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1999-12-11 03:00:00
2025-04-28 00:58:08
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A381007
Ordered hypothenuses of the Pythagorean triangles defined by a = 2^(4n) + 2^(2n+1), b = 2^(4n) - 2^(4n-2) - 2^(2n) - 1, c = 2^(4n) + 2^(4n-2) + 2^(2n) + 1.
[ "25", "337", "5185", "82177", "1311745", "20975617", "335560705", "5368774657", "85899608065", "1374390583297", "21990236749825", "351843737665537", "5629499601321985", "90071992815845377", "1441151881832300545", "23058430096431906817", "368934881491370901505", "5902958103655775993857" ]
[ "nonn", "easy" ]
30
1
1
[ "A020882", "A381005", "A381006", "A381007", "A381008", "A381009" ]
null
Robert C. Lyons, Feb 12 2025
2025-02-26T08:51:12
oeisdata/seq/A381/A381007.seq
ab90656f5d77fb060185515cdf717367
A381008
Ordered perimeters of the Pythagorean triangles defined by a = 2^(4n) + 2^(2n+1), b = 2^(4n) - 2^(4n-2) - 2^(2n) - 1, c = 2^(4n) + 2^(4n-2) + 2^(2n) + 1.
[ "56", "800", "12416", "197120", "3147776", "50339840", "805339136", "12885032960", "206158954496", "3298536980480", "52776566521856", "844424963686400", "13510799016329216", "216172782650654720", "3458764515968024576", "55340232229718589440", "885443715572418215936", "14167099448746374594560" ]
[ "nonn", "easy" ]
19
1
1
[ "A024364", "A381005", "A381006", "A381007", "A381008", "A381009" ]
null
Robert C. Lyons, Feb 12 2025
2025-02-26T08:51:19
oeisdata/seq/A381/A381008.seq
81fd5f380d8920c9b717e5ad9cbd4fa9
A381009
Ordered areas of the Pythagorean triangles defined by a = 2^(4n) + 2^(2n+1), b = 2^(4n) - 2^(4n-2) - 2^(2n) - 1, c = 2^(4n) + 2^(4n-2) + 2^(2n) + 1.
[ "84", "25200", "6350784", "1614708480", "412583721984", "105570270965760", "27022696873181184", "6917599389942743040", "1770891934572664848384", "453347470584212823736320", "116056897129722086198083584", "29710562123440325102508441600", "7605903676927233379495034486784", "1947111326786263531071061496954880" ]
[ "nonn", "easy" ]
17
1
1
[ "A024406", "A381005", "A381006", "A381007", "A381008", "A381009" ]
null
Robert C. Lyons, Feb 12 2025
2025-02-26T08:51:26
oeisdata/seq/A381/A381009.seq
80acd3f77b3792505d01696909f44553
A381010
Positive integers k such that 2^(k+2) - 1 is divisible by k.
[ "1", "7", "511", "713", "11023", "15553", "43873", "81079", "95263", "323593", "628153", "2275183", "6520633", "6955513", "7947583", "10817233", "12627943", "14223823", "15346303", "19852423", "27923663", "28529473", "29360527", "31019623", "39041863", "41007823", "79015273", "134217727", "143998193", "213444943", "227018383" ]
[ "nonn", "new" ]
29
1
2
[ "A000225", "A055685", "A069927", "A187787", "A381010" ]
null
Oisín Flynn-Connolly, Apr 10 2025
2025-04-23T16:58:24
oeisdata/seq/A381/A381010.seq
527eaf095b50deab07631bbf613f924b
A381011
a(n) = [(x*y)^n] Product_{k>=1} (1 - x^k - y^k)^k.
[ "1", "0", "2", "-6", "-14", "-10", "32", "76", "-80", "-340", "-200", "590", "2302", "1890", "-3470", "-11468", "-16254", "5244", "57406", "109340", "81396", "-158664", "-550388", "-829558", "-359856", "1509570", "4333256", "6198660", "2628406", "-10133230", "-30439512", "-46214582", "-29696680", "45589368" ]
[ "sign", "new" ]
10
0
3
[ "A073592", "A322213", "A322214", "A381011" ]
null
Ilya Gutkovskiy, Apr 10 2025
2025-04-15T17:23:18
oeisdata/seq/A381/A381011.seq
158cd62f7d89fe1e41ab232e2ab88f6f
A381012
a(n) = [(x*y)^n] Product_{k>=1} (1 - x^k - y^k)^n.
[ "1", "0", "-2", "-6", "-82", "530", "-2420", "11718", "-77458", "492834", "-1022532", "3574714", "-39670180", "-172880396", "3186538080", "-18558899356", "150869023214", "-1286538054802", "6854805868780", "-29675795883872", "168219184363308", "-618102310289316", "-1450440026397056", "26462673455854066" ]
[ "sign", "new" ]
10
0
3
[ "A008705", "A322213", "A322214", "A381012" ]
null
Ilya Gutkovskiy, Apr 10 2025
2025-04-15T17:23:22
oeisdata/seq/A381/A381012.seq
7a16d11aaf86f51798481b505a0df26c
A381013
If n = Product (p_j^k_j) then a(n) = Product partition(p_j^k_j).
[ "1", "2", "3", "5", "7", "6", "15", "22", "30", "14", "56", "15", "101", "30", "21", "231", "297", "60", "490", "35", "45", "112", "1255", "66", "1958", "202", "3010", "75", "4565", "42", "6842", "8349", "168", "594", "105", "150", "21637", "980", "303", "154", "44583", "90", "63261", "280", "210", "2510", "124754", "693", "173525", "3916", "891", "505", "329931", "6020", "392", "330", "1470", "9130", "831820", "105" ]
[ "nonn", "mult", "new" ]
15
1
2
[ "A000041", "A000688", "A381013" ]
null
Ilya Gutkovskiy, Apr 10 2025
2025-04-17T09:35:08
oeisdata/seq/A381/A381013.seq
1388f82672823027ff36da4f4cd6685c
A381014
If n = Product (p_j^k_j) then a(n) = Sum partition(p_j^k_j).
[ "0", "2", "3", "5", "7", "5", "15", "22", "30", "9", "56", "8", "101", "17", "10", "231", "297", "32", "490", "12", "18", "58", "1255", "25", "1958", "103", "3010", "20", "4565", "12", "6842", "8349", "59", "299", "22", "35", "21637", "492", "104", "29", "44583", "20", "63261", "61", "37", "1257", "124754", "234", "173525", "1960", "300", "106", "329931", "3012", "63", "37", "493", "4567", "831820", "15" ]
[ "nonn", "new" ]
15
1
2
[ "A000041", "A008481", "A381014" ]
null
Ilya Gutkovskiy, Apr 10 2025
2025-04-17T09:35:58
oeisdata/seq/A381/A381014.seq
30a990705b213c78e3cf57e1df71db32
A381015
a(n) = n + (number of trailing 0's of n).
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "11", "11", "12", "13", "14", "15", "16", "17", "18", "19", "21", "21", "22", "23", "24", "25", "26", "27", "28", "29", "31", "31", "32", "33", "34", "35", "36", "37", "38", "39", "41", "41", "42", "43", "44", "45", "46", "47", "48", "49", "51", "51", "52", "53", "54", "55", "56", "57", "58", "59", "61", "61", "62", "63", "64", "65", "66", "67", "68", "69", "71", "71", "72", "73", "74", "75", "76", "77" ]
[ "nonn", "base", "easy" ]
21
1
2
[ "A121520", "A122840", "A317905", "A372490", "A373387", "A379243", "A381015" ]
null
Marco Ripà, Feb 11 2025
2025-03-02T23:33:35
oeisdata/seq/A381/A381015.seq
7514c9c12ddaa95891002f11359db666
A381016
Expansion of e.g.f. -log(1-x) * sin(x).
[ "0", "0", "2", "3", "4", "20", "110", "651", "4520", "36000", "322618", "3213595", "35226860", "421419492", "5463436134", "76301056755", "1142009233872", "18236159031584", "309463272791538", "5561354285804115", "105510576441518164", "2107380222724155540", "44200537412519181278", "971311172969442165883" ]
[ "nonn" ]
13
0
3
[ "A002104", "A009410", "A009416", "A177699", "A381016" ]
null
Seiichi Manyama, Feb 12 2025
2025-02-12T11:55:44
oeisdata/seq/A381/A381016.seq
f81ec04c68f4f0810b389e10d95c8069
A381017
Prime terms of A000328.
[ "5", "13", "29", "113", "149", "197", "317", "613", "709", "797", "1009", "1129", "1373", "3001", "3209", "3853", "4513", "5261", "6361", "7213", "11681", "12853", "15373", "16729", "19577", "20593", "21101", "22133", "25997", "30757", "33317", "38669", "53077", "56401", "65101", "68777", "72533", "73517", "95093", "100621", "108637", "114553", "115781", "118213" ]
[ "nonn" ]
9
1
1
[ "A000040", "A000328", "A381017", "A381018" ]
null
Michel Marcus, Feb 12 2025
2025-02-12T09:27:31
oeisdata/seq/A381/A381017.seq
0c869a1f91e4fd9c98147e606aa012c5
A381018
a(n) is the number of primes in A000328 for r <= n.
[ "1", "2", "3", "3", "3", "4", "5", "6", "6", "7", "7", "7", "7", "8", "9", "10", "10", "11", "12", "12", "13", "13", "13", "13", "13", "13", "13", "13", "13", "13", "14", "15", "15", "15", "16", "16", "16", "17", "17", "17", "18", "18", "18", "18", "19", "19", "19", "20", "20", "20", "20", "20", "20", "20", "20", "20", "20", "20", "20", "20", "21", "21", "21", "22", "22", "22", "22", "22", "22", "23", "23", "23" ]
[ "nonn" ]
12
1
2
[ "A000328", "A000720", "A381017", "A381018", "A381020" ]
null
Michel Marcus, Feb 12 2025
2025-02-13T12:16:19
oeisdata/seq/A381/A381018.seq
88d8dffc2dab47e67a72651e9a39d353
A381019
a(n) is the smallest positive integer not yet in the sequence such that a(n) is relatively prime to a(n-i) for all 1 <= i <= min(a(n), n-1).
[ "1", "2", "3", "5", "7", "11", "4", "13", "17", "19", "23", "29", "9", "31", "37", "8", "41", "43", "47", "53", "59", "61", "6", "67", "71", "73", "79", "83", "89", "25", "97", "101", "103", "107", "109", "12", "113", "127", "131", "137", "139", "149", "151", "157", "163", "167", "10", "173", "179", "181", "191", "193", "197", "199", "49", "211", "223", "227", "229", "233" ]
[ "nonn", "look" ]
85
1
2
[ "A379810", "A381019", "A381115", "A381120", "A381167" ]
null
Ali Sada and Allan C. Wechsler, Feb 12 2025
2025-04-07T00:47:41
oeisdata/seq/A381/A381019.seq
8e51dd207f17fcce3fcdcc8114063694
A381020
a(n) = A381018(100*n).
[ "30", "45", "60", "75", "92", "106", "119", "133", "141", "157", "170", "177", "185", "204", "224", "236", "245", "260", "275", "292", "305", "318", "330", "342", "359", "371", "382", "390", "405", "419", "430", "444", "457", "472", "490", "507", "524", "535", "550", "561", "570", "583", "593", "604", "611", "621", "627", "638", "647", "659", "670", "679", "683", "697" ]
[ "nonn" ]
10
1
1
[ "A028505", "A381018", "A381020" ]
null
Michel Marcus, Feb 12 2025
2025-02-13T12:21:07
oeisdata/seq/A381/A381020.seq
dc7f66d95f40ca522713d7755efc527f
A381021
Expansion of e.g.f. log(1-x)^2 * exp(x) / 2.
[ "0", "0", "1", "6", "29", "145", "814", "5243", "38618", "321690", "2995011", "30840304", "348114711", "4274888891", "56744495872", "809667333733", "12358833406580", "200955441549140", "3467781770502885", "63298198354605210", "1218507112218768721", "24671782054230662277", "524152965820457130290" ]
[ "nonn" ]
11
0
4
[ "A073596", "A094816", "A381021" ]
null
Seiichi Manyama, Feb 12 2025
2025-02-12T16:54:03
oeisdata/seq/A381/A381021.seq
18f8b5a1f3f155f8cbad762e7f411483
A381022
Expansion of e.g.f. -log(1-x)^3 * exp(x) / 6.
[ "0", "0", "0", "1", "10", "75", "545", "4179", "34860", "318926", "3197210", "34975061", "415371726", "5328246417", "73470506291", "1084206640399", "17054915985752", "284945098917980", "5040033650314996", "94099409345964169", "1849525745917903666", "38176559589575462327", "825716052360614856485", "18675737859143938658251" ]
[ "nonn" ]
13
0
5
[ "A094816", "A381022", "A381024" ]
null
Seiichi Manyama, Feb 12 2025
2025-02-12T16:54:00
oeisdata/seq/A381/A381022.seq
660857a2ae5c08fa6e31d585855ddec2
A381023
Expansion of e.g.f. log(1-x)^4 * exp(x) / 24.
[ "0", "0", "0", "0", "1", "15", "160", "1575", "15659", "163191", "1809905", "21474255", "272757166", "3703523824", "53631736795", "826097224680", "13497286183354", "233291225507890", "4254733292942982", "81680724157089634", "1646873959921840191", "34800264421134754997", "769198023696181428250", "17751664780107823096301" ]
[ "nonn" ]
13
0
6
[ "A094816", "A381023", "A381025" ]
null
Seiichi Manyama, Feb 12 2025
2025-02-12T16:46:07
oeisdata/seq/A381/A381023.seq
64cc8819a55f54cb59a29047942fb6dc
A381024
Expansion of e.g.f. log(1-x)^2 * exp(x) / (2 * (1-x)).
[ "0", "0", "1", "9", "65", "470", "3634", "30681", "284066", "2878284", "31777851", "380396665", "4912874691", "68142259874", "1010736134108", "15970709345353", "267890182932228", "4755088551397016", "89059375695649173", "1755426336571939497", "36327033843657558661", "787539492771039394158", "17850021806783323801766" ]
[ "nonn" ]
13
0
4
[ "A269951", "A381022", "A381024" ]
null
Seiichi Manyama, Feb 12 2025
2025-02-12T16:47:20
oeisdata/seq/A381/A381024.seq
bd205877b35ac1843838fcde4867d6fd
A381025
Expansion of e.g.f. -log(1-x)^3 * exp(x) / (6 * (1-x)).
[ "0", "0", "0", "1", "14", "145", "1415", "14084", "147532", "1646714", "19664350", "251282911", "3430766658", "49928212971", "772465487885", "12671188958674", "219793939324536", "4021442067435092", "77425990864146652", "1565193235764750557", "33153390461212914806", "734397759275046673253", "16982466756411641668051" ]
[ "nonn" ]
13
0
5
[ "A269951", "A381023", "A381025" ]
null
Seiichi Manyama, Feb 12 2025
2025-02-12T16:46:27
oeisdata/seq/A381/A381025.seq
7874f5fca286ac0aee788f2d126c19ac
A381026
Primitive solutions k to the Diophantine equation k^7 = Sum_{i=1..7} y_i^7 with y_i > 0.
[ "568", "626" ]
[ "nonn", "bref", "hard", "more", "changed" ]
9
1
1
[ "A380716", "A381026" ]
null
Jinyuan Wang, Feb 12 2025
2025-04-18T17:45:18
oeisdata/seq/A381/A381026.seq
7538d7518594812efc4470f5f1f3edcf
A381027
Isolated primes in A381019.
[ "7643", "26357", "31643", "73517", "114073", "240263", "272347", "635821", "1719491", "2981159", "3610597", "4783469", "5294351", "7140083", "7170769", "9813593", "12521141", "13172477", "20443837", "22499627", "24098573", "24147133", "24891641", "50832209", "57741727", "60328483", "65714459", "84701363", "128297069" ]
[ "nonn" ]
25
1
1
[ "A381019", "A381027", "A381120" ]
null
Gonzalo Martínez, Mar 03 2025
2025-03-09T12:42:44
oeisdata/seq/A381/A381027.seq
6747beb453a06cac0a7a092303eba310
A381028
Decimal expansion of Sum_{k>=1} zeta(2k)/((2k-1)*2^(2k)).
[ "4", "3", "7", "6", "5", "8", "2", "4", "2", "3", "1", "1", "2", "6", "1", "0", "9", "3", "3", "1", "5", "9", "2", "0", "9", "2", "6", "4", "3", "8", "0", "5", "1", "4", "0", "1", "6", "4", "8", "4", "3", "5", "6", "4", "5", "3", "5", "2", "3", "0", "6", "9", "6", "8", "3", "0", "2", "7", "1", "5", "6", "1", "3", "1", "5", "1", "3", "3", "2", "3", "4", "3", "5", "7", "1", "5", "8", "9", "4", "1", "7", "2", "4", "1", "6", "0", "1", "6", "8", "3", "9", "4", "9", "8", "3", "0", "9", "8", "5", "4", "2", "3", "9", "3", "1" ]
[ "nonn", "cons" ]
24
0
1
[ "A256318", "A355922", "A381028" ]
null
R. J. Mathar, Feb 12 2025
2025-02-16T01:18:37
oeisdata/seq/A381/A381028.seq
0519d685123f1ccd560d9c473d48a197
A381029
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x*A(x)^2)^2).
[ "1", "1", "3", "16", "113", "955", "9178", "97427", "1121705", "13836694", "181295019", "2507119320", "36416096984", "553461581406", "8774534872463", "144744539399484", "2479088917439527", "44004108702467428", "808171916050540308", "15335535608825061803", "300272362335527090277", "6059534345675248667550" ]
[ "nonn" ]
19
0
3
[ "A088714", "A120971", "A143508", "A381029", "A381572", "A381600", "A381615" ]
null
Seiichi Manyama, Mar 01 2025
2025-03-01T22:48:15
oeisdata/seq/A381/A381029.seq
477ec037f60a7f93c1d3f922916e1716
A381030
Array read by diagonals downwards: A(n,k) for n>=2 and k>=0 is the number of (n,k)-polyominoes.
[ "1", "2", "2", "2", "4", "5", "3", "11", "20", "12", "3", "17", "60", "68", "35", "4", "32", "151", "302", "289", "108", "4", "45", "322", "955", "1523", "1151", "369", "5", "71", "633", "2617", "5942", "7384", "4792", "1285", "5", "94", "1132", "6179", "19061", "33819", "35188", "19603", "4655", "6", "134", "1930", "13374", "52966", "125940", "184938", "164036", "80820", "17073", "6", "170", "3095", "26567", "131717", "400119", "778318", "969972" ]
[ "nonn", "tabl" ]
21
2
2
[ "A000105", "A286194", "A286344", "A286345", "A381030", "A381057" ]
null
John Mason, Feb 12 2025
2025-02-16T10:26:35
oeisdata/seq/A381/A381030.seq
2f3ede81989530b1acd6b2ec7eeb4d87
A381031
The second smallest prime not dividing n minus the smallest prime not dividing n.
[ "1", "2", "3", "2", "1", "2", "1", "2", "3", "4", "1", "2", "1", "2", "5", "2", "1", "2", "1", "4", "3", "2", "1", "2", "1", "2", "3", "2", "1", "4", "1", "2", "3", "2", "1", "2", "1", "2", "3", "4", "1", "6", "1", "2", "5", "2", "1", "2", "1", "4", "3", "2", "1", "2", "1", "2", "3", "2", "1", "4", "1", "2", "3", "2", "1", "2", "1", "2", "3", "8", "1", "2", "1", "2", "5", "2", "1", "2", "1", "4", "3", "2", "1", "6", "1", "2", "3", "2", "1", "4", "1", "2", "3", "2", "1", "2", "1", "2", "3", "4", "1", "2", "1", "2", "9" ]
[ "nonn" ]
13
1
2
[ "A053669", "A249270", "A380539", "A381031", "A381113" ]
null
Antti Karttunen, Feb 12 2025
2025-02-15T14:29:13
oeisdata/seq/A381/A381031.seq
8c79ef5285ef61e3bc24a694e749ac69
A381032
The radix prime of the least significant digit > 1 in the primorial base expansion of n, or 1 if there is no such digit.
[ "1", "1", "1", "1", "3", "3", "1", "1", "1", "1", "3", "3", "5", "5", "5", "5", "3", "3", "5", "5", "5", "5", "3", "3", "5", "5", "5", "5", "3", "3", "1", "1", "1", "1", "3", "3", "1", "1", "1", "1", "3", "3", "5", "5", "5", "5", "3", "3", "5", "5", "5", "5", "3", "3", "5", "5", "5", "5", "3", "3", "7", "7", "7", "7", "3", "3", "7", "7", "7", "7", "3", "3", "5", "5", "5", "5", "3", "3", "5", "5", "5", "5", "3", "3", "5", "5", "5", "5", "3", "3", "7", "7", "7", "7", "3", "3", "7", "7", "7", "7", "3", "3", "5", "5", "5", "5", "3", "3", "5" ]
[ "nonn" ]
8
0
5
[ "A008578", "A020639", "A053669", "A088860", "A249739", "A276086", "A276156", "A327860", "A328572", "A328828", "A351566", "A381032", "A381033", "A381034" ]
null
Antti Karttunen, Feb 13 2025
2025-02-17T12:09:57
oeisdata/seq/A381/A381032.seq
7476f93f4b2eb4eb34be4dbccafd7ec2
A381033
a(n) = 1 if there is a digit > 1 in the primorial base expansion of n, and the corresponding radix prime of the least significant such digit is not a prime factor of n, otherwise 0.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "nonn" ]
21
0
null
[ "A049345", "A381032", "A381033", "A381034", "A381036" ]
null
Antti Karttunen, Feb 17 2025
2025-03-06T14:51:54
oeisdata/seq/A381/A381033.seq
13476da54a8186023b9ad3537671d90f
A381034
Numbers that have a digit > 1 in their primorial base expansion, and that are multiples of the corresponding radix prime of the least significant such digit.
[ "15", "20", "25", "45", "50", "55", "63", "75", "80", "85", "91", "98", "105", "110", "115", "126", "135", "140", "145", "165", "170", "175", "182", "189", "195", "200", "205", "225", "230", "235", "255", "260", "265", "273", "285", "290", "295", "301", "308", "315", "320", "325", "336", "345", "350", "355", "375", "380", "385", "392", "399", "405", "410", "415", "429", "435", "440", "445", "451", "465", "470", "475", "483", "495", "500", "505" ]
[ "nonn" ]
15
1
1
[ "A049345", "A177711", "A381032", "A381033", "A381034", "A381035", "A381037" ]
null
Antti Karttunen, Feb 17 2025
2025-02-17T12:00:36
oeisdata/seq/A381/A381034.seq
5fef5c3544adcb40ee47b13b680ae271
A381035
Numbers such that the least significant nonzero digit in their primorial base representation (A049345) is 1.
[ "1", "2", "3", "5", "6", "7", "8", "9", "11", "13", "14", "15", "17", "19", "20", "21", "23", "25", "26", "27", "29", "30", "31", "32", "33", "35", "36", "37", "38", "39", "41", "43", "44", "45", "47", "49", "50", "51", "53", "55", "56", "57", "59", "61", "62", "63", "65", "66", "67", "68", "69", "71", "73", "74", "75", "77", "79", "80", "81", "83", "85", "86", "87", "89", "91", "92", "93", "95", "96", "97", "98", "99", "101", "103", "104", "105", "107", "109", "110", "111" ]
[ "nonn", "base", "easy" ]
12
1
2
[ "A049345", "A064648", "A276088", "A276156", "A290249", "A380534", "A380535", "A381034", "A381035" ]
null
Antti Karttunen, Feb 17 2025
2025-02-18T19:02:07
oeisdata/seq/A381/A381035.seq
7cb0696af33325eda6d6c509a8265fef
A381036
a(n) = 1 if there is a digit > 1 in the primorial base expansion of n, and the corresponding radix primes of all such digits are also prime factors of n, otherwise 0.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "nonn" ]
11
0
null
[ "A049345", "A381033", "A381036", "A381037" ]
null
Antti Karttunen, Feb 17 2025
2025-03-06T14:52:05
oeisdata/seq/A381/A381036.seq
55282d45b78b5400ca2521d31c37391a
A381037
Numbers with a digit > 1 in their primorial base expansion that are multiples of the corresponding radix primes of all such digits.
[ "15", "20", "25", "45", "50", "55", "63", "91", "98", "105", "126", "140", "175", "182", "189", "225", "230", "235", "255", "260", "265", "273", "301", "308", "315", "336", "350", "385", "392", "399", "429", "440", "451", "638", "660", "693", "770", "847", "1056", "1089", "1100", "1155", "1232", "1298", "1386", "1485", "1507", "1683", "1705", "1716", "1771", "1892", "2079", "2101", "2145", "2325", "2330", "2335", "2355", "2360", "2365" ]
[ "nonn" ]
14
1
1
[ "A003557", "A007947", "A049345", "A177711", "A276086", "A328572", "A380527", "A381034", "A381035", "A381036", "A381037" ]
null
Antti Karttunen, Feb 17 2025
2025-02-17T14:28:15
oeisdata/seq/A381/A381037.seq
30d954af3564508a7d28d5d68f488dce
A381038
Coefficients of the first Mock Eisenstein series associated to partition ranks.
[ "0", "1", "3", "5", "7", "9", "10", "13", "12", "17", "14", "21", "16", "25", "19", "29", "20", "36", "22", "37", "29", "41", "26", "52", "28", "48", "39", "53", "32", "65", "34", "61", "49", "60", "38", "84", "40", "66", "59", "78", "44", "91", "46", "85", "72", "78", "50", "116", "52", "89", "79", "101", "56", "117", "65", "109", "88", "96", "62", "157", "64", "102", "96", "125", "79", "143", "70", "133", "104", "127", "74", "180", "76", "120", "127" ]
[ "nonn", "new" ]
24
1
3
null
null
Jan-Willem M. van Ittersum, Apr 14 2025
2025-04-20T10:59:56
oeisdata/seq/A381/A381038.seq
951bba6a29da9261cceb09142dd98b0c
A381039
Smallest palindromic prime with 2n+1 digits and middle digit 0.
[ "101", "16061", "1120211", "100404001", "10013031001", "1000030300001", "100001303100001", "10000003030000001", "1000000160610000001", "100000000303000000001", "10000000016061000000001", "1000000000030300000000001", "100000000004909400000000001", "10000000000013031000000000001", "1000000000000250520000000000001" ]
[ "nonn", "base", "new" ]
20
1
1
[ "A002385", "A381039" ]
null
Jean-Marc Rebert, Apr 14 2025
2025-04-22T07:46:40
oeisdata/seq/A381/A381039.seq
b0641a2cb7167983daa99f1b350e9833
A381040
Numbers k such that the concatenation of 1, k! and 1 is prime.
[ "7", "9", "10", "15", "21225" ]
[ "nonn", "base", "new" ]
16
1
1
[ "A000142", "A034886", "A262195", "A381040" ]
null
Michael S. Branicky, Apr 14 2025
2025-04-25T04:31:16
oeisdata/seq/A381/A381040.seq
1180a38b707edb10f516fb6186f0917a
A381042
Alternating sum of floor(n^(1/k)), with k >= 2.
[ "0", "0", "0", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "3", "3", "3", "3", "3", "3", "3", "3", "3", "4", "4", "3", "3", "3", "3", "3", "2", "2", "2", "2", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "7", "7", "7", "7", "7" ]
[ "nonn", "new" ]
13
0
17
[ "A000196", "A048766", "A089361", "A178487", "A178489", "A255270", "A381042", "A382691", "A382692" ]
null
Friedjof Tellkamp, Apr 14 2025
2025-04-22T07:49:47
oeisdata/seq/A381/A381042.seq
e32e9a148226f925dcd2eef747610e44
A381043
Centered pentagonal numbers which are squarefree semiprimes.
[ "6", "51", "106", "141", "226", "391", "526", "681", "766", "951", "1501", "1891", "2031", "2326", "2481", "2641", "3151", "3901", "4101", "4306", "6631", "6891", "7981", "8266", "8851", "10081", "10401", "11391", "13141", "14631", "15406", "16201", "20931", "23281", "24751", "27301", "27826", "28891", "29431", "30526", "32206", "33351", "35701", "36301", "38131", "38751", "41926" ]
[ "nonn", "new" ]
13
1
1
[ "A005891", "A006881", "A145838", "A364610", "A381043", "A382132" ]
null
Massimo Kofler, Apr 14 2025
2025-04-18T21:20:02
oeisdata/seq/A381/A381043.seq
d2945e2c9d048ecc1cfebc711551a7c6
A381045
Happy cubes: cubes whose trajectory under iteration of sum of squares of digits map includes 1.
[ "1", "1000", "4096", "12167", "13824", "15625", "74088", "226981", "250047", "300763", "531441", "704969", "778688", "1000000", "1092727", "1481544", "2460375", "2803221", "3176523", "3652264", "4096000", "4251528", "5000211", "6644672", "7645373", "8365427", "8489664", "8869743", "8998912", "11852352", "12167000" ]
[ "nonn", "base", "new" ]
12
1
2
[ "A000578", "A007770", "A381045" ]
null
Shyam Sunder Gupta, Apr 14 2025
2025-04-22T00:42:15
oeisdata/seq/A381/A381045.seq
ed675fea68740fd970c8f828f47008e9
A381046
Happy repdigit numbers.
[ "1", "7", "44", "888", "5555", "88888", "1111111", "2222222", "22222222", "77777777", "1111111111", "7777777777", "22222222222", "44444444444", "444444444444", "1111111111111", "4444444444444", "7777777777777", "999999999999999", "7777777777777777", "22222222222222222", "77777777777777777" ]
[ "nonn", "base", "new" ]
19
1
2
[ "A007770", "A010785", "A381046" ]
null
Shyam Sunder Gupta, Apr 14 2025
2025-04-22T18:45:47
oeisdata/seq/A381/A381046.seq
2a2be6bf07f240c5a809eac8f6a5b5fa
A381047
Numbers k such that Fibonacci(k) is a happy number.
[ "1", "2", "7", "18", "19", "25", "32", "33", "45", "50", "83", "84", "87", "93", "106", "109", "115", "117", "122", "126", "130", "132", "133", "134", "143", "145", "155", "160", "162", "166", "172", "177", "187", "190", "193", "200", "224", "232", "235", "238", "246", "247", "250", "251", "254", "270", "279", "280", "281", "288", "291", "295", "306", "309", "333" ]
[ "nonn", "base", "new" ]
18
1
2
[ "A000045", "A007770", "A381047" ]
null
Shyam Sunder Gupta, Apr 14 2025
2025-04-22T05:40:46
oeisdata/seq/A381/A381047.seq
98610e530cd5a7e3056a4ca9a127a5a3
A381052
Expansion of e.g.f. log(1 - x)^2 * exp(3*x) / 2.
[ "0", "0", "1", "12", "101", "755", "5494", "40971", "323658", "2764926", "25811091", "263989242", "2951126991", "35886116097", "472073225688", "6682068553689", "101277082202580", "1636520039991324", "28084499373387141", "510104266923895272", "9776178108160101369", "197153249728184351919", "4173367143545298444186" ]
[ "nonn", "new" ]
27
0
4
[ "A327997", "A381021", "A381052" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T11:06:33
oeisdata/seq/A381/A381052.seq
2c6201042c71c77169b8b9ba3793e069
A381054
a(n) is the least k such that floor(sqrt(n*k/d(n*k))) - floor(sqrt(d(n*k))) = 1, where d(k) is the largest divisor of k which is <= sqrt(k).
[ "5", "4", "4", "2", "1", "2", "1", "1", "2", "1", "4", "1", "4", "1", "1", "5", "9", "1", "9", "3", "1", "2", "9", "3", "2", "2", "2", "3", "16", "2", "16", "3", "2", "5", "2", "2", "25", "5", "2", "2", "25", "2", "25", "1", "1", "5", "25", "2", "2", "1", "3", "1", "36", "1", "1", "2", "3", "8", "36", "1", "36", "8", "1", "3", "1", "1", "49", "3", "3", "1", "49", "1", "49", "13", "1", "3", "1", "1", "49", "1" ]
[ "nonn", "new" ]
32
1
1
[ "A000196", "A033676", "A033677", "A048760", "A381054", "A382286", "A383115" ]
null
Hassan Baloui, Apr 14 2025
2025-04-25T03:08:00
oeisdata/seq/A381/A381054.seq
79ab4daa5334696a8f41fcf8cea04418
A381055
a(n) = -n/2 if n is even, 3n + 1 if n is odd.
[ "0", "4", "-1", "10", "-2", "16", "-3", "22", "-4", "28", "-5", "34", "-6", "40", "-7", "46", "-8", "52", "-9", "58", "-10", "64", "-11", "70", "-12", "76", "-13", "82", "-14", "88", "-15", "94", "-16", "100", "-17", "106", "-18", "112", "-19", "118", "-20", "124", "-21", "130", "-22", "136", "-23", "142", "-24", "148", "-25", "154", "-26", "160", "-27", "166", "-28", "172" ]
[ "sign", "new" ]
11
0
2
[ "A006370", "A381055", "A383131" ]
null
Ya-Ping Lu, Apr 14 2025
2025-04-18T21:30:46
oeisdata/seq/A381/A381055.seq
fabf57028e12d268dce8c6397b01e1c2
A381056
Product of row n of A329708.
[ "1", "16", "4320", "7680000", "56672000000", "1315328716800000", "79725223359774720000", "11041460968683995136000000", "3159164253667495772160000000000", "1725992749819407775039488000000000000", "1690274868390850110509130354524160000000000", "2816890048270042497343000411961733572198400000000" ]
[ "nonn" ]
80
0
2
[ "A000290", "A000292", "A000537", "A005408", "A007531", "A087047", "A329708", "A381056" ]
null
Darío Clavijo, Feb 12 2025
2025-04-01T03:28:14
oeisdata/seq/A381/A381056.seq
209e90355e88f569ba8cea14f30d1107
A381057
Array read by diagonals downwards: A(n,k) for n>=2 and k>=0 is the number of (n,k)-polyominoes counting as distinct different formations of transparent squares.
[ "1", "2", "2", "3", "5", "5", "6", "17", "24", "12", "10", "41", "101", "89", "35", "20", "106", "353", "535", "382", "108", "36", "243", "1091", "2355", "2769", "1566", "369", "72", "567", "3095", "8937", "14841", "13739", "6569", "1285", "136", "1259", "8209", "29744", "65651", "86322", "66499", "27205", "4655", "272", "2806", "20804", "90914", "252277", "439879", "479343", "314445", "112886", "17073", "528", "6113", "50801", "259078", "872526" ]
[ "nonn", "tabl" ]
18
2
2
[ "A000105", "A005418", "A381030", "A381057" ]
null
John Mason, Feb 12 2025
2025-02-16T10:26:25
oeisdata/seq/A381/A381057.seq
e471ab5b6a7ae9ed3c8d04c12cafc9ce
A381058
Irregular triangular array read by rows. Let S_n be the set of labeled graphs G on [n] with 2-colored nodes where black nodes are only connected to white nodes and vice versa. Orient the edges in each such graph G from black to white. T(n,k) is the number of graphs in S_n containing exactly k descents, n>=0, 0<=k<=A002620(n).
[ "1", "2", "5", "1", "16", "8", "2", "67", "56", "30", "8", "1", "374", "436", "358", "188", "68", "16", "2", "2825", "4143", "4508", "3460", "2032", "924", "320", "80", "13", "1", "29212", "50460", "66976", "66092", "52412", "34280", "18630", "8376", "3072", "892", "194", "28", "2", "417199", "811790", "1246486", "1471358", "1436404", "1195166", "859650", "537750", "292880", "138280", "56048", "19168", "5382", "1188", "192", "20", "1" ]
[ "nonn", "tabf" ]
21
0
2
[ "A006116", "A047863", "A111636", "A228890", "A381058", "A381102", "A381192" ]
null
Geoffrey Critzer, Feb 12 2025
2025-02-17T03:22:46
oeisdata/seq/A381/A381058.seq
a5146eb637a724917049886684e0c1f5
A381059
Array read by ascending antidiagonals: A(n,k) = numerator(binomial(n-1/2,k)) with k >=0.
[ "1", "1", "-1", "1", "1", "3", "1", "3", "-1", "-5", "1", "5", "3", "1", "35", "1", "7", "15", "-1", "-5", "-63", "1", "9", "35", "5", "3", "7", "231", "1", "11", "63", "35", "-5", "-3", "-21", "-429", "1", "13", "99", "105", "35", "3", "7", "33", "6435", "1", "15", "143", "231", "315", "-7", "-5", "-9", "-429", "-12155", "1", "17", "195", "429", "1155", "63", "7", "5", "99", "715", "46189" ]
[ "sign", "frac", "look", "tabl" ]
14
0
6
[ "A000012", "A000466", "A001790", "A002596", "A060747", "A161200", "A161202", "A162540", "A173755", "A381059" ]
null
Stefano Spezia, Feb 12 2025
2025-02-17T03:20:47
oeisdata/seq/A381/A381059.seq
416d1d90c087bc0a3c69cd00fd0d54ba
A381060
Numbers t which are the sum of some subset of the values of k satisfying the equation (t - floor((t - k)/k)) mod k = 0 (t > 1, 1 <= k < t).
[ "23", "29", "39", "41", "53", "59", "65", "71", "77", "79", "83", "89", "99", "101", "107", "111", "113", "119", "125", "137", "143", "149", "155", "161", "167", "173", "179", "185", "191", "197", "199", "209", "221", "227", "233", "239", "245", "251", "257", "263", "269", "279", "281", "287", "293", "299", "305", "311", "317", "323", "329", "335", "339", "341", "349", "353", "359", "365", "371" ]
[ "nonn" ]
6
1
1
[ "A005835", "A048158", "A375595", "A380153", "A380305", "A381060" ]
null
Lechoslaw Ratajczak, Feb 12 2025
2025-03-10T18:12:43
oeisdata/seq/A381/A381060.seq
aac8851014afd7ed67d0dbdffd3d7e4f
A381061
First of six consecutive primes such that sum of any five terms is prime.
[ "9733", "970217", "3218471", "5241937", "5691893", "8445251", "8788079", "11268497", "11881901", "16697419", "19604623", "22057961", "22926473", "26027723", "26939197", "38187463", "38938153", "39901963", "45190247", "52489691", "54887597", "58296113", "61909753", "62686369", "68142289", "69567359", "69799033", "72085687", "72973723", "79517741", "82464511" ]
[ "nonn" ]
18
1
1
[ "A298763", "A381061", "A381062" ]
null
Zak Seidov and Robert Israel, Feb 12 2025
2025-02-15T09:47:03
oeisdata/seq/A381/A381061.seq
35fac9e2dbd24dce704e6290313074cc
A381062
a(n) is the first prime p such that the sum of any 2*n-1 of the 2*n consecutive primes starting with p is prime.
[ "2", "19", "9733", "69398759" ]
[ "nonn", "more" ]
5
1
1
[ "A298763", "A381061", "A381062" ]
null
Robert Israel, Feb 12 2025
2025-02-13T10:00:46
oeisdata/seq/A381/A381062.seq
c6d1ddbcdce4e32cfbb3ee7b84d62e98
A381063
Lexicographically earliest sequence of positive integers such that each nonempty subset has a distinct geometric mean.
[ "1", "2", "3", "5", "7", "8", "11", "13", "17", "18", "19", "23", "29", "31", "37", "41", "43", "47", "50", "53", "59", "61", "67", "71", "73", "79", "83", "89", "97", "98", "101", "103", "107", "109", "113", "127", "131", "137", "139", "149", "151", "157", "163", "167", "173", "176", "179", "181", "191", "193", "197", "199", "211", "223", "227", "229", "233", "239", "241", "251" ]
[ "nonn" ]
9
1
2
[ "A066720", "A260873", "A381063" ]
null
Neal Gersh Tolunsky, Feb 12 2025
2025-02-22T21:30:28
oeisdata/seq/A381/A381063.seq
a3478156a9139670c1ae07eafd9cb2af
A381064
Expansion of e.g.f. log(1-x)^2 * exp(-x) / 2.
[ "0", "0", "1", "0", "5", "15", "94", "595", "4458", "37590", "354051", "3682646", "41935695", "518954293", "6935360496", "99553094537", "1527716784020", "24959724735564", "432572721886437", "7926615468800172", "153129657663788761", "3110514839038091643", "66278515188844197218", "1478222957082474301887" ]
[ "nonn" ]
8
0
5
[ "A269953", "A300490", "A381021", "A381064" ]
null
Seiichi Manyama, Feb 12 2025
2025-02-13T02:23:48
oeisdata/seq/A381/A381064.seq
38ddb7828a89602fb96c1e07ccff4311
A381065
Expansion of e.g.f. -log(1-x)^3 * exp(-x) / 6.
[ "0", "0", "0", "1", "2", "15", "85", "609", "4844", "43238", "427090", "4630241", "54683046", "699012093", "9617979007", "141755256889", "2228396376088", "37221746535564", "658390407698084", "12295201090394017", "241749652842156074", "4992277083472634507", "108032799218176059337", "2444797394606939402449" ]
[ "nonn" ]
11
0
5
[ "A269953", "A381022", "A381065", "A381067" ]
null
Seiichi Manyama, Feb 12 2025
2025-02-13T02:24:44
oeisdata/seq/A381/A381065.seq
ee20a9c73504ec6780569c004d47e61c
A381066
Expansion of e.g.f. log(1-x)^4 * exp(-x) / 24.
[ "0", "0", "0", "0", "1", "5", "40", "315", "2779", "26817", "282785", "3240325", "40144126", "535152332", "7642713715", "116465389950", "1886911421914", "32395513943998", "587627463812070", "11231176543495238", "225621300685737631", "4753177896741075823", "104793882332694641218", "2413274241933067193021" ]
[ "nonn" ]
10
0
6
[ "A269953", "A381023", "A381066", "A381068" ]
null
Seiichi Manyama, Feb 12 2025
2025-02-13T02:25:52
oeisdata/seq/A381/A381066.seq
74e075a4fb17dd41c28db6f4ed3c7e2f
A381067
Expansion of e.g.f. log(1-x)^2 * exp(-x) / (2 * (1-x)).
[ "0", "0", "1", "3", "17", "100", "694", "5453", "48082", "470328", "5057331", "59313287", "753695139", "10316991100", "151373235896", "2370151632977", "39450142911652", "695612154233648", "12953591498092101", "254044853932550091", "5234026736314790581", "113025076301648693844", "2552830193825115461786" ]
[ "nonn" ]
9
0
4
[ "A016269", "A269954", "A381024", "A381065", "A381067" ]
null
Seiichi Manyama, Feb 12 2025
2025-02-13T02:26:47
oeisdata/seq/A381/A381067.seq
326d58cdc0995f95677605bd6a9facaa
A381068
Expansion of e.g.f. -log(1-x)^3 * exp(-x) / (6 * (1-x)).
[ "0", "0", "0", "1", "6", "45", "355", "3094", "29596", "309602", "3523110", "43384451", "575296458", "8177866047", "124108103665", "2003376811864", "34282425365912", "620022977756068", "11818804007307308", "236852477229232869", "4978799197426813454", "109547060229435717041", "2518068124265761834239" ]
[ "nonn" ]
9
0
5
[ "A269954", "A381025", "A381066", "A381068" ]
null
Seiichi Manyama, Feb 12 2025
2025-02-13T02:27:49
oeisdata/seq/A381/A381068.seq
48db2fd10faee5640c1bc1f300731eec
A381069
Numbers k that have a record number of divisors that have the same binary weight as k.
[ "1", "2", "4", "8", "16", "32", "64", "72", "144", "288", "576", "1080", "2160", "4320", "8640", "17280", "34560", "69120", "99360", "136080", "198720", "272160", "397440", "529200", "544320", "1058400", "2116800", "3160080", "4233600", "6320160", "8467200", "12640320", "16934400", "25280640", "50561280", "76744800", "101122560", "102816000" ]
[ "nonn", "base" ]
8
1
2
[ "A000005", "A002182", "A380844", "A381069", "A381070" ]
null
Amiram Eldar, Feb 12 2025
2025-02-17T03:28:41
oeisdata/seq/A381/A381069.seq
3bad0d46b784eeb88aa226eaec3b4a6c
A381070
Numbers k such that A380845(k)/k > A380845(m)/m for all m < k.
[ "1", "2", "4", "8", "16", "18", "36", "72", "144", "288", "540", "1080", "2160", "4320", "8640", "17280", "34560", "45360", "68040", "90720", "106680", "136080", "213360", "272160", "320040", "640080", "1280160", "2560320", "2577960", "5155920", "10311840", "15467760", "30935520", "61871040", "123742080", "247484160", "494968320", "681080400" ]
[ "nonn", "base" ]
7
1
2
[ "A000203", "A004394", "A380845", "A380846", "A380929", "A380930", "A380931", "A381069", "A381070" ]
null
Amiram Eldar, Feb 13 2025
2025-02-17T03:28:49
oeisdata/seq/A381/A381070.seq
6c64e75c9aeca2118d06c14f629416d0
A381071
Numbers k such that the sum of the proper divisors of k that have the same binary weight as k is larger than k, and no subset of these divisors sums to k.
[ "1050", "3150", "4284", "4410", "5148", "6292", "6790", "7176", "8890", "10764", "17850", "18648", "19000", "19530", "32886", "33072", "33150", "35088", "35530", "35720", "35770", "38850", "41360", "43164", "45084", "49368", "49764", "50456", "50730", "52884", "54280", "54340", "58410", "58696", "59010", "59408", "63492", "66010", "68376" ]
[ "nonn", "base" ]
7
1
1
[ "A000396", "A006037", "A064114", "A292986", "A306984", "A321146", "A327948", "A339939", "A348525", "A348631", "A349285", "A364862", "A380845", "A380846", "A380929", "A381071", "A381072" ]
null
Amiram Eldar, Feb 13 2025
2025-02-17T03:28:55
oeisdata/seq/A381/A381071.seq
2d1a94ae9e167298535d36f157c980ed
A381072
Odd terms in A381071.
[ "322245", "590205", "874665", "3378375", "4729725", "6081075", "6818175", "8783775", "8906625", "9889425", "10135125", "13378365", "15049125", "15909075", "16253055", "18922365", "32684085", "34754265", "36916425", "38144925", "38439765", "39471705", "44778825", "46990125", "57506085", "75200265", "84047355", "88852995" ]
[ "nonn", "base" ]
8
1
1
[ "A005408", "A380929", "A380932", "A381071", "A381072" ]
null
Amiram Eldar, Feb 13 2025
2025-02-17T04:55:47
oeisdata/seq/A381/A381072.seq
0689ebde9fb961c921a5310cd15a4de0
A381073
Numbers k such that k and k+2 are both terms in A380846.
[ "8596", "9772", "10444", "17836", "19626", "21196", "23716", "27186", "35754", "36484", "38164", "42700", "45892", "54796", "56586", "85708", "91252", "98586", "100770", "104970", "112698", "132412", "136612", "139074", "140980", "141652", "144676", "149716", "152850", "165172", "166122", "171724", "182032", "182644", "184770", "190482" ]
[ "nonn", "base" ]
6
1
1
[ "A380845", "A380846", "A381073", "A381074" ]
null
Amiram Eldar, Feb 13 2025
2025-02-17T03:29:09
oeisdata/seq/A381/A381073.seq
d6811e9fdb5637a45ebaf39f9ff90cd4
A381074
Numbers k such that k, k+2 and k+4 are all terms in A380846.
[ "10820236", "24069388", "27802288", "39297580", "50717488", "56362960", "73070224", "97339504", "103605964", "112209580", "112526032", "140053564", "145315600", "155790124", "156415084", "158877232", "184667248", "185979664", "188913004", "189225484", "189541936", "224435536", "281740396", "292406380", "314388112" ]
[ "nonn", "base" ]
6
1
1
[ "A380845", "A380846", "A381073", "A381074" ]
null
Amiram Eldar, Feb 13 2025
2025-02-17T03:29:18
oeisdata/seq/A381/A381074.seq
edba58a7f7778d0bd0b1f47bea7989d8
A381075
Sorted positions of first appearances in A280292 (sum of prime factors minus sum of distinct prime factors).
[ "1", "4", "8", "9", "16", "25", "32", "49", "64", "81", "121", "128", "169", "256", "289", "361", "512", "529", "625", "841", "961", "1024", "1331", "1369", "1444", "1681", "1849", "2048", "2116", "2197", "2209", "2809", "3481", "3721", "3844", "4232", "4489", "4913", "5041", "5324", "5329", "5476", "6241", "6859", "6889", "7396", "7569", "7688", "7921" ]
[ "nonn", "changed" ]
11
1
2
[ "A000040", "A000720", "A001222", "A001223", "A001414", "A005117", "A008472", "A013929", "A046660", "A055396", "A056239", "A061395", "A066503", "A071625", "A075255", "A112798", "A116861", "A136565", "A151821", "A156061", "A175508", "A178503", "A280286", "A280292", "A290106", "A364916", "A366528", "A380955", "A380956", "A380957", "A380958", "A380987", "A380988", "A380989", "A381075", "A381076" ]
null
Gus Wiseman, Feb 18 2025
2025-04-15T08:25:33
oeisdata/seq/A381/A381075.seq
070294910ead64301d7d5b72e221cabe
A381076
Sorted positions of first appearances in A066503 (n minus squarefree kernel of n).
[ "1", "4", "8", "16", "18", "20", "24", "25", "27", "32", "44", "48", "50", "52", "54", "64", "68", "72", "75", "76", "80", "81", "92", "96", "98", "108", "112", "116", "121", "125", "128", "144", "148", "152", "160", "162", "164", "172", "175", "176", "188", "189", "192", "196", "198", "200", "212", "216", "232", "236", "242", "243", "244", "256", "260", "264", "268", "272" ]
[ "nonn" ]
7
1
2
[ "A000040", "A001221", "A001222", "A001223", "A001414", "A001694", "A003557", "A003963", "A005117", "A006530", "A007947", "A013929", "A020639", "A027746", "A038838", "A046660", "A055396", "A056239", "A061395", "A066503", "A075255", "A081770", "A112798", "A116861", "A136565", "A156061", "A175508", "A178503", "A280286", "A280292", "A290106", "A304038", "A380955", "A380956", "A380957", "A380986", "A380987", "A380988", "A380989", "A381075", "A381076", "A381077" ]
null
Gus Wiseman, Feb 18 2025
2025-02-19T22:12:01
oeisdata/seq/A381/A381076.seq
35d9c22d0cb00ff40b5d263826100c4d
A381077
Sorted positions of first appearances in A380986 (product of prime indices minus product of distinct prime indices).
[ "1", "9", "25", "49", "63", "81", "99", "121", "125", "135", "169", "171", "245", "279", "289", "343", "361", "363", "369", "375", "387", "477", "529", "531", "575", "603", "625", "675", "711", "729", "747", "833", "841", "847", "873", "875", "891", "909", "961", "981", "1029", "1083", "1125", "1127", "1179", "1225", "1251", "1377", "1413", "1445", "1467" ]
[ "nonn" ]
5
1
2
[ "A000040", "A000079", "A000720", "A001221", "A001222", "A001223", "A001694", "A003557", "A003963", "A005117", "A007947", "A013929", "A038838", "A046660", "A055396", "A056239", "A061395", "A064549", "A066328", "A066503", "A075255", "A081770", "A112798", "A116861", "A151821", "A156061", "A178503", "A280286", "A280292", "A290106", "A304038", "A374248", "A379681", "A380955", "A380956", "A380957", "A380958", "A380986", "A380987", "A380988", "A381075", "A381076", "A381077" ]
null
Gus Wiseman, Feb 20 2025
2025-02-22T09:56:39
oeisdata/seq/A381/A381077.seq
f2559256f7401c89636073c4114dd72e
A381078
Number of multisets that can be obtained by partitioning the prime indices of n into a multiset of sets (set multipartition) and taking their sums.
[ "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "2", "1", "1", "2", "1", "2", "2", "2", "1", "2", "1", "2", "1", "2", "1", "5", "1", "1", "2", "2", "2", "3", "1", "2", "2", "2", "1", "5", "1", "2", "2", "2", "1", "2", "1", "2", "2", "2", "1", "2", "2", "2", "2", "2", "1", "6", "1", "2", "2", "1", "2", "5", "1", "2", "2", "5", "1", "3", "1", "2", "2", "2", "2", "5", "1", "2", "1", "2", "1", "6", "2", "2", "2" ]
[ "nonn" ]
13
1
6
[ "A000009", "A000040", "A000041", "A000688", "A000720", "A001055", "A001222", "A002846", "A003963", "A005117", "A025487", "A045778", "A050320", "A050326", "A050361", "A055396", "A056239", "A061395", "A066328", "A089259", "A112798", "A116540", "A122111", "A213242", "A213385", "A213427", "A265947", "A270995", "A293243", "A296119", "A299201", "A299202", "A300383", "A300385", "A317141", "A318360", "A321469", "A381078", "A381441", "A381452", "A381453", "A381454", "A381455", "A381633", "A381634", "A381635", "A381636", "A381637", "A381716", "A381717" ]
null
Gus Wiseman, Mar 05 2025
2025-04-01T12:16:12
oeisdata/seq/A381/A381078.seq
b25ad133e6ffb4aaa1b6e73fa0886b70
A381079
Number of integer partitions of n whose greatest multiplicity is equal to their sum of distinct parts.
[ "0", "1", "0", "0", "1", "1", "0", "3", "1", "3", "1", "2", "0", "7", "2", "6", "7", "11", "3", "19", "8", "22", "16", "32", "17", "48", "21", "50", "39", "71", "35", "101", "58", "120", "89", "156", "97", "228", "133", "267", "203", "352", "228", "483", "322", "571", "444", "734", "524", "989", "683", "1160", "942", "1490", "1103", "1919", "1438", "2302", "1890", "2881", "2243", "3683", "2842", "4384", "3703", "5461" ]
[ "nonn" ]
7
0
8
[ "A000005", "A000009", "A000041", "A008284", "A008289", "A027193", "A047966", "A047993", "A048767", "A051903", "A051904", "A066328", "A091602", "A091605", "A106529", "A116861", "A212166", "A237984", "A239455", "A240312", "A241131", "A246655", "A362608", "A363724", "A381079", "A381542", "A381632" ]
null
Gus Wiseman, Mar 03 2025
2025-03-06T22:13:37
oeisdata/seq/A381/A381079.seq
6328bfeafb573be6c63c27b649aa83c7
A381080
a(n) is the number of transitive finite pure sets of depth at most n.
[ "1", "2", "3", "6", "4131" ]
[ "nonn", "nice" ]
81
0
2
null
null
Michel Bauer, Feb 13 2025
2025-04-12T12:28:10
oeisdata/seq/A381/A381080.seq
96701294c30cbe92a609ed83e791520b
A381081
Lexicographically earliest sequence of distinct positive integers such that the string value of a(n) begins with a divisor of a(n-1).
[ "1", "10", "2", "11", "12", "3", "13", "14", "7", "15", "5", "16", "4", "17", "18", "6", "19", "100", "20", "21", "30", "22", "23", "101", "102", "24", "8", "25", "50", "26", "27", "9", "31", "103", "104", "28", "29", "105", "32", "40", "41", "106", "53", "107", "108", "33", "34", "109", "110", "51", "35", "52", "42", "36", "37", "111", "38", "112", "43", "113", "114", "39", "115", "54", "60", "44", "45", "55", "56", "46", "116", "47", "117", "90", "57", "118", "59", "119", "70", "58", "120", "48", "49", "71", "121", "122" ]
[ "nonn", "base", "look" ]
8
1
2
[ "A000030", "A027750", "A248024", "A381081" ]
null
Scott R. Shannon, Feb 13 2025
2025-02-13T08:27:00
oeisdata/seq/A381/A381081.seq
f145fe01f941f22efccfe6b866134b66
A381082
Triangle T(n,k) read by rows, where the columns are the coefficients of the standard expansion of the function f(x) = (-log(1-x))^(k)*exp(-m*x)/k! for the case m=2.
[ "1", "-2", "1", "4", "-3", "1", "-8", "8", "-3", "1", "16", "-18", "11", "-2", "1", "-32", "44", "-20", "15", "0", "1", "64", "-80", "94", "5", "25", "3", "1", "-128", "272", "56", "294", "105", "49", "7", "1", "256", "112", "1868", "1596", "1169", "392", "98", "12", "1", "-512", "5280", "12216", "16148", "10290", "4305", "1092", "186", "18", "1" ]
[ "sign", "tabl" ]
17
0
2
[ "A000023", "A094816", "A122803", "A132393", "A137346", "A269953", "A327997", "A346397", "A381082" ]
null
Igor Victorovich Statsenko, Feb 13 2025
2025-02-26T19:22:44
oeisdata/seq/A381/A381082.seq
c4a35cc9ff2e78fd68364100204f1b2c
A381083
Brent's irregular triangle T[r,k] related to Hardy-Littlewood constants of prime gaps 2r.
[ "1", "1", "2", "2", "3", "4", "1", "4", "6", "2", "30", "56", "30", "4", "18", "40", "28", "6", "15", "40", "36", "12", "1", "30", "92", "100", "44", "6", "180", "624", "812", "480", "120", "8", "150", "504", "632", "350", "72", "2970", "10880", "15642", "11008", "3780", "504", "1620", "6688", "11090", "9378", "4224", "952", "84", "1782", "7400", "12312", "10400", "4634", "1008", "80", "3960", "19312", "38958", "41768", "25376", "8570", "1446", "90", "22275", "113792", "244829", "287904", "200805", "84280", "20583", "2656", "140", "23760", "122400", "265734", "315120", "220944", "92466", "22120", "2700", "128" ]
[ "nonn", "tabf" ]
8
1
3
[ "A381083", "A381084", "A381085", "A381086" ]
null
R. J. Mathar, Feb 13 2025
2025-02-13T08:33:32
oeisdata/seq/A381/A381083.seq
8f8d3a738ae9008f8bc7752941984d95
A381084
Column k=1 of Brent's table A381083 related to prime gaps 2n.
[ "1", "1", "2", "3", "4", "30", "18", "15", "30", "180", "150", "2970", "1620", "1782", "3960", "22275", "23760", "757350", "400950", "504900", "908820", "8835750", "8330850", "15904350", "10602900", "8675100", "15904350", "257650470", "222660900", "16604141400", "6441261750", "6226553025", "13836784500", "6641656560", "9962484840", "435858711750", "224155908900", "230748729750", "475482231000", "11332326505500", "8717174235000" ]
[ "nonn" ]
9
1
3
[ "A381083", "A381084", "A381085", "A381086" ]
null
R. J. Mathar, Feb 13 2025
2025-02-13T06:46:11
oeisdata/seq/A381/A381084.seq
c9d638e6f37394145cc248a935668ecc
A381085
Column k=2 of Brent's table A381083 related to prime gaps 2n.
[ "0", "0", "2", "4", "6", "56", "40", "40", "92", "624", "504", "10880", "6688", "7400", "19312", "113792", "122400", "3979008", "2239104", "2915840", "5777920", "56689920", "55372800", "110218240", "78453760", "65815552", "125480960", "2057036800", "1776107520", "137449159680", "56911196160", "54069370880", "127085826560", "63757824000", "96876953600", "4341200912384", "2258481971200", "2411472967680", "5056905641984", "122267833425920" ]
[ "nonn" ]
8
1
3
[ "A381083", "A381084", "A381085", "A381086" ]
null
R. J. Mathar, Feb 13 2025
2025-02-13T08:47:24
oeisdata/seq/A381/A381085.seq
4ea13e2aec0df0f045414845e260a436
A381086
Column k=3 of Brent's table A381083 related to prime gaps 2n.
[ "0", "0", "0", "1", "2", "30", "28", "36", "100", "812", "632", "15642", "11090", "12312", "38958", "244829", "265734", "8883060", "5333232", "7236810", "16006998", "159615504", "161805900", "337714368", "259208326", "222480280", "445109722", "7401008550", "6375729282", "514590231096", "228830896980", "213249174660", "532897145178", "280475561070", "432135635850", "19890493216704", "10485155702790", "11646227156256", "24879391641270" ]
[ "nonn" ]
6
1
5
[ "A381083", "A381084", "A381085", "A381086" ]
null
R. J. Mathar, Feb 13 2025
2025-02-13T07:19:38
oeisdata/seq/A381/A381086.seq
caac6ff3fc550a6dfed94f706dab5eec
A381087
The smallest positive integer that produces a product that contains the digit 2 when multiplied by 2 a total of n times.
[ "2", "1", "6", "31", "64", "64", "331", "331", "814", "1607", "4107", "5129", "5129", "5129", "10283", "12819", "16163", "16163", "16163", "40108", "40108", "40108", "40108", "40108", "40108", "80313", "80313", "80313", "80313", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153", "100153" ]
[ "nonn", "base" ]
10
0
1
[ "A011532", "A378138", "A381087", "A381183" ]
null
Scott R. Shannon, Feb 13 2025
2025-02-20T08:40:50
oeisdata/seq/A381/A381087.seq
b16e8fbf4dec5d94f548bbabe2e33871
A381088
Decimal expansion of the smallest number greater than 1 whose decimal and ternary expansions have the same succession of digits.
[ "1", "0", "1", "0", "0", "2", "2", "0", "1", "0", "0", "1", "1", "2", "2", "0", "0", "1", "2", "2", "0", "0", "1", "2", "0", "1", "2", "2", "0", "2", "2", "0", "1", "2", "2", "1", "1", "0", "2", "2", "2", "2", "2", "2", "1", "2", "2", "2", "0", "0", "1", "2", "2", "2", "2", "1", "1", "1", "1", "1", "0", "0", "2", "0", "0", "0", "0", "0", "2", "0", "0", "0", "2", "2", "1", "0", "0", "2", "0", "0", "2", "0", "2", "1", "0", "1", "0", "1", "2", "1" ]
[ "nonn", "cons" ]
7
2
6
[ "A379651", "A381088" ]
null
Paolo Xausa, Feb 13 2025
2025-02-13T09:28:39
oeisdata/seq/A381/A381088.seq
0206374bfcb4f55c6c758773cd79cd35
A381089
Number of binary relations on n unlabeled points without isolated points.
[ "1", "0", "7", "86", "2846", "285984", "96348100", "112089342912", "458072631172864", "6665705090236713408", "349377212708652631367712", "66602723210653815331014240512", "46557323276092409455163109412993536", "120168498152266645852126063743794842575872" ]
[ "nonn" ]
16
0
3
[ "A000595", "A381089" ]
null
Peter Dolland, Feb 13 2025
2025-02-21T12:29:49
oeisdata/seq/A381/A381089.seq
8ae2c3c3f15f89d82a300576d06dc2ef
A381090
Number of minimal dominating sets in the n X n X n grid graph.
[ "1", "12", "12039", "7406930236" ]
[ "nonn", "more" ]
8
1
2
null
null
Eric W. Weisstein, Feb 13 2025
2025-02-15T13:35:07
oeisdata/seq/A381/A381090.seq
6a630234c8628e5fab60c2f9b546b625
A381091
Connected domination number of the n X n queen graph.
[ "1", "1", "1", "2", "3", "4", "4", "5", "5", "6", "7", "7", "8" ]
[ "nonn", "more" ]
27
1
4
[ "A358062", "A381091" ]
null
Eric W. Weisstein, Mar 27 2025
2025-03-29T07:49:58
oeisdata/seq/A381/A381091.seq
c0e9592d6a62022400d8d3339721a6dd
A381092
Numbers k such that (43^k + 2^k)/45 is prime.
[ "31", "41", "61", "599", "1231", "1249", "35671" ]
[ "nonn", "hard", "more" ]
5
1
1
[ "A057187", "A057188", "A062587", "A062589", "A127996", "A127997", "A128344", "A204940", "A217320", "A225807", "A228922", "A229542", "A375161", "A375236", "A377031", "A377856", "A381092" ]
null
Robert Price, Feb 13 2025
2025-02-16T08:34:07
oeisdata/seq/A381/A381092.seq
800f400d9ccbaaae53ed3495e1787337
A381093
Numbers k such that (26^k - 3^k)/23 is prime.
[ "2", "31", "263", "743", "1439", "6661", "78593" ]
[ "nonn", "hard", "more" ]
4
1
1
[ "A062587", "A062589", "A127996", "A127997", "A128344", "A204940", "A217320", "A225807", "A229542", "A375161", "A375236", "A377031", "A381093" ]
null
Robert Price, Feb 13 2025
2025-02-16T22:38:17
oeisdata/seq/A381/A381093.seq
9e4ef1877f9b8ffc31ef865798709d1d
A381094
Triangle read by rows where row n contains k < n that are neither coprime to n nor have the same squarefree kernel as n, or 0 if there are no such k.
[ "0", "0", "0", "0", "0", "2", "3", "4", "0", "6", "6", "2", "4", "5", "6", "8", "0", "2", "3", "4", "8", "9", "10", "0", "2", "4", "6", "7", "8", "10", "12", "3", "5", "6", "9", "10", "12", "6", "10", "12", "14", "0", "2", "3", "4", "8", "9", "10", "14", "15", "16", "0", "2", "4", "5", "6", "8", "12", "14", "15", "16", "18", "3", "6", "7", "9", "12", "14", "15", "18", "2", "4", "6", "8", "10", "11", "12", "14", "16", "18", "20" ]
[ "nonn", "tabf", "easy" ]
12
1
6
[ "A007947", "A121998", "A133995", "A369609", "A381094", "A381096" ]
null
Michael De Vlieger, Feb 14 2025
2025-03-03T13:22:27
oeisdata/seq/A381/A381094.seq
dd5a710dee650eec1ebd2b61d70d466a
A381095
Indices of prime squares in A381019.
[ "7", "13", "30", "55", "178", "468", "541", "854", "1454", "2099", "3744", "7330", "9091", "10138", "11917", "14154", "14350", "19363", "21555", "23553", "26615", "36109", "36533", "37302", "51588", "52576", "57183", "58064", "58144", "63067", "69927", "70135", "80174", "81920", "85923", "89936", "93749", "99240", "121884", "124693", "151411" ]
[ "nonn" ]
15
1
1
[ "A001248", "A381019", "A381095", "A381116", "A381119" ]
null
Michael De Vlieger, Feb 16 2025
2025-04-01T03:28:20
oeisdata/seq/A381/A381095.seq
152bbef517f8153cbf9c238971d5ed11
A381096
Number of k <= n such that k is neither coprime to n and rad(k) != rad(n), where rad = A007947.
[ "0", "0", "0", "0", "0", "3", "0", "1", "1", "5", "0", "6", "0", "7", "6", "4", "0", "10", "0", "10", "8", "11", "0", "13", "3", "13", "6", "14", "0", "21", "0", "11", "12", "17", "10", "20", "0", "19", "14", "21", "0", "29", "0", "22", "19", "23", "0", "28", "5", "28", "18", "26", "0", "33", "14", "29", "20", "29", "0", "42", "0", "31", "25", "26", "16", "45", "0", "34", "24", "45", "0", "42", "0", "37" ]
[ "nonn", "easy" ]
4
1
6
[ "A000010", "A005361", "A008479", "A355432", "A359929", "A381094", "A381096" ]
null
Michael De Vlieger, Feb 14 2025
2025-02-16T23:02:47
oeisdata/seq/A381/A381096.seq
6bba1e50a8014375a56bd65fdd313ddc
A381097
Consider the polynomial P(m,z) = Sum_{i=1..k} d(i)*z^(i-1) where d(1), d(2), ..., d(k) are the k divisors of m. The sequence lists the numbers m such that P(m,z) is irreducible.
[ "2", "3", "4", "5", "7", "9", "11", "12", "13", "16", "17", "19", "23", "24", "25", "29", "30", "31", "36", "37", "40", "41", "43", "45", "47", "48", "49", "53", "56", "59", "60", "61", "63", "64", "67", "70", "71", "72", "73", "79", "80", "81", "83", "84", "89", "90", "96", "97", "101", "103", "105", "107", "108", "109", "112", "113", "120", "121", "126", "127", "131", "132", "135" ]
[ "nonn" ]
19
1
1
[ "A291127", "A381097" ]
null
Michel Lagneau, Feb 14 2025
2025-02-26T09:04:18
oeisdata/seq/A381/A381097.seq
6176895fb9badf302d51fdf6946b6bb3
A381098
Irregular triangle read by rows: row 1 = (1, 2); row n+1 has length L = last element of row n, and consists of the L smallest positive integers not occurring earlier that share a factor with L.
[ "1", "2", "4", "6", "3", "8", "9", "10", "12", "14", "7", "16", "18", "20", "21", "22", "24", "26", "28", "30", "32", "34", "35", "36", "15", "27", "33", "38", "39", "40", "42", "44", "45", "46", "48", "50", "51", "52", "54", "56", "57", "58", "60", "62", "63", "64", "66", "68", "69", "70", "72", "74", "75", "76", "78", "80", "81", "82", "84", "86", "43", "88", "90" ]
[ "nonn", "tabf", "changed" ]
28
1
2
null
null
Ali Sada and M. F. Hasler, Feb 13 2025
2025-04-14T05:31:27
oeisdata/seq/A381/A381098.seq
ca32fde1a45a9fdcc3e178b5d78a0f54
A381099
a(n) is the smallest prime number that contains Fibonacci(n) as a substring.
[ "101", "11", "11", "2", "3", "5", "83", "13", "211", "347", "557", "89", "1447", "233", "2377", "6101", "1987", "1597", "25841", "24181", "67651", "109469", "177113", "28657", "2463683", "1750253", "1213931", "1964189", "2317811", "514229", "8320409", "13462693", "22178309", "35245781", "135702887", "192274651", "149303521" ]
[ "nonn", "base" ]
10
0
1
[ "A000040", "A000045", "A001605", "A062584", "A381099" ]
null
Gonzalo Martínez, Feb 13 2025
2025-03-02T23:47:31
oeisdata/seq/A381/A381099.seq
9f6b65faf164fbb8862973248d50c591
A381100
Number of integer triples i <= j <= k such that a non-degenerate triangle with sides (i, j, k) fits inside an equilateral triangle with sides (n, n, n), possibly touching its boundary from inside.
[ "1", "2", "5", "10", "18", "29", "44", "62", "82", "109", "141", "180", "226", "279", "339", "403", "475", "557", "651", "755", "870", "993", "1125", "1269", "1425", "1595", "1780", "1976", "2188", "2417", "2652", "2905", "3173", "3461", "3769", "4090", "4436", "4788", "5161", "5558", "5968", "6405", "6857", "7340", "7840", "8355", "8893", "9463", "10048" ]
[ "easy", "nonn" ]
9
1
2
[ "A331250", "A381100" ]
null
Vladimir Reshetnikov, Feb 13 2025
2025-02-14T18:59:13
oeisdata/seq/A381/A381100.seq
af24164a3c153e6214bf579743b2762d
A381101
Allouche-Johnson binary sequence based on the Narayana's cows sequence A000930.
[ "0", "1", "1", "1", "1", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "0", "0", "1", "1", "1", "1", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "0", "0", "1", "1", "1", "1", "0", "1", "0", "0", "0", "1", "1", "1", "1", "0", "1", "0", "0", "1", "0", "0", "0", "1" ]
[ "nonn" ]
23
0
null
[ "A000930", "A381101" ]
null
Jeffrey Shallit, Feb 16 2025
2025-02-19T11:47:41
oeisdata/seq/A381/A381101.seq
bf003a34f67871605cb8ae0246ee8d65
A381102
Irregular triangle read by rows. For each j, 1<=j<=n properly color the vertices of a labeled graph on [n] using each of the first j colors in the color set {c1<c2<...<cn}. Orient the edges according to the strict order on the colors. T(n,k) is the number of such directed graphs containing k descents, n>=0, 0<=k<=binomial(n,2).
[ "1", "1", "4", "1", "36", "27", "9", "1", "696", "983", "731", "330", "93", "15", "1", "27808", "60615", "72662", "59113", "35197", "15731", "5269", "1287", "216", "22", "1", "2257888", "6803655", "11412586", "13504721", "12316799", "9026017", "5427090", "2700863", "1112555", "376459", "103002", "22203", "3619", "417", "30", "1" ]
[ "nonn", "tabf" ]
12
0
3
[ "A289545", "A334282", "A381058", "A381102", "A381192" ]
null
Geoffrey Critzer, Feb 16 2025
2025-02-17T03:25:17
oeisdata/seq/A381/A381102.seq
ae7865e3d5d4f1b5fe6e4ed0d9cfc727
A381104
a(n) is the number of prime factors with exponent 1 in the prime factorization of the n-th superabundant number.
[ "0", "1", "0", "2", "1", "1", "0", "1", "2", "2", "1", "2", "1", "1", "3", "2", "3", "2", "2", "2", "2", "1", "3", "3", "3", "3", "2", "3", "2", "3", "4", "4", "4", "3", "4", "3", "4", "3", "3", "5", "4", "5", "4", "5", "4", "4", "6", "4", "4", "5", "6", "5", "6", "5", "5", "5", "5", "5", "5", "4", "6", "6", "6", "6", "6", "6", "5", "6", "5", "5", "5", "7", "5", "7", "7", "7", "7", "6", "7", "6", "6", "6", "8", "6", "8", "8", "8", "8", "7", "8", "7", "7", "7", "7", "9", "7", "9", "7", "7", "9", "8", "9", "8", "8", "8" ]
[ "nonn" ]
27
1
4
[ "A004394", "A056169", "A381104" ]
null
Agustin T. Besteiro, Feb 14 2025
2025-02-14T16:11:52
oeisdata/seq/A381/A381104.seq
c53eb9e4ab02b6601c6873acbfd45ffe
A381105
Expansion of e.g.f. log(1-x)^2 * (exp(x) - 1) / 2.
[ "0", "0", "0", "3", "18", "95", "540", "3479", "25550", "212106", "1968435", "20211664", "227570871", "2788446011", "36941736832", "526201686373", "8019670404980", "130221159155540", "2244376179923685", "40921210296083610", "786941965401130321", "15918834017469062277", "337908155040286890290", "7510104219030171089935" ]
[ "nonn" ]
11
0
4
[ "A000254", "A052863", "A381021", "A381105", "A381106" ]
null
Seiichi Manyama, Feb 14 2025
2025-02-14T06:56:43
oeisdata/seq/A381/A381105.seq
79e72f4a3088eb8625e4d310889b2184
A381106
Expansion of e.g.f. -log(1-x)^3 * (exp(x) - 1) / 6.
[ "0", "0", "0", "0", "4", "40", "320", "2555", "21728", "200802", "2024510", "22221485", "264453750", "3396686865", "46873789235", "692049842575", "10889098371032", "181952854080860", "3218431205690356", "60087159752141449", "1180916015576750386", "24372799835934758327", "527084149497398472485", "11919591185373007970251" ]
[ "nonn" ]
11
0
5
[ "A000399", "A052863", "A381022", "A381105", "A381106" ]
null
Seiichi Manyama, Feb 14 2025
2025-02-14T05:22:26
oeisdata/seq/A381/A381106.seq
349cfd1a5876d43a8cf7b9342a7096f1
A381107
Expansion of e.g.f. -log(1-x) * (exp(x) - 1) / (1-x).
[ "0", "0", "2", "12", "66", "395", "2665", "20307", "173488", "1646745", "17216653", "196730567", "2440331300", "32666847941", "469457190501", "7210003071247", "117862325748960", "2043420738374545", "37453428525580725", "723643767046525111", "14700326905250293556", "313236372986056228013", "6985951253209713959645" ]
[ "nonn" ]
10
0
3
[ "A000254", "A002627", "A073596", "A381107", "A381108" ]
null
Seiichi Manyama, Feb 14 2025
2025-02-14T04:03:05
oeisdata/seq/A381/A381107.seq
dc850cbdfc39dc13bba429fec12a9acc
A381108
Expansion of e.g.f. log(1-x)^2 * (exp(x) - 1) / (2 * (1-x)).
[ "0", "0", "0", "3", "30", "245", "2010", "17549", "165942", "1705584", "19024275", "229478689", "2981315139", "41545542818", "618579336284", "9804891730633", "164897938095108", "2933486106772376", "55047126101826453", "1086816606230786217", "22523274090016854661", "488907589907823010158", "11093875133012393113766" ]
[ "nonn" ]
11
0
4
[ "A000399", "A002627", "A381024", "A381107", "A381108" ]
null
Seiichi Manyama, Feb 14 2025
2025-02-14T04:00:18
oeisdata/seq/A381/A381108.seq
3a9ae3025ae38d75cceacff8ddc8703d
A381109
a(n) = (21*n^2 + 9*n + 2)/2.
[ "1", "16", "52", "109", "187", "286", "406", "547", "709", "892", "1096", "1321", "1567", "1834", "2122", "2431", "2761", "3112", "3484", "3877", "4291", "4726", "5182", "5659", "6157", "6676", "7216", "7777", "8359", "8962", "9586", "10231", "10897", "11584", "12292", "13021", "13771", "14542", "15334", "16147", "16981", "17836", "18712" ]
[ "nonn", "easy" ]
44
0
2
[ "A003215", "A005892", "A381109", "A381424" ]
null
Aaron David Fairbanks, Mar 06 2025
2025-03-07T21:30:08
oeisdata/seq/A381/A381109.seq
0da004f5cfbfc66d3414208d5b45c55f
A381110
a(n) is the maximum number of points from the set {(k, f(k)); k = 0..n} belonging to a straight line passing through the point (n, f(n)), where f(n) = A060143(n) = floor(n/phi) and phi is the golden ratio (sqrt(5)+1)/2.
[ "1", "2", "2", "2", "3", "3", "4", "3", "5", "3", "4", "4", "4", "5", "3", "5", "4", "4", "6", "4", "5", "5", "5", "6", "5", "6", "7", "6", "5", "6", "7", "6", "7", "5", "7", "8", "6", "8", "6", "7", "9", "6", "9", "7", "6", "10", "6", "7", "8", "7", "11", "7", "7", "9", "7", "12", "7", "8", "10", "8", "8", "8", "8", "11", "8", "9", "9", "9", "9", "8", "9", "10", "9", "10", "9", "10", "11", "8", "10", "10", "10", "11", "8" ]
[ "nonn", "look" ]
9
0
2
[ "A060143", "A066096", "A375422", "A381110", "A381111" ]
null
Pontus von Brömssen, Feb 14 2025
2025-02-16T22:58:19
oeisdata/seq/A381/A381110.seq
23695f4ce19798d5df7cf0d88751d194
A381111
Least k such that A381110(k) = n.
[ "0", "1", "4", "6", "8", "18", "26", "35", "40", "45", "50", "55", "99", "107", "115", "123", "136", "157", "234", "247", "260", "273", "286", "299", "312", "325", "338", "351", "364", "377", "633", "654", "675", "696", "717", "738", "759", "780", "801", "822", "843", "869", "890", "911", "932", "966", "1021", "1598", "1632", "1666", "1700", "1734", "1768", "1802" ]
[ "nonn" ]
8
1
3
[ "A376488", "A381110", "A381111" ]
null
Pontus von Brömssen, Feb 14 2025
2025-02-17T01:59:33
oeisdata/seq/A381/A381111.seq
87087c459898571b9e58f76a6fc36cdb
A381112
a(1) = 1, let q = greatest prime in S(n) = {p; p = A053669(a(i)); 1 <= i <= n-1}. Then for n > 1, a(n) is the smallest number not yet in the sequence such that: (i) q|a(n), and (ii) p a prime and p^k|a(n) implies p in S(n) and k <= cardinality of p in S(n).
[ "1", "2", "3", "6", "5", "10", "15", "20", "30", "7", "14", "21", "28", "35", "42", "56", "63", "70", "84", "105", "112", "126", "140", "168", "175", "189", "210", "11", "22", "33", "44", "55", "66", "77", "88", "99", "110", "132", "154", "165", "176", "198", "220", "231", "264", "275", "297", "308", "330", "352", "385", "396", "440", "462", "495", "528", "539", "550", "594" ]
[ "nonn" ]
20
1
2
[ "A000040", "A002110", "A006530", "A053669", "A381112" ]
null
David James Sycamore, Feb 14 2025
2025-03-07T09:21:57
oeisdata/seq/A381/A381112.seq
cead0cc20ed6e8e30b329910d867e939
A381113
Decimal expansion of the asymptotic mean of the second smallest prime not dividing k, where k runs over the positive integers (A380539).
[ "5", "1", "5", "9", "1", "4", "2", "8", "5", "9", "6", "5", "1", "6", "4", "2", "0", "3", "0", "1", "3", "6", "5", "8", "0", "9", "7", "4", "5", "0", "1", "2", "5", "8", "1", "7", "2", "0", "0", "0", "7", "3", "0", "7", "2", "1", "4", "1", "9", "1", "6", "7", "9", "9", "3", "5", "0", "0", "6", "6", "3", "8", "8", "6", "6", "2", "4", "5", "4", "2", "4", "3", "7", "8", "8", "1", "0", "7", "1", "2", "1", "2", "1", "9", "9", "5", "3", "5", "3", "3", "9", "3", "6", "1", "5", "1", "0", "5", "0", "0", "1", "1", "9", "4", "9" ]
[ "nonn", "cons" ]
4
1
1
[ "A002110", "A007504", "A249270", "A380539", "A381113" ]
null
Amiram Eldar, Feb 14 2025
2025-02-17T03:29:52
oeisdata/seq/A381/A381113.seq
fa3149d9040b062e06d2b9ff41c8cb19
A381114
Triangle read by rows: T(n,k) is the number of the k-th eliminated person in a variation of the Josephus elimination process for n people, where the number of people skipped is equal to the number of letters in the previous number's English name.
[ "1", "1", "2", "1", "3", "2", "1", "2", "4", "3", "1", "5", "2", "4", "3", "1", "5", "4", "3", "6", "2", "1", "5", "3", "6", "2", "4", "7", "1", "5", "2", "3", "4", "7", "6", "8", "1", "5", "9", "8", "7", "2", "3", "6", "4", "1", "5", "9", "7", "4", "3", "2", "10", "8", "6", "1", "5", "9", "6", "2", "10", "7", "11", "8", "3", "4", "1", "5", "9", "4", "11", "7", "2", "3", "8", "12", "10", "6", "1", "5", "9", "3", "10", "4", "11", "8", "12", "13", "2", "6", "7", "1", "5", "9", "2", "8", "14", "7", "4", "3", "13", "12" ]
[ "nonn", "tabl", "word" ]
27
1
3
[ "A005589", "A006257", "A225381", "A321298", "A378635", "A380201", "A380202", "A380204", "A380246", "A380247", "A380248", "A381114", "A381127", "A381128", "A381129" ]
null
Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Feb 14 2025
2025-03-02T22:54:52
oeisdata/seq/A381/A381114.seq
11b96f3d403857e0ee4d53d0ced950fb