"85",
"111",
"131",
"166",
"197",
"247",
"291",
"362",
"428",
"525",
"620",
"756",
"890",
"1078",
"1268",
"1523",
"1791",
"2140",
"2507",
"2983",
"3490",
"4131",
"4824",
"5688",
"6626",
"7785",
"9052",
"10595",
"12298",
"14351",
"16618",
"19339",
"22355",
"25938"
]
| [
"nonn"
]
| 16 | 1 | 10 | [
"A000041",
"A063995",
"A105806",
"A363214"
]
| null | Seiichi Manyama, May 21 2023 | 2024-02-24T13:41:20 | oeisdata/seq/A363/A363214.seq | bb4b06450c30399724e2303576b0ea3a |
A363215 | Integers p > 1 such that 3^d == 1 (mod p) where d = A000265(p-1). | [
"2",
"11",
"13",
"23",
"47",
"59",
"71",
"83",
"107",
"109",
"121",
"131",
"167",
"179",
"181",
"191",
"227",
"229",
"239",
"251",
"263",
"277",
"286",
"311",
"313",
"347",
"359",
"383",
"419",
"421",
"431",
"433",
"443",
"467",
"479",
"491",
"503",
"541",
"563",
"587",
"599",
"601",
"647",
"659",
"683",
"709",
"719",
"733",
"743",
"757",
"827",
"829",
"839",
"863"
]
| [
"nonn"
]
| 18 | 1 | 1 | [
"A000265",
"A005935",
"A020229",
"A130433",
"A363215"
]
| null | Jeppe Stig Nielsen, May 21 2023 | 2023-05-22T14:18:23 | oeisdata/seq/A363/A363215.seq | ac65c156721a23b77e39a1bfc18492d0 |
A363216 | Even powerful numbers that are not prime powers. | [
"36",
"72",
"100",
"108",
"144",
"196",
"200",
"216",
"288",
"324",
"392",
"400",
"432",
"484",
"500",
"576",
"648",
"676",
"784",
"800",
"864",
"900",
"968",
"972",
"1000",
"1152",
"1156",
"1296",
"1352",
"1372",
"1444",
"1568",
"1600",
"1728",
"1764",
"1800",
"1936",
"1944",
"2000",
"2116",
"2304",
"2312",
"2500",
"2592",
"2700",
"2704",
"2744",
"2888",
"2916",
"3136",
"3200",
"3364",
"3456",
"3528",
"3600"
]
| [
"nonn"
]
| 17 | 1 | 1 | [
"A001694",
"A002117",
"A013661",
"A013664",
"A062739",
"A082695",
"A126706",
"A286708",
"A363101",
"A363216",
"A363217"
]
| null | Michael De Vlieger, May 21 2023 | 2023-05-28T20:49:23 | oeisdata/seq/A363/A363216.seq | 1c2c6f176635a023036458abc49f5845 |
A363217 | Odd powerful numbers that are not powers of primes. | [
"225",
"441",
"675",
"1089",
"1125",
"1225",
"1323",
"1521",
"2025",
"2601",
"3025",
"3087",
"3249",
"3267",
"3375",
"3969",
"4225",
"4563",
"4761",
"5625",
"5929",
"6075",
"6125",
"7225",
"7569",
"7803",
"8281",
"8575",
"8649",
"9025",
"9261",
"9747",
"9801",
"10125",
"11025",
"11907",
"11979",
"12321",
"13225",
"13689",
"14161",
"14283",
"15125",
"15129",
"16641",
"16875",
"17689",
"18225",
"19773"
]
| [
"nonn"
]
| 17 | 1 | 1 | [
"A000961",
"A001694",
"A002117",
"A013661",
"A013664",
"A062739",
"A082695",
"A126706",
"A136141",
"A286708",
"A363216",
"A363217"
]
| null | Michael De Vlieger, May 21 2023 | 2023-05-28T20:49:33 | oeisdata/seq/A363/A363217.seq | f214b50e28091faa4b9cc3f5befb2a2f |
A363218 | Positive integers whose prime indices satisfy: (length) = 2*(maximum). | [
"4",
"24",
"36",
"54",
"81",
"160",
"240",
"360",
"400",
"540",
"600",
"810",
"896",
"900",
"1000",
"1215",
"1344",
"1350",
"1500",
"2016",
"2025",
"2240",
"2250",
"2500",
"3024",
"3136",
"3360",
"3375",
"3750",
"4536",
"4704",
"5040",
"5600",
"5625",
"5632",
"6250",
"6804",
"7056",
"7560",
"7840",
"8400",
"8448",
"9375",
"10206",
"10584",
"10976"
]
| [
"nonn"
]
| 7 | 1 | 1 | [
"A001221",
"A001222",
"A035363",
"A056239",
"A061395",
"A067801",
"A106529",
"A112798",
"A118096",
"A237752",
"A237753",
"A237757",
"A324521",
"A326567",
"A326568",
"A344415",
"A361855",
"A361908",
"A361909",
"A363134",
"A363218",
"A363222"
]
| null | Gus Wiseman, May 23 2023 | 2023-05-27T16:46:01 | oeisdata/seq/A363/A363218.seq | 3e82448ea06e9150f59d5a64ded48000 |
A363219 | Twice the median of the conjugate of the integer partition with Heinz number n. | [
"0",
"2",
"2",
"4",
"2",
"3",
"2",
"6",
"4",
"2",
"2",
"4",
"2",
"2",
"4",
"8",
"2",
"5",
"2",
"2",
"3",
"2",
"2",
"5",
"4",
"2",
"6",
"2",
"2",
"4",
"2",
"10",
"2",
"2",
"4",
"6",
"2",
"2",
"2",
"2",
"2",
"3",
"2",
"2",
"6",
"2",
"2",
"6",
"4",
"4",
"2",
"2",
"2",
"7",
"4",
"2",
"2",
"2",
"2",
"4",
"2",
"2",
"4",
"12",
"3",
"2",
"2",
"2",
"2",
"4",
"2",
"7",
"2",
"2",
"6",
"2",
"4",
"2",
"2",
"2",
"8",
"2",
"2",
"3",
"2",
"2"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A000700",
"A001221",
"A001222",
"A046682",
"A056239",
"A088902",
"A112798",
"A118914",
"A122111",
"A124010",
"A258116",
"A296150",
"A321648",
"A321649",
"A321650",
"A325040",
"A326567",
"A326568",
"A326839",
"A326840",
"A326848",
"A352491",
"A360005",
"A362617",
"A362618",
"A363219",
"A363220",
"A363223",
"A363224"
]
| null | Gus Wiseman, May 25 2023 | 2023-05-27T16:45:20 | oeisdata/seq/A363/A363219.seq | de4d0ed50664064eb60e794f913a6dab |
A363220 | Number of integer partitions of n whose conjugate has the same median. | [
"1",
"0",
"1",
"1",
"1",
"3",
"3",
"8",
"8",
"12",
"12",
"15",
"21",
"27",
"36",
"49",
"65",
"85",
"112",
"149",
"176",
"214",
"257",
"311",
"378",
"470",
"572",
"710",
"877",
"1080",
"1322",
"1637",
"1983",
"2416",
"2899",
"3465",
"4107",
"4891",
"5763",
"6820",
"8071",
"9542",
"11289",
"13381",
"15808",
"18710",
"22122",
"26105",
"30737",
"36156",
"42377"
]
| [
"nonn"
]
| 7 | 1 | 6 | [
"A000700",
"A000701",
"A000975",
"A046682",
"A047993",
"A067538",
"A088902",
"A114638",
"A122111",
"A325039",
"A325040",
"A325347",
"A330644",
"A352486",
"A352487",
"A352490",
"A352491",
"A360068",
"A360242",
"A360244",
"A360245",
"A360248",
"A362617",
"A362618",
"A362621",
"A363219",
"A363220",
"A363223",
"A363260",
"A363261"
]
| null | Gus Wiseman, May 29 2023 | 2023-05-31T10:48:53 | oeisdata/seq/A363/A363220.seq | 3bd0d3d52781d6a0a136563b83065330 |
A363221 | Number of strict integer partitions of n such that (length) * (maximum) <= 2n. | [
"1",
"1",
"2",
"2",
"3",
"4",
"5",
"6",
"8",
"9",
"11",
"14",
"15",
"19",
"23",
"26",
"29",
"37",
"39",
"49",
"55",
"62",
"71",
"84",
"93",
"108",
"118",
"141",
"149",
"188",
"193",
"217",
"257",
"279",
"318",
"369",
"376",
"441",
"495",
"572",
"587",
"692",
"760",
"811",
"960",
"1046",
"1065",
"1307",
"1387",
"1550",
"1703",
"1796",
"2041",
"2295",
"2456",
"2753",
"3014"
]
| [
"nonn"
]
| 7 | 1 | 3 | [
"A000009",
"A000041",
"A008284",
"A051293",
"A058398",
"A067538",
"A111907",
"A237984",
"A240219",
"A241061",
"A241086",
"A324521",
"A324562",
"A349156",
"A360068",
"A360241",
"A361394",
"A361848",
"A361849",
"A361850",
"A361851",
"A361852",
"A361853",
"A361854",
"A361855",
"A361856",
"A361906",
"A363221"
]
| null | Gus Wiseman, May 23 2023 | 2023-05-27T16:44:55 | oeisdata/seq/A363/A363221.seq | 93f5fb989ee9feee3dd8020659a58a4e |
A363222 | Numbers whose multiset of prime indices satisfies (maximum) - (minimum) = (length). | [
"10",
"21",
"28",
"42",
"55",
"70",
"88",
"91",
"98",
"99",
"132",
"165",
"187",
"198",
"208",
"220",
"231",
"247",
"308",
"312",
"325",
"330",
"351",
"363",
"391",
"455",
"462",
"468",
"484",
"520",
"544",
"550",
"551",
"585",
"702",
"713",
"715",
"726",
"728",
"770",
"780",
"816",
"819",
"833",
"845",
"975",
"1073",
"1078",
"1092",
"1144",
"1170",
"1210",
"1216"
]
| [
"nonn"
]
| 6 | 1 | 1 | [
"A001221",
"A001222",
"A056239",
"A067801",
"A111907",
"A112798",
"A118096",
"A237821",
"A237832",
"A243055",
"A360005",
"A360457",
"A361205",
"A361908",
"A361909",
"A363222"
]
| null | Gus Wiseman, May 29 2023 | 2023-06-03T23:56:48 | oeisdata/seq/A363/A363222.seq | 9c74df18d9c41a6c83d2147338486c88 |
A363223 | Numbers with bigomega equal to median prime index. | [
"2",
"9",
"10",
"50",
"70",
"75",
"105",
"110",
"125",
"130",
"165",
"170",
"175",
"190",
"195",
"230",
"255",
"275",
"285",
"290",
"310",
"325",
"345",
"370",
"410",
"425",
"430",
"435",
"465",
"470",
"475",
"530",
"555",
"575",
"590",
"610",
"615",
"645",
"670",
"686",
"705",
"710",
"725",
"730",
"775",
"790",
"795",
"830",
"885",
"890",
"915",
"925",
"970"
]
| [
"nonn"
]
| 6 | 1 | 1 | [
"A000040",
"A000975",
"A001222",
"A006141",
"A013580",
"A027746",
"A047993",
"A053263",
"A056239",
"A079309",
"A106529",
"A112798",
"A240219",
"A307683",
"A324522",
"A325347",
"A327473",
"A327476",
"A359893",
"A359901",
"A359908",
"A360005",
"A361800",
"A361860",
"A362049",
"A362050",
"A362619",
"A362621",
"A362622",
"A362980",
"A363223"
]
| null | Gus Wiseman, May 29 2023 | 2023-06-03T23:56:43 | oeisdata/seq/A363/A363223.seq | f6ba3df5b8b9187d8c13bf126df5e872 |
A363224 | Number of integer compositions of n in which the least part appears more than once. | [
"0",
"1",
"1",
"5",
"8",
"21",
"44",
"94",
"197",
"416",
"857",
"1766",
"3621",
"7392",
"15032",
"30493",
"61708",
"124646",
"251359",
"506203",
"1018279",
"2046454",
"4109534",
"8246985",
"16540791",
"33160051",
"66451484",
"133122753",
"266612828",
"533839069",
"1068701695",
"2139110054",
"4281063708",
"8566862025"
]
| [
"nonn"
]
| 10 | 1 | 4 | [
"A000009",
"A000041",
"A002865",
"A007690",
"A008284",
"A032020",
"A067029",
"A071178",
"A097979",
"A105039",
"A117989",
"A238341",
"A238342",
"A240085",
"A241862",
"A243737",
"A261982",
"A362607",
"A362608",
"A362609",
"A362610",
"A363224",
"A363262"
]
| null | Gus Wiseman, Jun 04 2023 | 2024-07-06T21:09:59 | oeisdata/seq/A363/A363224.seq | 88576e5ee3be7a63f5f4f760f8eec06d |
A363225 | Number of integer partitions of n containing three parts (a,b,c) (repeats allowed) such that a + b = c. A variation of sum-full partitions. | [
"0",
"0",
"0",
"1",
"1",
"2",
"4",
"5",
"9",
"14",
"21",
"29",
"43",
"58",
"81",
"109",
"148",
"195",
"263",
"339",
"445",
"574",
"744",
"942",
"1209",
"1515",
"1923",
"2399",
"3005",
"3721",
"4629",
"5693",
"7024",
"8589",
"10530",
"12804",
"15596",
"18876",
"22870",
"27538",
"33204",
"39816",
"47766",
"57061",
"68161",
"81099",
"96510",
"114434",
"135634"
]
| [
"nonn"
]
| 18 | 0 | 6 | [
"A000009",
"A000041",
"A002865",
"A007865",
"A008284",
"A008289",
"A025065",
"A026905",
"A085489",
"A088809",
"A093971",
"A108917",
"A236912",
"A237113",
"A237667",
"A237668",
"A237984",
"A320340",
"A323092",
"A326083",
"A363225",
"A363226",
"A363260",
"A364345",
"A364346",
"A364347",
"A364348",
"A364350"
]
| null | Gus Wiseman, Jul 19 2023 | 2024-03-23T22:12:51 | oeisdata/seq/A363/A363225.seq | 600b6babe86352bd47d05b6d82a97fa2 |
A363226 | Number of strict integer partitions of n containing some three possibly equal parts (a,b,c) such that a + b = c. A variation of sum-full strict partitions. | [
"0",
"0",
"0",
"1",
"0",
"0",
"2",
"1",
"2",
"3",
"5",
"4",
"6",
"7",
"11",
"11",
"16",
"18",
"26",
"29",
"34",
"42",
"51",
"62",
"72",
"84",
"101",
"119",
"142",
"166",
"191",
"226",
"262",
"300",
"354",
"405",
"467",
"540",
"623",
"705",
"807",
"927",
"1060",
"1206",
"1369",
"1551",
"1760",
"1998",
"2248",
"2556",
"2861",
"3236",
"3628",
"4100",
"4587",
"5152",
"5756"
]
| [
"nonn"
]
| 18 | 0 | 7 | [
"A000009",
"A000041",
"A002865",
"A007865",
"A008284",
"A008289",
"A025065",
"A026905",
"A085489",
"A093971",
"A108917",
"A236912",
"A237113",
"A237667",
"A237668",
"A240861",
"A275972",
"A320340",
"A320347",
"A323092",
"A326083",
"A363225",
"A363226",
"A364345",
"A364346",
"A364347",
"A364348"
]
| null | Gus Wiseman, Jul 19 2023 | 2023-10-18T04:44:04 | oeisdata/seq/A363/A363226.seq | e6b4e751049128fcd1f02b720e6eebdc |
A363227 | Positive integers m such that every k with 1 <= k <= m is a linear combination of distinct divisors of m with coefficients +1 or -1. | [
"1",
"2",
"3",
"4",
"6",
"8",
"9",
"10",
"12",
"14",
"15",
"16",
"18",
"20",
"21",
"24",
"27",
"28",
"30",
"32",
"36",
"40",
"42",
"44",
"45",
"48",
"50",
"52",
"54",
"56",
"60",
"63",
"64",
"66",
"70",
"72",
"75",
"78",
"80",
"81",
"84",
"88",
"90",
"96",
"98",
"99",
"100",
"102",
"104",
"105",
"108",
"110",
"112",
"114",
"117",
"120",
"126",
"128",
"130",
"132",
"135",
"136",
"138",
"140",
"144",
"147",
"150"
]
| [
"nonn"
]
| 60 | 1 | 2 | [
"A005153",
"A363227"
]
| null | Guy Ziv, May 21 2023 | 2023-11-12T13:04:08 | oeisdata/seq/A363/A363227.seq | 63567fbb63dc11446c195c2f3e44cd89 |
A363228 | Exponent of 4 in 9^n - 1. | [
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"4",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"4",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"4",
"1",
"2",
"1",
"2"
]
| [
"nonn",
"easy"
]
| 42 | 1 | 2 | [
"A007814",
"A024101",
"A090739",
"A147648",
"A235127",
"A244415",
"A363228"
]
| null | Ruud H.G. van Tol, May 21 2023 | 2025-06-28T12:26:09 | oeisdata/seq/A363/A363228.seq | 551e0000e912831a718e828bffc9e208 |
A363229 | Decimal expansion of e^(-2*LambertW(-log(2)/4)). | [
"1",
"5",
"3",
"6",
"6",
"7",
"6",
"9",
"0",
"7",
"8",
"0",
"1",
"7",
"5",
"8",
"3",
"3",
"4",
"6",
"1",
"2",
"4",
"7",
"5",
"0",
"3",
"0",
"9",
"0",
"5",
"0",
"3",
"7",
"8",
"3",
"1",
"7",
"9",
"8",
"3",
"6",
"1",
"0",
"5",
"6",
"6",
"0",
"9",
"0",
"3",
"8",
"8",
"1",
"2",
"0",
"7",
"6",
"8",
"3",
"4",
"8",
"5",
"6",
"5",
"8",
"9",
"1",
"9",
"8",
"5",
"9",
"4",
"4",
"7",
"8",
"4",
"7",
"5",
"5",
"7",
"5",
"8",
"7",
"1",
"7",
"1",
"0",
"5",
"5",
"7",
"1",
"4",
"6",
"9",
"8",
"2",
"3",
"7"
]
| [
"nonn",
"cons"
]
| 34 | 1 | 2 | [
"A073084",
"A104750",
"A363229"
]
| null | Thomas Scheuerle, May 22 2023 | 2023-05-23T08:16:27 | oeisdata/seq/A363/A363229.seq | 1ca689ee07c3c9250f37ef2f30956cf4 |
A363230 | Number of partitions of n with rank 3 or higher (the rank of a partition is the largest part minus the number of parts). | [
"0",
"0",
"0",
"1",
"1",
"2",
"3",
"5",
"7",
"11",
"14",
"21",
"28",
"39",
"51",
"70",
"90",
"120",
"154",
"201",
"256",
"330",
"415",
"529",
"662",
"833",
"1035",
"1293",
"1595",
"1976",
"2425",
"2982",
"3640",
"4449",
"5401",
"6565",
"7935",
"9592",
"11543",
"13891",
"16645",
"19943",
"23808",
"28408",
"33792",
"40172",
"47619",
"56413",
"66661",
"78708",
"92724",
"109149",
"128213",
"150486",
"176293"
]
| [
"nonn"
]
| 26 | 1 | 6 | [
"A000041",
"A064173",
"A064174",
"A101200",
"A115067",
"A123975",
"A363230",
"A363231"
]
| null | Seiichi Manyama, May 22 2023 | 2023-05-26T09:54:24 | oeisdata/seq/A363/A363230.seq | 8aeea0e63fc11301293258bf7ed68f7f |
A363231 | Number of partitions of n with rank 4 or higher (the rank of a partition is the largest part minus the number of parts). | [
"0",
"0",
"0",
"0",
"1",
"1",
"2",
"3",
"5",
"7",
"11",
"15",
"21",
"29",
"40",
"53",
"72",
"94",
"124",
"161",
"209",
"267",
"343",
"435",
"551",
"693",
"870",
"1084",
"1351",
"1672",
"2066",
"2542",
"3121",
"3815",
"4658",
"5664",
"6875",
"8319",
"10049",
"12102",
"14553",
"17452",
"20894",
"24959",
"29766",
"35420",
"42089",
"49911",
"59100",
"69856",
"82452",
"97152",
"114324",
"134315"
]
| [
"nonn"
]
| 31 | 1 | 7 | [
"A000041",
"A064173",
"A064174",
"A123975",
"A140090",
"A363213",
"A363230",
"A363231"
]
| null | Seiichi Manyama, May 22 2023 | 2024-07-29T12:20:19 | oeisdata/seq/A363/A363231.seq | 1735f6148ba66fd96b69772c8afe56a1 |
A363232 | Triangular array read by rows. T(n,k) is the number of idempotent Boolean relation matrices with rank k, n >= 0, 0 <= k <= n. | [
"1",
"1",
"1",
"1",
"7",
"3",
"1",
"37",
"66",
"19",
"1",
"175",
"975",
"990",
"219",
"1",
"781",
"12090",
"32575",
"23345",
"4231",
"1",
"3367",
"135903",
"866550",
"1514610",
"814903",
"130023"
]
| [
"nonn",
"tabl",
"more"
]
| 12 | 0 | 5 | [
"A001035",
"A005061",
"A121337",
"A363232"
]
| null | Geoffrey Critzer, May 22 2023 | 2023-05-23T08:16:06 | oeisdata/seq/A363/A363232.seq | 5996e136ed8e9217dee8bcab825adcd2 |
A363233 | Number of partitions of n with rank a multiple of 4. | [
"1",
"0",
"1",
"1",
"3",
"1",
"5",
"4",
"10",
"8",
"16",
"17",
"29",
"29",
"48",
"53",
"81",
"89",
"130",
"149",
"208",
"238",
"325",
"381",
"506",
"592",
"770",
"910",
"1165",
"1374",
"1738",
"2057",
"2571",
"3038",
"3761",
"4451",
"5461",
"6447",
"7855",
"9270",
"11219",
"13214",
"15899",
"18703",
"22386",
"26276",
"31306",
"36691",
"43525",
"50902",
"60149",
"70221",
"82679",
"96325"
]
| [
"nonn"
]
| 22 | 1 | 5 | [
"A000041",
"A328988",
"A340601",
"A363233",
"A363237",
"A363238",
"A363239"
]
| null | Seiichi Manyama, May 23 2023 | 2023-05-23T10:46:54 | oeisdata/seq/A363/A363233.seq | c41a736d45eab85c7dd88f6811cf8cfe |
A363234 | Least number divisible by the first n primes whose factorization into maximal prime powers, if ordered by increasing prime divisor, then has these prime power factors in decreasing order. | [
"1",
"2",
"12",
"720",
"151200",
"4191264000",
"251727315840000",
"1542111744113740800000",
"10769764221549079560253440000000",
"12109394351419848024974600399142912000000000",
"78344066654781231654807043124290195568885760000000000",
"188552692884723759943358058475004257579791386442930585600000000000"
]
| [
"nonn",
"easy"
]
| 29 | 0 | 2 | [
"A002110",
"A067255",
"A347284",
"A347355",
"A363063",
"A363098",
"A363234"
]
| null | Michael De Vlieger and David A. Corneth, May 22 2023 | 2023-06-05T17:29:00 | oeisdata/seq/A363/A363234.seq | 861ff382c82acb0af9d5d2eabd034242 |
A363235 | a(0) = 1; let e be the largest multiplicity such that p^e | a(n); for n>0, a(n) = Sum_{j=1..k} 2^(e(j)-1) where k is the index of the greatest power factor p(k)^e(k) such that p(k-1)^e(k-1) > p(k)^(e(k)+1). | [
"0",
"1",
"2",
"3",
"4",
"5",
"8",
"9",
"10",
"11",
"16",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"32",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"64",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"72",
"73",
"74",
"75",
"128",
"129",
"130",
"131",
"132",
"133",
"134",
"135",
"136",
"137",
"138",
"139",
"144",
"145",
"146",
"147",
"148",
"149",
"150",
"151",
"256",
"257",
"258",
"259",
"260",
"261",
"262",
"263",
"264",
"265",
"266",
"267"
]
| [
"nonn"
]
| 5 | 0 | 3 | [
"A000079",
"A067255",
"A272011",
"A347284",
"A363063",
"A363235",
"A363250"
]
| null | Michael De Vlieger, Jun 09 2023 | 2023-06-11T12:29:23 | oeisdata/seq/A363/A363235.seq | 2bc7ea79b39e5a3c7508e55a0b43f344 |
A363236 | Number of permutations p of [n] such that each element in p has at least one neighbor with opposite parity. | [
"1",
"0",
"2",
"2",
"16",
"36",
"288",
"1152",
"10368",
"57600",
"604800",
"4320000",
"51840000",
"453600000",
"6147187200",
"63605606400",
"962415820800",
"11500218777600",
"192255565824000",
"2605984690176000",
"47721518530560000",
"723526168780800000",
"14407079038894080000",
"241602987041095680000"
]
| [
"nonn"
]
| 19 | 0 | 3 | [
"A001622",
"A092186",
"A363180",
"A363181",
"A363236"
]
| null | Alois P. Heinz, May 22 2023 | 2023-05-26T08:36:41 | oeisdata/seq/A363/A363236.seq | c8a5dd2df2a43506984a8ef6d2bbea42 |
A363237 | Number of partitions of n with rank a multiple of 5. | [
"1",
"0",
"1",
"1",
"1",
"3",
"3",
"4",
"6",
"8",
"12",
"15",
"21",
"27",
"34",
"47",
"59",
"77",
"98",
"125",
"160",
"200",
"251",
"315",
"390",
"488",
"602",
"744",
"913",
"1120",
"1370",
"1669",
"2029",
"2462",
"2975",
"3597",
"4327",
"5203",
"6237",
"7466",
"8919",
"10634",
"12653",
"15035",
"17824",
"21114",
"24950",
"29455",
"34705",
"40844",
"47991",
"56317",
"65987",
"77231",
"90252"
]
| [
"nonn"
]
| 10 | 1 | 6 | [
"A000041",
"A328988",
"A340601",
"A363233",
"A363237",
"A363238",
"A363239"
]
| null | Seiichi Manyama, May 23 2023 | 2023-05-23T10:46:58 | oeisdata/seq/A363/A363237.seq | 3dd6415e73aae830c3bfae1110b8fc03 |
A363238 | Number of partitions of n with rank a multiple of 6. | [
"1",
"0",
"1",
"1",
"1",
"1",
"5",
"2",
"6",
"6",
"10",
"11",
"21",
"19",
"32",
"37",
"51",
"59",
"90",
"97",
"138",
"162",
"215",
"253",
"340",
"392",
"514",
"610",
"771",
"916",
"1166",
"1367",
"1711",
"2032",
"2503",
"2965",
"3647",
"4293",
"5237",
"6188",
"7469",
"8808",
"10613",
"12459",
"14920",
"17530",
"20862",
"24457",
"29029",
"33924",
"40099",
"46829",
"55101",
"64215",
"75386"
]
| [
"nonn"
]
| 10 | 1 | 7 | [
"A000041",
"A328988",
"A340601",
"A363233",
"A363237",
"A363238",
"A363239"
]
| null | Seiichi Manyama, May 23 2023 | 2023-05-23T10:46:48 | oeisdata/seq/A363/A363238.seq | 4f12709448b84e0b5a65ec43c6565763 |
A363239 | Number of partitions of n with rank a multiple of 7. | [
"1",
"0",
"1",
"1",
"1",
"1",
"3",
"4",
"4",
"6",
"8",
"11",
"15",
"19",
"26",
"33",
"43",
"55",
"70",
"89",
"114",
"144",
"179",
"225",
"280",
"348",
"430",
"532",
"653",
"800",
"978",
"1193",
"1449",
"1758",
"2127",
"2569",
"3091",
"3717",
"4455",
"5334",
"6369",
"7596",
"9039",
"10739",
"12734",
"15080",
"17822",
"21039",
"24791",
"29176",
"34277",
"40227",
"47133",
"55165",
"64468"
]
| [
"nonn"
]
| 10 | 1 | 7 | [
"A000041",
"A328988",
"A340601",
"A363233",
"A363237",
"A363238",
"A363239"
]
| null | Seiichi Manyama, May 23 2023 | 2023-05-23T10:46:43 | oeisdata/seq/A363/A363239.seq | 4d74ea929af4762126125e0040b6915b |
A363240 | Number of distinct resistances that can be produced from a circuit that is a 2-connected loopless multigraph with n edges and each edge having a unit resistor. | [
"1",
"2",
"5",
"12",
"32",
"88",
"260",
"819",
"2680",
"8642",
"27976",
"88946",
"281541",
"893028",
"2841344",
"9092174",
"29176634",
"93854841",
"302611365"
]
| [
"nonn",
"more"
]
| 22 | 2 | 2 | [
"A010357",
"A337517",
"A363240"
]
| null | Zhao Hui Du, May 23 2023 | 2023-07-11T08:57:33 | oeisdata/seq/A363/A363240.seq | 305a07be74e4ea51c0b8ffa8e57eedc0 |
A363241 | Number of partitions of n with prime rank. | [
"0",
"0",
"1",
"1",
"1",
"3",
"3",
"6",
"6",
"10",
"12",
"19",
"22",
"33",
"38",
"54",
"65",
"91",
"106",
"145",
"173",
"228",
"274",
"356",
"424",
"545",
"652",
"823",
"986",
"1232",
"1468",
"1822",
"2172",
"2665",
"3173",
"3869",
"4590",
"5568",
"6591",
"7938",
"9386",
"11249",
"13256",
"15821",
"18608",
"22100",
"25941",
"30695",
"35933",
"42373",
"49501",
"58160",
"67814",
"79434",
"92396",
"107932"
]
| [
"nonn",
"easy"
]
| 23 | 1 | 6 | [
"A000041",
"A010051",
"A037032",
"A063995",
"A363241"
]
| null | Seiichi Manyama, May 23 2023 | 2024-12-20T11:27:25 | oeisdata/seq/A363/A363241.seq | 95afda65a3a5ddf46b20bcb04083e3d5 |
A363242 | Numbers whose primorial-base representation contains only odd digits. | [
"1",
"3",
"9",
"21",
"39",
"51",
"99",
"111",
"159",
"171",
"249",
"261",
"309",
"321",
"369",
"381",
"669",
"681",
"729",
"741",
"789",
"801",
"1089",
"1101",
"1149",
"1161",
"1209",
"1221",
"1509",
"1521",
"1569",
"1581",
"1629",
"1641",
"1929",
"1941",
"1989",
"2001",
"2049",
"2061",
"2559",
"2571",
"2619",
"2631",
"2679",
"2691",
"2979",
"2991",
"3039"
]
| [
"nonn",
"base"
]
| 10 | 1 | 2 | [
"A002110",
"A003462",
"A014261",
"A032911",
"A032912",
"A033032",
"A033033",
"A033034",
"A033035",
"A033036",
"A033037",
"A033038",
"A033039",
"A033040",
"A033041",
"A049345",
"A126646",
"A143293",
"A328849",
"A351894",
"A363242"
]
| null | Amiram Eldar, May 23 2023 | 2023-05-25T07:27:36 | oeisdata/seq/A363/A363242.seq | 10c6ba5bcc8f15cabe14e9b279be6ec5 |
A363243 | Numbers with an equal number of odd and even digits in their primorial-base representation. | [
"2",
"5",
"31",
"32",
"35",
"36",
"40",
"43",
"44",
"47",
"48",
"52",
"55",
"56",
"59",
"63",
"67",
"68",
"71",
"75",
"79",
"80",
"83",
"87",
"91",
"92",
"95",
"96",
"100",
"103",
"104",
"107",
"108",
"112",
"115",
"116",
"119",
"123",
"127",
"128",
"131",
"135",
"139",
"140",
"143",
"147",
"151",
"152",
"155",
"156",
"160",
"163",
"164",
"167",
"168",
"172",
"175",
"176",
"179"
]
| [
"nonn",
"base"
]
| 8 | 1 | 1 | [
"A002110",
"A031443",
"A049345",
"A227870",
"A351895",
"A363243"
]
| null | Amiram Eldar, May 23 2023 | 2023-05-25T07:27:48 | oeisdata/seq/A363/A363243.seq | 43e015ccf31789dd757058fe8ea86d8c |
A363244 | Numbers that in primorial-base representation have digits with an alternating parity. | [
"0",
"1",
"2",
"5",
"7",
"11",
"14",
"19",
"23",
"26",
"32",
"44",
"56",
"67",
"71",
"79",
"83",
"92",
"104",
"116",
"127",
"131",
"139",
"143",
"152",
"164",
"176",
"187",
"191",
"199",
"203",
"217",
"221",
"229",
"233",
"277",
"281",
"289",
"293",
"337",
"341",
"349",
"353",
"397",
"401",
"409",
"413",
"452",
"464",
"476",
"512",
"524",
"536",
"572",
"584",
"596",
"637"
]
| [
"nonn",
"base"
]
| 11 | 1 | 3 | [
"A000975",
"A002110",
"A030141",
"A033068",
"A049345",
"A179970",
"A351897",
"A363244"
]
| null | Amiram Eldar, May 23 2023 | 2025-04-22T21:55:33 | oeisdata/seq/A363/A363244.seq | b067167d9fd80ddf95f807681c19aa39 |
A363245 | Lexicographically first sequence of positive integers such that all terms are pairwise coprime and no subset sum is a power of 2. | [
"3",
"7",
"10",
"11",
"17",
"31",
"41",
"71",
"169",
"199",
"263",
"337",
"367",
"1553",
"2129",
"2287",
"2297",
"4351",
"10433",
"16391",
"16433",
"34829",
"65543",
"69557",
"165887",
"262151",
"358481",
"817153",
"952319",
"1048583",
"3704737",
"3932167",
"4518071",
"12582919",
"17305417",
"17367019",
"50069497",
"50593799",
"87228517"
]
| [
"nonn"
]
| 34 | 1 | 1 | [
"A353889",
"A363245"
]
| null | Julian Zbigniew Kuryllowicz-Kazmierczak, May 23 2023 | 2023-06-14T18:41:49 | oeisdata/seq/A363/A363245.seq | 7b2b7655fd4674914e804d6466a5c116 |
A363246 | Base-10 palindromes whose arithmetic derivative is also a base-10 palindrome. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"9",
"11",
"101",
"121",
"131",
"151",
"181",
"191",
"222",
"313",
"353",
"373",
"383",
"717",
"727",
"757",
"787",
"797",
"919",
"929",
"989",
"1331",
"10201",
"10301",
"10501",
"10601",
"11311",
"11411",
"12421",
"12721",
"12821",
"13231",
"13331",
"13831",
"13931",
"14341",
"14741",
"15251",
"15451",
"15551",
"15751",
"15851",
"16061",
"16361",
"16561"
]
| [
"nonn",
"base"
]
| 8 | 1 | 3 | [
"A002113",
"A002385",
"A003415",
"A363246"
]
| null | Robert Israel, May 23 2023 | 2023-05-25T07:52:03 | oeisdata/seq/A363/A363246.seq | fc1845ef19588dda068073211d0a5dea |
A363247 | a(0) = 0. a(n) = the smallest nonnegative integer, excluding a(n-1), not occurring in all occurrences of a(n-1)'s eight neighbors thus far in a square spiral. | [
"0",
"1",
"2",
"3",
"4",
"1",
"5",
"2",
"4",
"5",
"3",
"6",
"0",
"7",
"1",
"8",
"0",
"9",
"2",
"8",
"6",
"4",
"7",
"8",
"10",
"0",
"11",
"1",
"10",
"2",
"11",
"4",
"12",
"2",
"13",
"3",
"9",
"5",
"12",
"3",
"14",
"0",
"15",
"1",
"14",
"5",
"13",
"4",
"15",
"2",
"16",
"1",
"17",
"0",
"18",
"1",
"19",
"0",
"20",
"1",
"21",
"0",
"22",
"1",
"23",
"0",
"24",
"1",
"25",
"0",
"26",
"1",
"27",
"0",
"28",
"2",
"17",
"3"
]
| [
"nonn"
]
| 40 | 0 | 3 | [
"A275609",
"A358048",
"A363247"
]
| null | Gavin Lupo, May 24 2023 | 2023-05-31T22:35:54 | oeisdata/seq/A363/A363247.seq | e69126990dd087d23a9df1fa71986074 |
A363248 | Nonprime base-10 palindromes whose arithmetic derivative is a base-10 palindrome. | [
"0",
"1",
"4",
"6",
"9",
"121",
"222",
"717",
"989",
"1331",
"10201",
"13231",
"15251",
"15751",
"15851",
"18281",
"19291",
"28882",
"28982",
"31613",
"34043",
"35653",
"37073",
"37673",
"37873",
"38383",
"38683",
"40304",
"41814",
"50405",
"97079",
"98789",
"99899",
"536635",
"913319",
"980089",
"1030301",
"1115111",
"1226221",
"1336331",
"1794971",
"2630362",
"2882882",
"3303033"
]
| [
"nonn",
"base"
]
| 6 | 1 | 3 | [
"A002113",
"A002385",
"A003415",
"A363246",
"A363248"
]
| null | Robert Israel, May 23 2023 | 2023-05-25T07:52:16 | oeisdata/seq/A363/A363248.seq | 23d84fbddb02d724b8c79ff4acbf7632 |
A363249 | Leading digit of 9^n. | [
"1",
"9",
"8",
"7",
"6",
"5",
"5",
"4",
"4",
"3",
"3",
"3",
"2",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"9",
"8",
"7",
"7",
"6",
"5",
"5",
"4",
"4",
"3",
"3",
"3",
"2",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"9",
"8",
"7",
"7",
"6",
"5",
"5",
"4",
"4",
"3",
"3",
"3",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"9",
"8",
"7",
"6",
"6",
"5",
"5",
"4",
"4",
"3",
"3",
"2",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"9",
"8",
"7",
"6",
"6",
"5",
"4",
"4",
"4",
"3",
"3",
"2",
"2"
]
| [
"nonn",
"base",
"easy"
]
| 52 | 0 | 2 | [
"A000030",
"A001019",
"A008570",
"A008952",
"A060956",
"A111395",
"A362871",
"A363093",
"A363249",
"A364185"
]
| null | Seiichi Manyama, Jul 15 2023 | 2024-12-15T00:10:35 | oeisdata/seq/A363/A363249.seq | 826e0ce7806ede1d412eed965f575d91 |
A363250 | Numbers in A363063 arranged in lexicographic order according to ordered prime signature (i.e., multiplicities of prime power factors p^k, written in order of p). | [
"1",
"2",
"4",
"12",
"8",
"24",
"16",
"48",
"144",
"720",
"32",
"96",
"288",
"1440",
"864",
"4320",
"21600",
"151200",
"64",
"192",
"576",
"2880",
"1728",
"8640",
"43200",
"302400",
"128",
"384",
"1152",
"5760",
"3456",
"17280",
"86400",
"604800",
"10368",
"51840",
"259200",
"1814400",
"256",
"768",
"2304",
"11520",
"6912",
"34560",
"172800",
"1209600",
"20736",
"103680",
"518400",
"3628800",
"62208"
]
| [
"nonn",
"tabf"
]
| 26 | 0 | 2 | [
"A000079",
"A025487",
"A055932",
"A067255",
"A087980",
"A124010",
"A347284",
"A362227",
"A363063",
"A363250"
]
| null | Michael De Vlieger, May 23 2023 | 2025-06-21T00:44:52 | oeisdata/seq/A363/A363250.seq | 170a6b7e5161d23062cd9fc33f14ac38 |
A363251 | Number of nonisomorphic open quipus with n nodes. | [
"1",
"1",
"1",
"1",
"2",
"2",
"4",
"6",
"11",
"18",
"36",
"64",
"127",
"241",
"480",
"935",
"1868",
"3688",
"7373",
"14655",
"29305",
"58432",
"116859",
"233367",
"466727",
"932761",
"1865513",
"3729648",
"7459286",
"14915826",
"29831640",
"59657802",
"119315589",
"238620236",
"477240456",
"954459044",
"1908918069",
"3817792423"
]
| [
"nonn",
"easy"
]
| 34 | 0 | 5 | [
"A000672",
"A130131",
"A363251"
]
| null | Didrik Fosse, May 31 2023 | 2025-01-13T06:34:35 | oeisdata/seq/A363/A363251.seq | 45a09a4673ab2c561e20fbeb20427db5 |
A363252 | a(n) = gcd(A000041(n), A000009(n)). | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"5",
"2",
"2",
"2",
"4",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"4",
"1",
"1",
"1",
"2",
"3",
"2",
"2",
"1",
"4",
"2",
"3",
"7",
"2",
"3",
"1",
"1",
"1",
"1",
"21",
"21",
"2",
"1",
"1",
"2",
"6",
"14",
"3",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"3",
"4",
"4",
"17",
"1",
"2",
"1",
"2",
"2",
"4",
"1",
"3",
"5",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"2",
"4",
"1",
"1",
"1",
"2",
"11",
"2"
]
| [
"nonn"
]
| 11 | 0 | 8 | [
"A000009",
"A000041",
"A051177",
"A056848",
"A093952",
"A304991",
"A363252"
]
| null | Vaclav Kotesovec, May 23 2023, inspired by Zhi-Wei Sun | 2023-05-24T03:55:08 | oeisdata/seq/A363/A363252.seq | 0365e52c53a040817f7c6f706783ed19 |
A363253 | a(n) is the smallest n-gonal number which can be represented as the sum of distinct nonzero n-gonal numbers in exactly n ways, or -1 if no such number exists. | [
"28",
"121",
"210"
]
| [
"nonn",
"bref",
"more",
"hard"
]
| 8 | 3 | 1 | [
"A057145",
"A350207",
"A350405",
"A350423",
"A363253"
]
| null | Ilya Gutkovskiy, May 23 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A363/A363253.seq | 70f82408f68bae0bb58247c052a00d1a |
A363254 | Product_{n>=1} (1 + a(n)*x^n) = 1 + 1!!*x + 3!!*x^2 + 5!!*x^3 + 7!!*x^4 + ... | [
"1",
"3",
"12",
"93",
"816",
"9264",
"122028",
"1863849",
"32001504",
"614224272",
"12989299596",
"300599511744",
"7550646317520",
"204694926767040",
"5955892801274796",
"185160666502244433",
"6125200081143892800",
"214838236392631067424",
"7963817560398871790604",
"311101474513327693885056"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A001147",
"A158094",
"A305868",
"A305870",
"A363254",
"A363255"
]
| null | Ilya Gutkovskiy, May 23 2023 | 2023-05-24T07:33:10 | oeisdata/seq/A363/A363254.seq | 1f5d44fffd26600b611d5d3a8a301cff |
A363255 | Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + 1!!*x + 3!!*x^2 + 5!!*x^3 + 7!!*x^4 + ... | [
"1",
"2",
"12",
"86",
"816",
"9126",
"122028",
"1855802",
"32001504",
"613558458",
"12989299596",
"300515004558",
"7550646317520",
"204680035934550",
"5955892801274796",
"185157207502788074",
"6125200081143892800",
"214837212308039658666",
"7963817560398871790604",
"311101097650387613661510"
]
| [
"nonn"
]
| 5 | 1 | 2 | [
"A001147",
"A305868",
"A305870",
"A316084",
"A363254",
"A363255"
]
| null | Ilya Gutkovskiy, May 23 2023 | 2023-05-24T07:33:17 | oeisdata/seq/A363/A363255.seq | 327c80558cad81012f20ffaaf5452a05 |
A363256 | Number of length n strings on the alphabet {0,1,2,3} with digit sum at most 4. | [
"1",
"4",
"13",
"32",
"66",
"121",
"204",
"323",
"487",
"706",
"991",
"1354",
"1808",
"2367",
"3046",
"3861",
"4829",
"5968",
"7297",
"8836",
"10606",
"12629",
"14928",
"17527",
"20451",
"23726",
"27379",
"31438",
"35932",
"40891",
"46346",
"52329",
"58873",
"66012",
"73781",
"82216",
"91354",
"101233",
"111892",
"123371",
"135711"
]
| [
"nonn",
"easy"
]
| 15 | 0 | 2 | [
"A005718",
"A105163",
"A227259",
"A363256"
]
| null | Daniel T. Martin, May 23 2023 | 2023-07-10T21:50:34 | oeisdata/seq/A363/A363256.seq | ee24bfa1d4a380471d47f2a36116a436 |
A363257 | a(n) = floor( ((a(n-1) + 1) / 2)^2 ) + 1 for n >= 1, with a(0) = 0. | [
"0",
"1",
"2",
"3",
"5",
"10",
"31",
"257",
"16642",
"69247363",
"1198799355237125",
"359279973529237254190922184970",
"32270524844792355518177347536627638351478874995525184567711"
]
| [
"nonn"
]
| 22 | 0 | 3 | [
"A003095",
"A006894",
"A014980",
"A033638",
"A363257"
]
| null | Harry Richman, May 23 2023 | 2025-01-09T10:00:46 | oeisdata/seq/A363/A363257.seq | e37d0f34efa39505112308c188c39252 |
A363258 | Expansion of Sum_{k>0} k * x^(2*k-1) / (1 - x^(4*k-3)). | [
"1",
"1",
"3",
"1",
"4",
"1",
"5",
"3",
"6",
"1",
"7",
"1",
"10",
"4",
"9",
"1",
"10",
"3",
"11",
"5",
"12",
"1",
"18",
"1",
"14",
"6",
"15",
"3",
"16",
"1",
"17",
"10",
"24",
"1",
"19",
"1",
"20",
"10",
"21",
"1",
"25",
"1",
"30",
"9",
"24",
"5",
"25",
"3",
"26",
"13",
"27",
"1",
"36",
"1",
"29",
"11",
"30",
"3",
"38",
"6",
"32",
"12",
"42",
"1",
"34",
"1",
"35",
"18",
"36",
"1",
"37",
"5",
"48",
"20",
"39",
"1",
"48",
"3",
"41",
"15",
"42",
"1",
"54",
"1",
"48",
"19",
"45",
"10"
]
| [
"nonn"
]
| 16 | 1 | 3 | [
"A363258",
"A363316",
"A364082",
"A364083"
]
| null | Seiichi Manyama, Jul 08 2023 | 2023-07-08T08:05:18 | oeisdata/seq/A363/A363258.seq | 6f941a3bd684acebe4b549f3f9a166d1 |
A363259 | Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(4*k-1)). | [
"0",
"1",
"0",
"2",
"1",
"3",
"0",
"5",
"0",
"5",
"3",
"6",
"0",
"8",
"0",
"8",
"4",
"11",
"0",
"11",
"0",
"11",
"5",
"12",
"2",
"14",
"0",
"17",
"6",
"15",
"0",
"19",
"0",
"17",
"7",
"18",
"0",
"24",
"5",
"20",
"8",
"21",
"0",
"23",
"0",
"25",
"9",
"29",
"0",
"29",
"0",
"26",
"16",
"27",
"0",
"29",
"0",
"35",
"11",
"32",
"3",
"32",
"0",
"32",
"12",
"33",
"7",
"46",
"0",
"35",
"13",
"39",
"0",
"40",
"0",
"38",
"14",
"47",
"0",
"41",
"8",
"41",
"22",
"42",
"0",
"49",
"0"
]
| [
"nonn"
]
| 14 | 1 | 4 | [
"A363259",
"A363392",
"A364084",
"A364085"
]
| null | Seiichi Manyama, Jul 08 2023 | 2023-07-08T08:05:14 | oeisdata/seq/A363/A363259.seq | 7c1347bbb3520277a62b42e6df1bfc95 |
A363260 | Number of integer partitions of n with parts disjoint from first differences of parts, meaning no part is the difference of two consecutive parts. | [
"1",
"1",
"2",
"2",
"4",
"5",
"7",
"10",
"13",
"17",
"21",
"28",
"35",
"46",
"57",
"70",
"87",
"110",
"130",
"165",
"198",
"238",
"285",
"349",
"410",
"498",
"583",
"702",
"819",
"983",
"1136",
"1353",
"1570",
"1852",
"2137",
"2520",
"2898",
"3390",
"3891",
"4540",
"5191",
"6028",
"6889",
"7951",
"9082",
"10450",
"11884",
"13650",
"15508",
"17728",
"20113"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A000009",
"A000041",
"A002865",
"A008284",
"A008289",
"A025065",
"A108917",
"A229816",
"A236912",
"A237113",
"A237667",
"A240861",
"A320340",
"A320347",
"A323092",
"A325325",
"A326083",
"A363225",
"A363260",
"A364345",
"A364347",
"A364463",
"A364464"
]
| null | Gus Wiseman, Jul 19 2023 | 2023-09-26T13:39:33 | oeisdata/seq/A363/A363260.seq | a94971366e569ce2199dc4d108708c93 |
A363261 | The partial sums of the prime indices of n include half the sum of all prime indices of n. | [
"4",
"9",
"12",
"16",
"25",
"30",
"40",
"48",
"49",
"63",
"64",
"70",
"81",
"84",
"108",
"112",
"121",
"144",
"154",
"160",
"165",
"169",
"192",
"198",
"220",
"256",
"264",
"270",
"273",
"286",
"289",
"325",
"351",
"352",
"360",
"361",
"364",
"390",
"442",
"448",
"468",
"480",
"520",
"529",
"561",
"567",
"576",
"595",
"624",
"625",
"640",
"646",
"675",
"714",
"729"
]
| [
"nonn"
]
| 6 | 1 | 1 | [
"A001222",
"A001414",
"A025065",
"A027746",
"A035363",
"A056239",
"A106529",
"A110618",
"A112798",
"A265640",
"A301987",
"A322109",
"A322439",
"A327473",
"A327476",
"A334201",
"A340387",
"A344415",
"A360005",
"A363261"
]
| null | Gus Wiseman, Jun 06 2023 | 2023-06-12T08:42:33 | oeisdata/seq/A363/A363261.seq | d2be264d907b8e3b75f23be07a1fa9c6 |
A363262 | Number of integer compositions of n in which the greatest part appears more than once. | [
"0",
"1",
"1",
"2",
"4",
"9",
"18",
"37",
"73",
"145",
"287",
"570",
"1134",
"2264",
"4526",
"9061",
"18152",
"36374",
"72884",
"146011",
"292416",
"585422",
"1171632",
"2344136",
"4688821",
"9376832",
"18749169",
"37485358",
"74939850",
"149813328",
"299492966",
"598729533",
"1196987066",
"2393137399",
"4784846896",
"9567357951"
]
| [
"nonn"
]
| 7 | 1 | 4 | [
"A000009",
"A000041",
"A002865",
"A007690",
"A008284",
"A032020",
"A067029",
"A071178",
"A097979",
"A105039",
"A117989",
"A238341",
"A238342",
"A240085",
"A243737",
"A261982",
"A362607",
"A362608",
"A362612",
"A362614",
"A363224",
"A363262"
]
| null | Gus Wiseman, Jun 04 2023 | 2023-06-06T08:17:57 | oeisdata/seq/A363/A363262.seq | f486e69eddca9f6d774a4b336996be8b |
A363263 | Number of integer partitions of n covering an initial interval of positive integers with a unique co-mode. | [
"0",
"1",
"1",
"1",
"2",
"3",
"2",
"4",
"4",
"5",
"7",
"10",
"8",
"13",
"13",
"15",
"19",
"25",
"24",
"35",
"35",
"43",
"50",
"61",
"59",
"79",
"83",
"98",
"111",
"137",
"137",
"176",
"187",
"219",
"240",
"284",
"298",
"360",
"385",
"444",
"485",
"568",
"600",
"706",
"763",
"867",
"951",
"1088",
"1168",
"1345",
"1453",
"1641",
"1792",
"2023",
"2179",
"2467",
"2673",
"2988"
]
| [
"nonn"
]
| 5 | 0 | 5 | [
"A000009",
"A000041",
"A002865",
"A008284",
"A025147",
"A087897",
"A096765",
"A097979",
"A105039",
"A117989",
"A243737",
"A362607",
"A362608",
"A362609",
"A362610",
"A362612",
"A362614",
"A362615",
"A363224",
"A363262",
"A363263",
"A363264",
"A363484",
"A363485"
]
| null | Gus Wiseman, Jun 06 2023 | 2023-06-07T08:32:00 | oeisdata/seq/A363/A363263.seq | 0cf16e90a21511ed16e7e79532a59191 |
A363264 | Number of integer partitions of n covering an initial interval of positive integers with a more than one co-mode. | [
"0",
"0",
"0",
"1",
"0",
"0",
"2",
"1",
"2",
"3",
"3",
"2",
"7",
"5",
"9",
"12",
"13",
"13",
"22",
"19",
"29",
"33",
"39",
"43",
"63",
"63",
"82",
"94",
"111",
"119",
"159",
"164",
"203",
"229",
"272",
"301",
"370",
"400",
"479",
"538",
"628",
"692",
"826",
"904",
"1053",
"1181",
"1353",
"1502",
"1742",
"1919",
"2205",
"2456",
"2790",
"3097",
"3539",
"3911",
"4435",
"4929"
]
| [
"nonn"
]
| 5 | 0 | 7 | [
"A000009",
"A000041",
"A002865",
"A008284",
"A067029",
"A071178",
"A087897",
"A096765",
"A097979",
"A105039",
"A117989",
"A243737",
"A275870",
"A362607",
"A362608",
"A362609",
"A362610",
"A362611",
"A362612",
"A362613",
"A362614",
"A362615",
"A363224",
"A363262",
"A363263",
"A363264",
"A363484",
"A363485"
]
| null | Gus Wiseman, Jun 06 2023 | 2023-06-07T08:31:56 | oeisdata/seq/A363/A363264.seq | eee316e9c86e5f0bc186b07aebb015f4 |
A363265 | Number of integer factorizations of n with a unique mode. | [
"0",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"4",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"3",
"2",
"1",
"2",
"2",
"1",
"1",
"1",
"5",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"6",
"2",
"2",
"1",
"2",
"1",
"3",
"1",
"3",
"1",
"1",
"1",
"3",
"1",
"1",
"2",
"7",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"8",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"6",
"4",
"1",
"1",
"3",
"1",
"1",
"1"
]
| [
"nonn"
]
| 10 | 1 | 4 | [
"A001055",
"A008284",
"A045778",
"A074206",
"A089723",
"A240219",
"A316439",
"A326622",
"A333487",
"A335434",
"A339846",
"A339890",
"A347438",
"A356862",
"A362605",
"A362607",
"A362608",
"A362610",
"A362611",
"A362612",
"A362614",
"A363265",
"A363723"
]
| null | Gus Wiseman, Jun 27 2023 | 2023-08-16T11:04:11 | oeisdata/seq/A363/A363265.seq | cc6a72dc8ca5b4ad52fbb18e54883b49 |
A363266 | Maximum product of distinct primes with sum n, or -1 if n is not the sum of distinct primes. | [
"1",
"-1",
"2",
"3",
"-1",
"6",
"-1",
"10",
"15",
"14",
"30",
"11",
"42",
"22",
"70",
"105",
"66",
"210",
"110",
"165",
"154",
"330",
"182",
"462",
"170",
"770",
"1155",
"910",
"2310",
"858",
"2730",
"1430",
"2145",
"2002",
"4290",
"1870",
"6006",
"2618",
"10010",
"15015",
"7854",
"30030",
"13090",
"19635",
"15470",
"39270",
"17290",
"46410",
"24310",
"51870"
]
| [
"sign"
]
| 48 | 0 | 3 | [
"A000586",
"A000792",
"A064502",
"A363266"
]
| null | Zhao Hui Du, May 23 2023 | 2023-05-26T20:12:20 | oeisdata/seq/A363/A363266.seq | 257253bf730510363ffc03acf43be8ba |
A363267 | Squares (A000290) alternating with centered squares (A001844). | [
"1",
"1",
"4",
"5",
"9",
"13",
"16",
"25",
"25",
"41",
"36",
"61",
"49",
"85",
"64",
"113",
"81",
"145",
"100",
"181",
"121",
"221",
"144",
"265",
"169",
"313",
"196",
"365",
"225",
"421",
"256",
"481",
"289",
"545",
"324",
"613",
"361",
"685",
"400",
"761",
"441",
"841",
"484",
"925",
"529",
"1013",
"576",
"1105",
"625",
"1201",
"676",
"1301",
"729",
"1405",
"784"
]
| [
"nonn"
]
| 16 | 1 | 3 | [
"A000290",
"A001844",
"A123596",
"A363267",
"A363268",
"A363269",
"A363282",
"A363319"
]
| null | Clark Kimberling, May 24 2023 | 2023-06-15T06:54:19 | oeisdata/seq/A363/A363267.seq | f5f6cc191d9af4c95105ebd0f32e9bff |
A363268 | Squares (A000290) alternating with 1+squares (A002522). | [
"1",
"1",
"4",
"2",
"9",
"5",
"16",
"10",
"25",
"17",
"36",
"26",
"49",
"37",
"64",
"50",
"81",
"65",
"100",
"82",
"121",
"101",
"144",
"122",
"169",
"145",
"196",
"170",
"225",
"197",
"256",
"226",
"289",
"257",
"324",
"290",
"361",
"325",
"400",
"362",
"441",
"401",
"484",
"442",
"529",
"485",
"576",
"530",
"625",
"577",
"676",
"626",
"729",
"677",
"784",
"730",
"841"
]
| [
"nonn",
"easy"
]
| 10 | 1 | 3 | [
"A000290",
"A002522",
"A123596",
"A363267",
"A363268",
"A363269",
"A363283"
]
| null | Clark Kimberling, May 24 2023 | 2023-06-04T08:55:39 | oeisdata/seq/A363/A363268.seq | 51d2663424b6ee97163c9691ddec8417 |
A363269 | Positive squares (A000290) alternating with positive square pyramidal numbers (A000330). | [
"1",
"1",
"4",
"5",
"9",
"14",
"16",
"30",
"25",
"55",
"36",
"91",
"49",
"140",
"64",
"204",
"81",
"285",
"100",
"385",
"121",
"506",
"144",
"650",
"169",
"819",
"196",
"1015",
"225",
"1240",
"256",
"1496",
"289",
"1785",
"324",
"2109",
"361",
"2470",
"400",
"2870",
"441",
"3311",
"484",
"3795",
"529",
"4324",
"576",
"4900",
"625",
"5525",
"676",
"6201",
"729"
]
| [
"nonn",
"easy"
]
| 26 | 1 | 3 | [
"A000290",
"A000330",
"A123596",
"A363267",
"A363268",
"A363269",
"A363284"
]
| null | Clark Kimberling, May 24 2023 | 2023-07-30T09:56:24 | oeisdata/seq/A363/A363269.seq | fb7dc163d9889e5c0ac00866210236cc |
A363270 | The result, starting from n, of Collatz steps x -> (3x+1)/2 while odd, followed by x -> x/2 while even. | [
"1",
"1",
"1",
"1",
"1",
"3",
"13",
"1",
"7",
"5",
"13",
"3",
"5",
"7",
"5",
"1",
"13",
"9",
"11",
"5",
"1",
"11",
"5",
"3",
"19",
"13",
"31",
"7",
"11",
"15",
"121",
"1",
"25",
"17",
"5",
"9",
"7",
"19",
"67",
"5",
"31",
"21",
"49",
"11",
"17",
"23",
"121",
"3",
"37",
"25",
"29",
"13",
"5",
"27",
"47",
"7",
"43",
"29",
"67",
"15",
"23",
"31",
"91",
"1",
"49",
"33",
"19",
"17",
"13",
"35",
"121",
"9",
"55"
]
| [
"nonn",
"easy"
]
| 35 | 1 | 6 | [
"A000265",
"A075677",
"A085062",
"A160541",
"A363270"
]
| null | Dustin Theriault, May 23 2023 | 2023-07-02T00:02:19 | oeisdata/seq/A363/A363270.seq | 91464ed047254213d51976a5eed4656a |
A363271 | Vertical sum of n in base 10. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"10",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"11",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"12",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"13",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"14",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"15",
"6",
"7",
"8",
"9",
"10",
"11",
"12"
]
| [
"nonn",
"base"
]
| 20 | 1 | 2 | [
"A021085",
"A089400",
"A363271"
]
| null | Simon Plouffe, May 24 2023 | 2023-05-26T08:51:49 | oeisdata/seq/A363/A363271.seq | dcc679474f6f41b4f8ce6035af91f21b |
A363272 | Irregular triangle read by rows: T(n,k) = number of unlabeled binary rooted trees with n leaves, where some child tree has k leaves, 1 <= k <= n/2. | [
"1",
"1",
"1",
"1",
"2",
"1",
"3",
"2",
"1",
"6",
"3",
"2",
"11",
"6",
"3",
"3",
"23",
"11",
"6",
"6",
"46",
"23",
"11",
"12",
"6",
"98",
"46",
"23",
"22",
"18",
"207",
"98",
"46",
"46",
"33",
"21",
"451",
"207",
"98",
"92",
"69",
"66",
"983",
"451",
"207",
"196",
"138",
"138",
"66",
"2179",
"983",
"451",
"414",
"294",
"276",
"253",
"4850",
"2179",
"983",
"902",
"621",
"588",
"506",
"276"
]
| [
"nonn",
"tabf"
]
| 16 | 2 | 5 | [
"A000671",
"A001190",
"A363272",
"A363273"
]
| null | Harry Richman, May 24 2023 | 2024-01-01T19:51:25 | oeisdata/seq/A363/A363272.seq | 729c2d59818f3bc3a000b12df97c82b0 |
A363273 | Irregular triangle read by rows: T(n,k) = number of unlabeled binary rooted trees with n leaves, where both children have at least k leaves, 1 <= k <= n/2. | [
"1",
"1",
"2",
"1",
"3",
"1",
"6",
"3",
"1",
"11",
"5",
"2",
"23",
"12",
"6",
"3",
"46",
"23",
"12",
"6",
"98",
"52",
"29",
"18",
"6",
"207",
"109",
"63",
"40",
"18",
"451",
"244",
"146",
"100",
"54",
"21",
"983",
"532",
"325",
"227",
"135",
"66",
"2179",
"1196",
"745",
"538",
"342",
"204",
"66",
"4850",
"2671",
"1688",
"1237",
"823",
"529",
"253",
"10905",
"6055",
"3876",
"2893",
"1991",
"1370",
"782",
"276"
]
| [
"nonn",
"tabf"
]
| 17 | 2 | 3 | [
"A000671",
"A001190",
"A363272",
"A363273"
]
| null | Harry Richman, May 24 2023 | 2024-01-01T19:46:27 | oeisdata/seq/A363/A363273.seq | 7659e0656a5ea472855ef457a12a548f |
A363274 | a(n) is the smallest prime such that a(1)*a(2)*...*a(n) +/- 1 is prime. | [
"2",
"2",
"2",
"2",
"2",
"3",
"2",
"2",
"2",
"11",
"3",
"3",
"2",
"2",
"5",
"2",
"2",
"3",
"3",
"5",
"2",
"2",
"5",
"2",
"2",
"7",
"3",
"3",
"2",
"2",
"23",
"47",
"2",
"2",
"2",
"29",
"2",
"53",
"13",
"5",
"17",
"29",
"5",
"3",
"3",
"3",
"5",
"17",
"2",
"3",
"3",
"79",
"31",
"11",
"7",
"23",
"2",
"7",
"3",
"7",
"2",
"13",
"5",
"7",
"5",
"7",
"23",
"17",
"23",
"13",
"31",
"29",
"7",
"67",
"47",
"7",
"2",
"23",
"13",
"23",
"23",
"31",
"73",
"13",
"23",
"3",
"17"
]
| [
"nonn"
]
| 32 | 1 | 1 | [
"A036014",
"A236465",
"A363274"
]
| null | Dmitry Kamenetsky, Jul 08 2023 | 2023-07-11T08:56:55 | oeisdata/seq/A363/A363274.seq | e4f392565dde43c0fa46c5d00e6322f9 |
A363275 | Expansion of 1 / Sum_{k>=0} x^(k*(3*k - 2)). | [
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"0",
"1",
"-2",
"3",
"-4",
"5",
"-6",
"7",
"-7",
"6",
"-4",
"1",
"3",
"-9",
"16",
"-24",
"32",
"-39",
"44",
"-46",
"44",
"-35",
"18",
"8",
"-43",
"86",
"-135",
"187",
"-238",
"280",
"-304",
"300",
"-259",
"171",
"-28",
"-174",
"435",
"-746",
"1088",
"-1431",
"1736",
"-1952",
"2017",
"-1864",
"1425",
"-641",
"-527",
"2086",
"-4002"
]
| [
"sign"
]
| 6 | 0 | 11 | [
"A000567",
"A106507",
"A195848",
"A308806",
"A317665",
"A322800",
"A361979",
"A363149",
"A363275"
]
| null | Ilya Gutkovskiy, May 25 2023 | 2023-05-26T08:50:46 | oeisdata/seq/A363/A363275.seq | d82fbd6f176efd0cb4d362acab4341d2 |
A363276 | Number of partitions of n such that 4*(least part) <= greatest part. | [
"0",
"0",
"0",
"0",
"1",
"2",
"4",
"7",
"12",
"19",
"29",
"42",
"61",
"85",
"119",
"161",
"217",
"288",
"380",
"496",
"643",
"826",
"1055",
"1340",
"1695",
"2129",
"2663",
"3316",
"4113",
"5084",
"6260",
"7681",
"9394",
"11456",
"13929",
"16892",
"20428",
"24646",
"29658",
"35618",
"42669",
"51021",
"60872",
"72496",
"86165",
"102239",
"121078",
"143171",
"168995",
"199187",
"234380",
"275414"
]
| [
"nonn"
]
| 13 | 1 | 6 | [
"A237821",
"A237826",
"A363076",
"A363211",
"A363276"
]
| null | Seiichi Manyama, May 27 2023 | 2023-05-27T10:33:05 | oeisdata/seq/A363/A363276.seq | b38274d7954ab2119eabe6f324d977c5 |
A363277 | Sum of the divisor complements of the squarefree divisors of n that are <= sqrt(n). | [
"1",
"2",
"3",
"6",
"5",
"9",
"7",
"12",
"12",
"15",
"11",
"22",
"13",
"21",
"20",
"24",
"17",
"33",
"19",
"30",
"28",
"33",
"23",
"44",
"30",
"39",
"36",
"42",
"29",
"61",
"31",
"48",
"44",
"51",
"42",
"72",
"37",
"57",
"52",
"68",
"41",
"84",
"43",
"66",
"69",
"69",
"47",
"96",
"56",
"85",
"68",
"78",
"53",
"108",
"66",
"92",
"76",
"87",
"59",
"132",
"61",
"93",
"93",
"96",
"78",
"132",
"67",
"102",
"92"
]
| [
"nonn",
"easy"
]
| 9 | 1 | 2 | [
"A070038",
"A333749",
"A363277"
]
| null | Wesley Ivan Hurt, May 25 2023 | 2023-05-26T07:33:27 | oeisdata/seq/A363/A363277.seq | 2993a9cd3f715d2f3a168f6ded3acf3b |
A363278 | Total number of parts coprime to n in the partitions of n into 3 parts. | [
"0",
"0",
"3",
"2",
"6",
"3",
"12",
"8",
"15",
"10",
"30",
"12",
"42",
"21",
"32",
"32",
"72",
"27",
"90",
"40",
"66",
"55",
"132",
"48",
"130",
"78",
"126",
"84",
"210",
"60",
"240",
"128",
"170",
"136",
"216",
"108",
"342",
"171",
"240",
"160",
"420",
"126",
"462",
"220",
"276",
"253",
"552",
"192",
"525",
"250",
"416",
"312",
"702",
"243",
"560",
"336",
"522",
"406",
"870",
"240",
"930",
"465"
]
| [
"nonn",
"easy"
]
| 9 | 1 | 3 | [
"A000010",
"A363278",
"A363322",
"A363323",
"A363324",
"A363325",
"A363326",
"A363327",
"A363328"
]
| null | Wesley Ivan Hurt, May 25 2023 | 2023-05-27T23:25:46 | oeisdata/seq/A363/A363278.seq | 848ce490e937ca15b05cf4cdf06883c5 |
A363279 | a(0)=1; a(1)=2. For n>1, a(n) is the number of contiguous groups in the sequence thus far whose sum is n. | [
"1",
"2",
"1",
"2",
"1",
"1",
"2",
"3",
"1",
"2",
"4",
"1",
"3",
"5",
"4",
"3",
"5",
"5",
"2",
"4",
"6",
"4",
"4",
"5",
"2",
"8",
"5",
"4",
"7",
"6",
"6",
"3",
"8",
"7",
"5",
"7",
"5",
"6",
"11",
"5",
"6",
"9",
"11",
"2",
"6",
"10",
"8",
"6",
"6",
"11",
"7",
"7",
"10",
"6",
"10",
"7",
"6",
"11",
"11",
"4",
"9",
"13",
"6",
"10",
"11",
"9",
"8",
"7",
"9",
"9",
"10",
"10",
"6",
"14",
"10",
"9",
"8",
"11",
"7",
"11",
"12",
"9",
"11",
"11",
"10",
"7"
]
| [
"nonn"
]
| 19 | 0 | 2 | [
"A331614",
"A358537",
"A359634",
"A363279"
]
| null | Neal Gersh Tolunsky, May 25 2023 | 2023-05-27T02:40:16 | oeisdata/seq/A363/A363279.seq | 8dca2207410404491a743072075d8bf6 |
A363280 | Products of primorials that are not highly composite. | [
"8",
"16",
"30",
"32",
"64",
"72",
"96",
"128",
"144",
"192",
"210",
"216",
"256",
"288",
"384",
"420",
"432",
"480",
"512",
"576",
"768",
"864",
"900",
"960",
"1024",
"1080",
"1152",
"1296",
"1440",
"1536",
"1728",
"1800",
"1920",
"2048",
"2160",
"2304",
"2310",
"2592",
"2880",
"3072",
"3360",
"3456",
"3600",
"3840",
"4096",
"4320",
"4608",
"4620",
"5184"
]
| [
"nonn"
]
| 64 | 1 | 1 | [
"A000079",
"A002110",
"A002182",
"A025487",
"A055932",
"A363280"
]
| null | Michael De Vlieger, Dec 12 2023 | 2023-12-16T05:43:40 | oeisdata/seq/A363/A363280.seq | 83abfea3b0b2d459a579606d9c899a1f |
A363281 | Numbers which are the sum of 4 squares of distinct primes. | [
"87",
"159",
"183",
"199",
"204",
"207",
"231",
"247",
"252",
"303",
"319",
"324",
"327",
"343",
"348",
"351",
"364",
"367",
"372",
"399",
"423",
"439",
"444",
"463",
"468",
"471",
"484",
"487",
"492",
"495",
"511",
"516",
"532",
"535",
"540",
"543",
"556",
"559",
"564",
"567",
"583",
"588",
"591",
"604",
"607",
"612",
"628",
"655",
"660",
"663",
"676",
"679",
"684",
"700",
"703",
"708"
]
| [
"easy",
"nonn"
]
| 19 | 1 | 1 | [
"A051395",
"A133524",
"A363281"
]
| null | Zhining Yang, May 25 2023 | 2025-03-27T05:43:30 | oeisdata/seq/A363/A363281.seq | 68b5b2b21039172134c43f5ee0bfd7a4 |
A363282 | Squares (A000290) and centered squares (A001844), in increasing order (i.e., sorted and without duplicates). | [
"1",
"4",
"5",
"9",
"13",
"16",
"25",
"36",
"41",
"49",
"61",
"64",
"81",
"85",
"100",
"113",
"121",
"144",
"145",
"169",
"181",
"196",
"221",
"225",
"256",
"265",
"289",
"313",
"324",
"361",
"365",
"400",
"421",
"441",
"481",
"484",
"529",
"545",
"576",
"613",
"625",
"676",
"685",
"729",
"761",
"784",
"841",
"900",
"925",
"961",
"1013",
"1024",
"1089",
"1105"
]
| [
"nonn"
]
| 10 | 1 | 2 | [
"A000290",
"A001844",
"A363267",
"A363282",
"A363319"
]
| null | Clark Kimberling, May 25 2023 | 2023-06-12T11:51:07 | oeisdata/seq/A363/A363282.seq | e937b33d98afa6882b4d94baaff347c4 |
A363283 | Squares (A000290) and (1+squares) (A002522), in increasing order. | [
"1",
"2",
"4",
"5",
"9",
"10",
"16",
"17",
"25",
"26",
"36",
"37",
"49",
"50",
"64",
"65",
"81",
"82",
"100",
"101",
"121",
"122",
"144",
"145",
"169",
"170",
"196",
"197",
"225",
"226",
"256",
"257",
"289",
"290",
"324",
"325",
"361",
"362",
"400",
"401",
"441",
"442",
"484",
"485",
"529",
"530",
"576",
"577",
"625",
"626",
"676",
"677",
"729",
"730",
"784",
"785"
]
| [
"nonn",
"easy"
]
| 21 | 1 | 2 | [
"A000290",
"A002522",
"A363267",
"A363268",
"A363282",
"A363283"
]
| null | Clark Kimberling, May 25 2023 | 2024-08-28T09:37:41 | oeisdata/seq/A363/A363283.seq | 35ad79336a522d05a96e1405633f703c |
A363284 | Numbers that are square or square pyramidal. | [
"0",
"1",
"4",
"5",
"9",
"14",
"16",
"25",
"30",
"36",
"49",
"55",
"64",
"81",
"91",
"100",
"121",
"140",
"144",
"169",
"196",
"204",
"225",
"256",
"285",
"289",
"324",
"361",
"385",
"400",
"441",
"484",
"506",
"529",
"576",
"625",
"650",
"676",
"729",
"784",
"819",
"841",
"900",
"961",
"1015",
"1024",
"1089",
"1156",
"1225",
"1240",
"1296",
"1369",
"1444",
"1496"
]
| [
"nonn"
]
| 20 | 1 | 3 | [
"A000290",
"A000330",
"A363269",
"A363284"
]
| null | Clark Kimberling, May 25 2023 | 2023-08-04T04:58:20 | oeisdata/seq/A363/A363284.seq | 9c2424b7afa5a127ab65bab349671666 |
A363285 | a(n) is the smallest multiple k of 2^n such that |sigma(k) - 2*k| = 2^n, where sigma = A000203. | [
"1",
"10",
"12",
"56",
"752",
"992",
"12224",
"16256",
"654848",
"7337984",
"10483712",
"12580864",
"167763968",
"67100672",
"2684321792",
"38654574592",
"584115027968",
"17179738112",
"206158168064",
"274877382656",
"149533572988928",
"123145293922304",
"9288674164342784",
"34902896977903616"
]
| [
"nonn"
]
| 35 | 0 | 2 | [
"A000079",
"A000203",
"A292557",
"A292558",
"A363285"
]
| null | Jesiah Darnell, May 25 2023 | 2023-07-17T12:39:28 | oeisdata/seq/A363/A363285.seq | dc295c1c9f2e6408e835ca64624ede70 |
A363286 | Odd primes p such that the congruence 2^x == 1 (mod p) has no solution for 0 < x < (p - 1)/2. | [
"3",
"5",
"7",
"11",
"13",
"17",
"19",
"23",
"29",
"37",
"41",
"47",
"53",
"59",
"61",
"67",
"71",
"79",
"83",
"97",
"101",
"103",
"107",
"131",
"137",
"139",
"149",
"163",
"167",
"173",
"179",
"181",
"191",
"193",
"197",
"199",
"211",
"227",
"239",
"263",
"269",
"271",
"293",
"311",
"313",
"317",
"347",
"349",
"359",
"367",
"373",
"379",
"383",
"389",
"401",
"409",
"419"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A001917",
"A014664",
"A363286"
]
| null | Arkadiusz Wesolowski, May 25 2023 | 2023-07-17T09:03:29 | oeisdata/seq/A363/A363286.seq | 39ad5d5108d0cd2580e423ae5746b2b4 |
A363287 | Numbers which cannot be written as the sum of 4 distinct proper prime powers (A246547). | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"32",
"33",
"34",
"35",
"36",
"38",
"39",
"40",
"41",
"42",
"43",
"44",
"45",
"47",
"49",
"50",
"51",
"52",
"57",
"59",
"62",
"63",
"66",
"67",
"68",
"73",
"75",
"80",
"90",
"95",
"107",
"134",
"135",
"136",
"140",
"145",
"151",
"152",
"256",
"2040",
"340473"
]
| [
"nonn"
]
| 24 | 1 | 2 | [
"A246547",
"A363287"
]
| null | Zhao Hui Du, May 25 2023 | 2023-07-13T17:42:32 | oeisdata/seq/A363/A363287.seq | f578015b0fe4e70ef512bb523e6fa56a |
A363288 | a(n) = (2*n^3 - n^2 + 3*n - 2)/2. | [
"1",
"8",
"26",
"61",
"119",
"206",
"328",
"491",
"701",
"964",
"1286",
"1673",
"2131",
"2666",
"3284",
"3991",
"4793",
"5696",
"6706",
"7829",
"9071",
"10438",
"11936",
"13571",
"15349",
"17276",
"19358",
"21601",
"24011",
"26594",
"29356",
"32303",
"35441",
"38776",
"42314",
"46061",
"50023",
"54206",
"58616",
"63259",
"68141",
"73268",
"78646",
"84281"
]
| [
"nonn",
"easy"
]
| 26 | 1 | 2 | [
"A000217",
"A002411",
"A002414",
"A046092",
"A162264",
"A363288"
]
| null | Wesley Ivan Hurt, May 25 2023 | 2023-06-05T02:46:35 | oeisdata/seq/A363/A363288.seq | c840902320ffea9c5e28c7fbbd23619c |
A363289 | Sum of the divisor complements of the unitary squarefree divisors of n. | [
"1",
"3",
"4",
"4",
"6",
"12",
"8",
"8",
"9",
"18",
"12",
"16",
"14",
"24",
"24",
"16",
"18",
"27",
"20",
"24",
"32",
"36",
"24",
"32",
"25",
"42",
"27",
"32",
"30",
"72",
"32",
"32",
"48",
"54",
"48",
"36",
"38",
"60",
"56",
"48",
"42",
"96",
"44",
"48",
"54",
"72",
"48",
"64",
"49",
"75",
"72",
"56",
"54",
"81",
"72",
"64",
"80",
"90",
"60",
"96",
"62",
"96",
"72",
"64",
"84",
"144",
"68",
"72",
"96",
"144",
"72"
]
| [
"nonn",
"easy"
]
| 10 | 1 | 2 | [
"A092261",
"A363289"
]
| null | Wesley Ivan Hurt, May 26 2023 | 2023-05-26T12:29:07 | oeisdata/seq/A363/A363289.seq | ccc97faa170b505df03fbceb80bb74f7 |
A363290 | Decimal expansion of the unique x > 0 such that Sum_{n>=0} 1/x^(n!) = 1. | [
"2",
"4",
"2",
"4",
"4",
"1",
"0",
"4",
"4",
"9",
"0",
"1",
"5",
"6",
"5",
"3",
"2",
"3",
"6",
"3",
"7",
"2",
"3",
"7",
"4",
"5",
"9",
"7",
"0",
"7",
"9",
"4",
"9",
"7",
"0",
"8",
"4",
"1",
"9",
"5",
"8",
"4",
"7",
"7",
"3",
"2",
"7",
"1",
"4",
"7",
"6",
"9",
"4",
"3",
"4",
"2",
"1",
"2",
"6",
"5",
"5",
"9",
"0",
"0",
"1",
"5",
"2",
"7",
"9",
"8",
"7",
"0",
"6",
"7",
"0",
"7",
"5",
"4",
"7",
"4",
"6",
"7",
"5",
"0",
"9",
"1",
"3",
"6",
"4",
"4",
"0",
"0",
"7",
"7",
"0",
"3",
"5"
]
| [
"nonn",
"cons"
]
| 15 | 1 | 1 | [
"A076187",
"A363290"
]
| null | M. F. Hasler, May 26 2023 | 2023-07-06T13:48:29 | oeisdata/seq/A363/A363290.seq | e9dbefcc2c2560c34d5197d96f85088f |
A363291 | Sum of divisors of 4*n-1 of form 4*k+1. | [
"1",
"1",
"1",
"6",
"1",
"1",
"10",
"1",
"6",
"14",
"1",
"1",
"18",
"6",
"1",
"31",
"1",
"1",
"31",
"1",
"1",
"30",
"14",
"6",
"43",
"1",
"1",
"38",
"6",
"18",
"42",
"1",
"1",
"60",
"1",
"14",
"71",
"1",
"6",
"54",
"1",
"1",
"67",
"31",
"1",
"62",
"18",
"1",
"84",
"1",
"30",
"79",
"1",
"6",
"74",
"1",
"1",
"132",
"6",
"1",
"91",
"14",
"1",
"108",
"38",
"1",
"90",
"1",
"31",
"103",
"1",
"42",
"98",
"6",
"14",
"102",
"1",
"1",
"186",
"30",
"18",
"110",
"1",
"6",
"114",
"50",
"1"
]
| [
"nonn"
]
| 14 | 1 | 4 | [
"A050449",
"A078703",
"A363291",
"A364082"
]
| null | Seiichi Manyama, Jul 08 2023 | 2023-07-08T08:05:10 | oeisdata/seq/A363/A363291.seq | a2ca7ddb77b2bf7d024dbc8f0c172440 |
A363292 | Numbers whose sum of (distinct) prime divisors (A008472) equals 7. | [
"7",
"10",
"20",
"40",
"49",
"50",
"80",
"100",
"160",
"200",
"250",
"320",
"343",
"400",
"500",
"640",
"800",
"1000",
"1250",
"1280",
"1600",
"2000",
"2401",
"2500",
"2560",
"3200",
"4000",
"5000",
"5120",
"6250",
"6400",
"8000",
"10000",
"10240",
"12500",
"12800",
"16000",
"16807",
"20000",
"20480",
"25000",
"25600",
"31250",
"32000",
"40000",
"40960"
]
| [
"nonn",
"easy"
]
| 13 | 1 | 1 | [
"A000420",
"A008472",
"A033846",
"A362948",
"A363292"
]
| null | M. F. Hasler, Jul 20 2023 | 2023-07-27T15:23:21 | oeisdata/seq/A363/A363292.seq | ab55d04e8c3364250509727b584119f4 |
A363293 | G.f. A(x) satisfies: A(x) = x * exp( A(x)^2/x - A(-x^2)^2/(2*x^2) + A(x^3)^2/(3*x^3) - A(-x^4)^2/(4*x^4) + ... ). | [
"1",
"1",
"2",
"7",
"26",
"101",
"412",
"1756",
"7692",
"34350",
"155980",
"718312",
"3345890",
"15735091",
"74613107",
"356348561",
"1712593184",
"8276207120",
"40192085383",
"196045684833",
"960042529894",
"4718201036195",
"23263440797758",
"115042992517035",
"570463195069614",
"2835840294969867",
"14129895469191476"
]
| [
"nonn"
]
| 10 | 1 | 3 | [
"A005750",
"A005754",
"A049075",
"A363293",
"A363294"
]
| null | Ilya Gutkovskiy, May 26 2023 | 2025-04-22T21:55:17 | oeisdata/seq/A363/A363293.seq | 0f5a9da34cebda4969f236d2070208e7 |
A363294 | G.f. A(x) satisfies: A(x) = x * exp( A(x)^2/x + A(-x^2)^2/(2*x^2) + A(x^3)^2/(3*x^3) + A(-x^4)^2/(4*x^4) + ... ). | [
"1",
"1",
"3",
"10",
"37",
"154",
"676",
"3053",
"14187",
"67459",
"326241",
"1599480",
"7933272",
"39736160",
"200700204",
"1021052197",
"5227501077",
"26912956631",
"139244637915",
"723631840568",
"3775598797694",
"19770494002049",
"103865161431895",
"547291750362216",
"2891718659119578",
"15317429567883000"
]
| [
"nonn"
]
| 5 | 1 | 3 | [
"A005750",
"A005754",
"A045648",
"A363293",
"A363294"
]
| null | Ilya Gutkovskiy, May 26 2023 | 2023-05-26T08:51:00 | oeisdata/seq/A363/A363294.seq | 1c498102a1b0f7af7bc9b9f4d364e033 |
A363295 | Numbers k such that k and k+20 are consecutive unitary weird numbers (A064114). | [
"34121990",
"34428290",
"34766810",
"34936070",
"38014970",
"38152010",
"39506090",
"39844610",
"41400170",
"42044990",
"42552770",
"42584990",
"43769810",
"46276490",
"46308710",
"47155010",
"47324270",
"47461310",
"49016870",
"49153910",
"49323170",
"49661690",
"49863170",
"50540210",
"51015770",
"51354290",
"53079110"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A064114",
"A306952",
"A363295",
"A363296"
]
| null | Amiram Eldar, May 26 2023 | 2023-05-26T05:46:14 | oeisdata/seq/A363/A363295.seq | cbed0b2c9dee0fcff5349a3173f81d52 |
A363296 | Unitary weird numbers (A064114) with a record gap to the next unitary weird number. | [
"70",
"5830",
"2197790",
"902388130",
"2013240110"
]
| [
"nonn",
"hard",
"more"
]
| 5 | 1 | 1 | [
"A064114",
"A306953",
"A363295",
"A363296"
]
| null | Amiram Eldar, May 26 2023 | 2023-05-26T05:45:54 | oeisdata/seq/A363/A363296.seq | cccc9ad821f0fdd4bc253edb7ff5568e |
A363297 | Unitary weird numbers (A064114) with more unitary divisors than any smaller weird number. | [
"70",
"4030",
"4199030",
"5702250610"
]
| [
"nonn",
"hard",
"more"
]
| 8 | 1 | 1 | [
"A034444",
"A064114",
"A335008",
"A363297"
]
| null | Amiram Eldar, May 26 2023 | 2025-04-22T21:55:12 | oeisdata/seq/A363/A363297.seq | 9871ef7bfb9a437f2d575d72750fbdf1 |
A363298 | Number of refactorable unitary divisors of n. | [
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"2",
"2",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"3",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"4",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"3",
"1",
"4"
]
| [
"nonn",
"easy"
]
| 9 | 1 | 2 | [
"A034444",
"A336041",
"A363085",
"A363298"
]
| null | Wesley Ivan Hurt, May 26 2023 | 2023-05-27T13:06:33 | oeisdata/seq/A363/A363298.seq | 71c4683cd843037321f76a5a49d8b3d0 |
A363299 | a(n) is the sum of the n-th powers of the terms of row 4 of Pascal's triangle. | [
"5",
"16",
"70",
"346",
"1810",
"9826",
"54850",
"312706",
"1810690",
"10601986",
"62563330",
"371185666",
"2210336770",
"13194911746",
"78901035010",
"472332468226",
"2829699842050",
"16961019183106",
"101697395621890",
"609909495824386",
"3658357463318530",
"21945746733400066",
"131656888214355970",
"789870960541958146"
]
| [
"nonn",
"easy"
]
| 37 | 0 | 1 | [
"A000012",
"A007318",
"A007395",
"A052548",
"A115099",
"A363299"
]
| null | J. Lowell, May 26 2023 | 2025-06-02T16:49:53 | oeisdata/seq/A363/A363299.seq | 1ac09907d629909f2c23e15c0045b99a |
A363300 | Number of fractions of the Farey sequence of order n, F_n, that can be expressed as x/y, where y = #{F_n} - 1. | [
"2",
"3",
"3",
"5",
"7",
"9",
"7",
"3",
"11",
"9",
"13",
"3",
"3",
"9",
"23",
"25",
"25",
"23",
"33",
"17",
"33",
"23",
"5",
"49",
"45",
"5",
"33",
"23",
"53",
"3",
"49",
"43",
"9",
"69",
"49",
"77",
"75",
"63",
"7",
"47",
"11",
"3",
"9",
"5",
"5",
"55",
"53",
"9",
"55",
"61",
"57",
"11",
"97",
"133",
"67",
"5",
"81",
"5",
"7",
"95",
"15",
"9",
"5",
"217",
"13",
"17",
"75",
"107",
"133",
"19",
"113",
"5",
"21",
"85",
"117",
"5",
"9",
"121",
"3",
"3"
]
| [
"nonn"
]
| 24 | 1 | 1 | [
"A005728",
"A262669",
"A262670",
"A363300",
"A363321"
]
| null | Andres Cicuttin, May 26 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A363/A363300.seq | 8d387f23fd6adb26314a9f77af7b73a8 |
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