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2
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int64
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666,262,453B
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1999-12-11 03:00:00
2025-04-28 00:58:08
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A378401
Rectangular array read by descending antidiagonals: (row 1) = u, and for n >= 2, (row n) = u-inverse runlength sequence of u, where u = A006338. See Comments.
[ "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "1", "2", "1", "1", "2", "1", "2", "2", "2", "2", "1", "2", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "2", "2", "2", "2", "1", "1", "2", "2", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "2", "2", "2", "2", "1", "1", "1", "2", "1", "2", "2", "2", "2", "1", "1", "2", "1", "1" ]
[ "nonn", "tabl" ]
7
1
1
[ "A006338", "A378282", "A378396", "A378397", "A378398", "A378399", "A378401" ]
null
Clark Kimberling, Dec 21 2024
2025-01-11T04:10:55
oeisdata/seq/A378/A378401.seq
d9cd879d4416538226372673ddbaa5d3
A378402
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+3*k,n).
[ "1", "5", "49", "533", "6081", "71365", "853105", "10331221", "126321409", "1556044805", "19280812849", "240054516245", "3000687934401", "37634567169477", "473365023172209", "5968699720282453", "75422513665403905", "954877942305602053", "12109526474814388273", "153801537443722913813", "1956059583033416379841" ]
[ "nonn" ]
10
0
2
[ "A001850", "A243116", "A378378", "A378402" ]
null
Seiichi Manyama, Nov 25 2024
2024-11-27T15:12:45
oeisdata/seq/A378/A378402.seq
eddeb887de04437c6ac64b96f39d0478
A378403
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+2*k,n-k).
[ "1", "2", "10", "53", "290", "1632", "9349", "54231", "317538", "1872800", "11109520", "66213215", "396181229", "2378362248", "14318234311", "86409741438", "522592913026", "3166515425796", "19218755044816", "116820035092706", "711037336745440", "4333057549362840", "26434747722608191", "161433098212966732" ]
[ "nonn" ]
6
0
2
[ "A000984", "A082759", "A378403", "A378404" ]
null
Seiichi Manyama, Nov 25 2024
2024-11-25T09:07:41
oeisdata/seq/A378/A378403.seq
c6a226c47ebb2443bbc32dadb6666a92
A378404
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+3*k,n-k).
[ "1", "2", "12", "74", "464", "2997", "19704", "131140", "880912", "5960000", "40555117", "277251834", "1902791048", "13101878220", "90468268336", "626202992439", "4343671952768", "30186478566432", "210131106485088", "1464920605002240", "10226302297174509", "71474029751497258", "500097817634501780" ]
[ "nonn" ]
7
0
2
[ "A000984", "A082759", "A378403", "A378404" ]
null
Seiichi Manyama, Nov 25 2024
2024-11-25T09:07:45
oeisdata/seq/A378/A378404.seq
0881bdf0ff60f9273ae980c6b52a5c56
A378405
a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(n+k,n-2*k).
[ "1", "1", "3", "13", "47", "171", "651", "2507", "9703", "37831", "148393", "584673", "2312267", "9174179", "36500257", "145566333", "581746503", "2329206823", "9341025429", "37516150599", "150874376997", "607479424817", "2448608334087", "9879562243961", "39897969991075", "161260133795371" ]
[ "nonn" ]
9
0
3
[ "A001850", "A005725", "A082759", "A378405", "A378406" ]
null
Seiichi Manyama, Nov 25 2024
2024-11-25T07:35:39
oeisdata/seq/A378/A378405.seq
f7392a896202110c5ab17ec3cfdc1014
A378406
a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(n+2*k,n-2*k).
[ "1", "1", "3", "16", "67", "266", "1116", "4803", "20707", "89665", "390868", "1712283", "7527664", "33196606", "146800811", "650724896", "2890442051", "12862496583", "57331583055", "255915024714", "1143845768892", "5118643987872", "22930389117771", "102824420890590", "461502269341936", "2073064313021416" ]
[ "nonn" ]
7
0
3
[ "A005725", "A378405", "A378406" ]
null
Seiichi Manyama, Nov 25 2024
2024-11-25T09:07:49
oeisdata/seq/A378/A378406.seq
0bb6cb0c21ce7b46ee70c4b0e732a3bb
A378407
a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(n+2*k,n-3*k).
[ "1", "1", "1", "4", "25", "106", "352", "1114", "3865", "14539", "54886", "201763", "732568", "2679535", "9917818", "36903049", "137265337", "510201961", "1898730307", "7082472358", "26468394430", "99026247688", "370771000975", "1389387381691", "5211329801272", "19564292736706", "73504888190371", "276350941918741" ]
[ "nonn" ]
5
0
4
[ "A228960", "A378407" ]
null
Seiichi Manyama, Nov 25 2024
2024-11-25T09:07:54
oeisdata/seq/A378/A378407.seq
96d84fdd4ed9b74bf03086b0c8fd0d18
A378408
Decimal expansion of Pi^5/90.
[ "3", "4", "0", "0", "2", "1", "8", "7", "1", "9", "8", "3", "6", "4", "6", "0", "5", "9", "1", "8", "0", "8", "2", "3", "6", "7", "7", "8", "2", "6", "0", "3", "9", "5", "6", "2", "7", "5", "5", "8", "8", "9", "6", "7", "4", "0", "3", "1", "1", "9", "4", "4", "3", "3", "9", "4", "8", "3", "2", "4", "9", "3", "7", "4", "2", "9", "1", "4", "9", "9", "9", "1", "2", "5", "9", "5", "7", "1", "1", "3", "8", "3", "1", "7", "5", "3", "7", "2", "2", "2" ]
[ "nonn", "cons", "easy" ]
15
1
1
[ "A000796", "A013662", "A092731", "A279037", "A378408" ]
null
Paolo Xausa, Nov 25 2024
2024-12-01T03:41:03
oeisdata/seq/A378/A378408.seq
a6bbe2d2c047fd74ad36d7d16ca3ca83
A378409
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n*k,k) / ((n-1)*k+1).
[ "1", "0", "1", "5", "73", "1409", "36601", "1198798", "47594289", "2225255777", "119896198381", "7320401163591", "499766786359501", "37739036987427515", "3123975386959740223", "281348109008473891049", "27391364013973766381281", "2866934827195653717595713", "321048532728871544387444869", "38303867032042004479765603315" ]
[ "nonn" ]
9
0
4
[ "A346668", "A378326", "A378327", "A378409", "A378410" ]
null
Vaclav Kotesovec, Nov 25 2024
2024-11-27T07:13:52
oeisdata/seq/A378/A378409.seq
bd27acff7fb497e9bbf405b8018d76e2
A378410
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,k-1) * binomial(n*k,k) / ((n-1)*k+1).
[ "1", "1", "1", "7", "85", "1581", "40006", "1288729", "50578445", "2344950745", "125538581926", "7626452229331", "518557071012696", "39027861427630167", "3221686807607369921", "289464281567009809303", "28124498248184961490621", "2938498159807193630239281", "328556126358414341918608978" ]
[ "nonn" ]
5
0
4
[ "A349364", "A378326", "A378327", "A378409", "A378410" ]
null
Vaclav Kotesovec, Nov 25 2024
2024-11-27T07:14:56
oeisdata/seq/A378/A378410.seq
7f37bbc9d3c1f333210f7ba341ac6192
A378411
G.f. A(x) satisfies A(x) = ( 1 + x * (1 + x*A(x)^(3/2)) )^2.
[ "1", "2", "3", "8", "19", "50", "137", "380", "1088", "3152", "9270", "27576", "82794", "250700", "764454", "2345688", "7237318", "22438988", "69876356", "218456216", "685400835", "2157396738", "6810801959", "21559694364", "68417766207", "217617573110", "693655532081", "2215401956720", "7088605614314", "22720370822508" ]
[ "nonn" ]
20
0
2
[ "A019497", "A371607", "A371608", "A378411" ]
null
Seiichi Manyama, Dec 08 2024
2024-12-08T10:19:32
oeisdata/seq/A378/A378411.seq
a76a1d5047756a8b2acbb99d69e1cc14
A378412
Irregular triangle read by rows: T(n,k) is the coefficient of x^k in the domination polynomial of the n X n grid graph (n>=1, A104519(n+2)<=k<=n^2).
[ "1", "6", "4", "1", "10", "57", "98", "80", "36", "9", "1", "2", "40", "554", "2484", "5494", "7268", "6402", "3964", "1760", "556", "120", "16", "1", "22", "1545", "22594", "140304", "492506", "1126091", "1823057", "2204694", "2063202", "1528544", "908623", "435832", "168426", "51953", "12550", "2296", "300", "25", "1", "288", "20896", "478624" ]
[ "nonn", "tabf", "hard" ]
8
1
2
[ "A000290", "A104519", "A133515", "A378412" ]
null
Eric W. Weisstein, Nov 25 2024
2024-11-26T09:32:11
oeisdata/seq/A378/A378412.seq
29f4394315e5c467f631c2df2affa88c
A378413
Irregular triangle read by rows: T(n,k) is the coefficient of x^k in the domination polynomial of the n-prism graph (n>=1, A004524(n+2)<=k<=2*n).
[ "2", "1", "6", "4", "1", "9", "20", "15", "6", "1", "4", "24", "62", "56", "28", "8", "1", "10", "85", "192", "200", "120", "45", "10", "1", "51", "288", "618", "696", "483", "220", "66", "12", "1", "14", "210", "966", "2018", "2408", "1862", "987", "364", "91", "14", "1", "4", "80", "824", "3248", "6646", "8304", "6992", "4176", "1804", "560", "120", "16", "1", "18", "405" ]
[ "nonn", "tabf" ]
17
1
1
[ "A004524", "A005843", "A284702", "A378413" ]
null
Eric W. Weisstein, Nov 25 2024
2024-11-26T09:32:15
oeisdata/seq/A378/A378413.seq
aa0fbc8f552a2cc4301c52156130d295
A378414
Sum of the integers from 1 to n that are not antidivisors of n.
[ "1", "3", "4", "7", "10", "17", "18", "28", "37", "41", "54", "65", "72", "89", "102", "122", "125", "143", "172", "186", "209", "217", "242", "277", "286", "327", "336", "360", "411", "429", "454", "470", "513", "565", "578", "634", "653", "671", "728", "765", "820", "837", "890", "950", "949", "1023", "1068", "1120", "1153", "1195", "1284", "1284", "1343", "1433" ]
[ "nonn", "easy" ]
9
1
2
[ "A000217", "A024816", "A066417", "A378414" ]
null
Paolo P. Lava, Nov 25 2024
2024-12-03T15:10:36
oeisdata/seq/A378/A378414.seq
691c0673909807a14b81b12e7ea62259
A378415
Primes with repeated digits that remain prime when any two of the same-valued digits are deleted.
[ "113", "131", "151", "211", "223", "227", "233", "277", "311", "337", "353", "373", "443", "557", "577", "599", "727", "733", "757", "773", "883", "887", "929", "997", "1009", "1013", "1021", "1031", "1051", "1103", "1117", "1123", "1129", "1153", "1171", "1213", "1223", "1229", "1231", "1291", "1373", "1399", "1447", "1471", "1531", "1553", "1559", "1663", "1667", "1669", "1733", "1777" ]
[ "nonn", "base" ]
23
1
1
[ "A051362", "A226108", "A378081", "A378415" ]
null
Enrique Navarrete, Nov 25 2024
2024-12-03T12:48:44
oeisdata/seq/A378/A378415.seq
ec37a3e009cd330a5142aa23d1bdd517
A378416
Number of fixed site animals with n nodes on the nodes of the rhombille tiling.
[ "3", "6", "21", "73", "273", "1049", "4117", "16416", "66263", "270211", "1111443", "4605575", "19204920", "80515734", "339137432", "1434319849" ]
[ "nonn", "hard", "more" ]
14
1
1
[ "A001168", "A001207", "A001420", "A196991", "A196992", "A196993", "A197158", "A197160", "A197461", "A197464", "A197467", "A378416" ]
null
Johann Peters, Nov 25 2024
2024-12-17T11:18:16
oeisdata/seq/A378/A378416.seq
26e78cf1408c789f929699d6bad3a364
A378417
a(n) is the least k such that A127064(k) = n.
[ "0", "1", "2", "3", "4", "17", "24", "62", "68", "162", "169", "176", "183", "188", "369", "694", "897", "988", "1027", "4183", "5510", "6063", "6341", "6444", "6465", "25787", "32844", "37722", "38811", "39450", "151679", "200946", "226703", "240056", "248947", "430398", "612633", "633473", "635344", "637227", "637237", "637256", "637306", "1095790", "1353912", "1554970", "7045573" ]
[ "nonn" ]
6
1
3
[ "A004648", "A127064", "A378417" ]
null
Robert Israel, Nov 25 2024
2024-11-28T11:09:00
oeisdata/seq/A378/A378417.seq
43fc8784355ede9e5943d13777685608
A378418
Irregular triangle read by rows: T(n,k) is the coefficient of x^k in the domination polynomial of the n X n torus grid graph (n>=1, A094087(n)<=k<=n^2).
[ "1", "6", "4", "1", "48", "117", "126", "84", "36", "9", "1", "40", "560", "2736", "6800", "10310", "10560", "7832", "4352", "1820", "560", "120", "16", "1", "10", "200", "3050", "31525", "188700", "677690", "1610700", "2740775", "3527075", "3562700", "2895610", "1923600", "1053175", "475950", "176600", "53105", "12650", "2300", "300", "25", "1", "18" ]
[ "nonn", "tabf", "hard" ]
7
1
2
[ "A000290", "A094087", "A303334", "A378418" ]
null
Eric W. Weisstein, Nov 25 2024
2024-11-26T09:32:06
oeisdata/seq/A378/A378418.seq
8ef2212b4936f1d1c31ad7c19478ed79
A378419
Positive integers in A376842, sorted according to their appearance in that sequence.
[ "8", "46", "6248", "5", "4268", "2684", "6842", "2", "4", "64", "28", "2486", "4862", "8426", "82", "6", "8624", "9", "3971", "7931", "19" ]
[ "nonn", "fini", "more" ]
14
1
1
[ "A317905", "A372490", "A373387", "A376842", "A378419" ]
null
Marco Ripà, Nov 25 2024
2024-12-27T11:13:36
oeisdata/seq/A378/A378419.seq
855f0a4e946bd6f4509d56bfe10c73e4
A378420
Irregular triangle read by rows: T(n,k) is the coefficient of x^k in the domination polynomial of the n X n king graph (n>=1, A075561(n)<=k<=n^2).
[ "1", "4", "6", "4", "1", "1", "10", "48", "106", "122", "84", "36", "9", "1", "256", "1536", "4480", "8320", "10896", "10560", "7744", "4320", "1816", "560", "120", "16", "1", "79", "1593", "14672", "81524", "307244", "842506", "1764068", "2918828", "3909834", "4311034", "3955232", "3038092", "1957940", "1056965", "475304", "176256", "53046", "12646" ]
[ "nonn", "tabf", "hard" ]
7
1
2
[ "A000290", "A075561", "A133791", "A378420" ]
null
Eric W. Weisstein, Nov 25 2024
2024-11-26T09:31:54
oeisdata/seq/A378/A378420.seq
d01212951a96d1393f7d0e53d2e014be
A378421
Positive integers in A376446 sorted according to their appearance in that sequence.
[ "8", "64", "2486", "5", "4268", "8426", "2", "4", "4862", "46", "82", "6248", "6842", "8624", "2684", "28", "6", "9", "7139", "3179", "19", "1397", "1793", "91", "3971", "7931", "9713", "9317" ]
[ "nonn", "fini", "more" ]
23
2
1
[ "A000007", "A018247", "A018248", "A063006", "A091661", "A091663", "A091664", "A120817", "A120818", "A290372", "A290373", "A290374", "A290375", "A317905", "A370211", "A372490", "A373387", "A376446", "A376842", "A377124", "A378421" ]
null
Marco Ripà, Nov 25 2024
2024-12-27T11:13:25
oeisdata/seq/A378/A378421.seq
929c013c8368a4a93780ee159a58dd70
A378422
Primes of the form floor(k*log(k)).
[ "3", "5", "13", "19", "23", "29", "59", "97", "271", "281", "307", "313", "383", "421", "443", "449", "499", "557", "691", "709", "727", "733", "739", "751", "757", "769", "787", "947", "953", "971", "1009", "1021", "1091", "1097", "1103", "1129", "1231", "1237", "1283", "1289", "1321", "1367", "1373", "1399", "1439", "1511", "1531", "1571", "1597" ]
[ "nonn" ]
6
1
1
[ "A050504", "A066928", "A378422" ]
null
Tristan M. Phillips, Nov 25 2024
2024-12-12T23:09:01
oeisdata/seq/A378/A378422.seq
c8e28353d8df770af8e775e91801c820
A378423
a(n) is the number of distinct terms reached by iterating the function f(x) = 2 + A008472(x), starting from x=n.
[ "3", "2", "4", "1", "3", "4", "3", "2", "3", "4", "7", "4", "6", "8", "5", "2", "7", "4", "6", "4", "5", "6", "5", "4", "4", "8", "4", "8", "5", "5", "4", "2", "3", "6", "9", "4", "6", "6", "5", "4", "7", "9", "6", "6", "5", "5", "5", "4", "4", "4", "7", "8", "6", "4", "5", "8", "5", "4", "7", "5", "6", "10", "5", "2", "5", "5", "10", "6", "9", "3", "7", "4", "6", "8", "5", "6", "5", "5", "5", "4", "4", "6", "6", "9", "5", "6", "7", "6", "8", "5", "7", "5", "5", "8", "9", "4", "4", "8", "3", "4" ]
[ "nonn" ]
12
1
1
[ "A008472", "A378423" ]
null
Rafik Khalfi, Nov 25 2024
2024-12-12T23:16:25
oeisdata/seq/A378/A378423.seq
998d1fed8d426278ab52f3888ea50ee5
A378424
Product_{n>=1} (1+x^n)^a(n) = Sum_{k>=0} C(k)*x^k, where C(k) = A000108(k).
[ "1", "2", "3", "10", "25", "78", "245", "810", "2700", "9250", "32065", "112710", "400023", "1432858", "5170575", "18784170", "68635477", "252088416", "930138521", "3446167850", "12815663595", "47820447026", "178987624513", "671825132838", "2528212128750", "9536895064398", "36054433807398", "136583761444354", "518401146543811", "1971076361996550", "7506908923471953", "28634752211620266" ]
[ "nonn" ]
27
1
2
[ "A000108", "A157161", "A179277", "A327937", "A378424" ]
null
Thomas Scheuerle, Nov 26 2024
2024-12-06T11:16:31
oeisdata/seq/A378/A378424.seq
17ed53de83452a2c99441d4044dfa8bf
A378425
Expansion of (1/x) * Series_Reversion( x / (1 + x + x^2 * (1 + x)^3) ).
[ "1", "1", "2", "7", "24", "82", "297", "1121", "4317", "16900", "67185", "270480", "1100122", "4513809", "18661618", "77666327", "325117967", "1368001765", "5782686120", "24545144206", "104573104040", "447036252525", "1916918691196", "8243075111450", "35538551601880", "153584392913986", "665201585797986", "2887012910233897" ]
[ "nonn" ]
12
0
3
[ "A036765", "A300048", "A378406", "A378425", "A378426", "A378427" ]
null
Seiichi Manyama, Nov 25 2024
2024-11-26T09:32:22
oeisdata/seq/A378/A378425.seq
fc185b514bd1e2b8dea44ab6b1854520
A378426
Expansion of (1/x) * Series_Reversion( x / (1 + x + x^2 * (1 + x)^2) ).
[ "1", "1", "2", "6", "18", "56", "184", "624", "2161", "7621", "27283", "98869", "361967", "1336843", "4974763", "18634683", "70207751", "265874119", "1011475368", "3863846328", "14814818017", "56994831109", "219941836172", "851138940402", "3302281633591", "12842844277471", "50056915575566", "195503017533502" ]
[ "nonn" ]
11
0
3
[ "A036765", "A378405", "A378425", "A378426" ]
null
Seiichi Manyama, Nov 25 2024
2024-11-26T09:32:25
oeisdata/seq/A378/A378426.seq
191d9b904dcb5e7ff83a2fa71fce8503
A378427
Expansion of (1/x) * Series_Reversion( x / (1 + x + x^3 * (1 + x)^3) ).
[ "1", "1", "1", "2", "8", "29", "88", "253", "775", "2575", "8797", "29833", "100635", "342408", "1181727", "4120223", "14435969", "50738813", "179038408", "634696939", "2259677734", "8072923814", "28924907573", "103915759961", "374302237154", "1351541722226", "4891132336481", "17736792240766", "64440831300682" ]
[ "nonn" ]
13
0
4
[ "A198951", "A300048", "A378407", "A378425", "A378427" ]
null
Seiichi Manyama, Nov 25 2024
2024-11-26T03:00:20
oeisdata/seq/A378/A378427.seq
616606e333870e3148386d7f56491ef3
A378428
Composites that become prime when any two of their digits are deleted.
[ "222", "225", "232", "235", "237", "252", "253", "255", "272", "273", "275", "322", "323", "325", "327", "332", "333", "335", "352", "355", "357", "372", "375", "377", "522", "525", "527", "532", "533", "535", "537", "552", "553", "555", "572", "573", "575", "722", "723", "725", "732", "735", "737", "752", "753", "755", "772", "775", "777", "1111", "1113", "1119", "1131", "1137", "1173", "1179", "1197", "1311", "1317", "1371" ]
[ "nonn", "base" ]
12
1
1
[ "A002275", "A002808", "A004023", "A061371", "A378081", "A378428" ]
null
Enrique Navarrete, Nov 26 2024
2024-12-03T12:48:52
oeisdata/seq/A378/A378428.seq
1ac1965e75baa39c23cf26dcbefd7a0f
A378429
Numbers k such that the prime gap between the consecutive primes p1 < k# = primorial(k) < p2 sets a new record.
[ "3", "7", "13", "17", "23", "29", "37", "43", "47", "61", "71", "79", "83", "97", "101", "109", "137", "193", "347", "349", "409", "457", "587", "599", "887", "929", "967", "1319", "1801", "1877", "2081", "2687", "2731", "2741", "2843", "2939", "2957", "3673", "3823", "4621", "5717", "6011", "6151", "6563", "6863", "7393", "8389", "9833", "11903", "12547" ]
[ "nonn" ]
44
1
1
[ "A001223", "A034386", "A058044", "A350100", "A378429" ]
null
Jean-Marc Rebert, Dec 20 2024
2024-12-23T04:39:49
oeisdata/seq/A378/A378429.seq
fbbb469f9b06be53f0c0637e2f58bb74
A378430
a(n) = Sqrt(A378984(n)).
[ "180", "252", "300", "360", "396", "450", "468", "504", "540", "588", "600", "612", "684", "700", "720", "756", "792", "828", "882", "900", "936", "980", "1008", "1044", "1080", "1100", "1116", "1176", "1188", "1200", "1224", "1260", "1300", "1332", "1350", "1368", "1400", "1404", "1440", "1452", "1476", "1500", "1512", "1548", "1575", "1584", "1620", "1656" ]
[ "nonn", "easy" ]
18
1
1
[ "A126706", "A286708", "A350372", "A378430", "A378984" ]
null
Michael De Vlieger, Dec 23 2024
2024-12-23T21:58:59
oeisdata/seq/A378/A378430.seq
616265a7813ce8386c795063344dbd51
A378431
Number of cyclic edge cuts in the n-barbell graph.
[ "1", "727", "580369" ]
[ "nonn", "bref", "more" ]
4
3
2
null
null
Eric W. Weisstein, Nov 26 2024
2024-11-26T09:30:55
oeisdata/seq/A378/A378431.seq
0a5eda6d1695dc0d8b35e867ed5783be
A378432
Dirichlet inverse of A296075, where A296075 is the sum of deficiencies of divisors of n.
[ "1", "-2", "-3", "1", "-5", "8", "-7", "0", "1", "12", "-11", "-3", "-13", "16", "17", "0", "-17", "-4", "-19", "-5", "23", "24", "-23", "2", "1", "28", "-1", "-7", "-29", "-44", "-31", "0", "35", "36", "37", "5", "-37", "40", "41", "2", "-41", "-60", "-43", "-11", "-7", "48", "-47", "4", "1", "-8", "53", "-13", "-53", "0", "57", "2", "59", "60", "-59", "25", "-61", "64", "-9", "0", "67", "-92", "-67", "-17", "71", "-92", "-71", "6", "-73", "76", "-9", "-19", "79" ]
[ "sign" ]
8
1
2
[ "A033879", "A296075", "A323910", "A378432" ]
null
Antti Karttunen, Nov 26 2024
2024-11-26T15:21:56
oeisdata/seq/A378/A378432.seq
4f1214c1ab002e17efe3c795035d93e6
A378433
Dirichlet inverse of A325973, where A325973 is the arithmetic mean of {sum of unitary divisors} and {sum of squarefree divisors}.
[ "1", "-3", "-4", "5", "-6", "12", "-8", "-9", "9", "18", "-12", "-20", "-14", "24", "24", "15", "-18", "-27", "-20", "-30", "32", "36", "-24", "36", "20", "42", "-24", "-40", "-30", "-72", "-32", "-27", "48", "54", "48", "42", "-38", "60", "56", "54", "-42", "-96", "-44", "-60", "-54", "72", "-48", "-60", "35", "-60", "72", "-70", "-54", "72", "72", "72", "80", "90", "-60", "120", "-62", "96", "-72", "45", "84", "-144", "-68", "-90", "96", "-144", "-72", "-72" ]
[ "sign" ]
6
1
2
[ "A034448", "A048111", "A048250", "A325973", "A378433", "A378434" ]
null
Antti Karttunen, Nov 26 2024
2024-11-26T15:21:39
oeisdata/seq/A378/A378433.seq
8c233a9ce558f1bace55f86414265076
A378434
Arithmetic mean between the Dirichlet inverses of {sum of unitary divisors} and {sum of squarefree divisors}.
[ "1", "-3", "-4", "5", "-6", "12", "-8", "-9", "9", "18", "-12", "-20", "-14", "24", "24", "16", "-18", "-27", "-20", "-30", "32", "36", "-24", "36", "20", "42", "-24", "-40", "-30", "-72", "-32", "-30", "48", "54", "48", "48", "-38", "60", "56", "54", "-42", "-96", "-44", "-60", "-54", "72", "-48", "-64", "35", "-60", "72", "-70", "-54", "72", "72", "72", "80", "90", "-60", "120", "-62", "96", "-72", "56", "84", "-144", "-68", "-90", "96", "-144", "-72", "-90" ]
[ "sign" ]
6
1
2
[ "A034448", "A048111", "A048250", "A158523", "A178450", "A325973", "A378433", "A378434", "A378435" ]
null
Antti Karttunen, Nov 26 2024
2024-11-26T17:14:17
oeisdata/seq/A378/A378434.seq
32fa905d83cbcbbded7c7570165c7732
A378435
Dirichlet inverse of the arithmetic mean between the Dirichlet inverses of {sum of unitary divisors} and {sum of squarefree divisors}.
[ "1", "3", "4", "4", "6", "12", "8", "6", "7", "18", "12", "16", "14", "24", "24", "9", "18", "21", "20", "24", "32", "36", "24", "24", "16", "42", "16", "32", "30", "72", "32", "15", "48", "54", "48", "25", "38", "60", "56", "36", "42", "96", "44", "48", "42", "72", "48", "36", "29", "48", "72", "56", "54", "48", "72", "48", "80", "90", "60", "96", "62", "96", "56", "24", "84", "144", "68", "72", "96", "144", "72", "33", "74", "114", "64", "80", "96", "168", "80", "54", "34" ]
[ "sign" ]
7
1
2
[ "A034448", "A048111", "A048250", "A158523", "A178450", "A325973", "A378433", "A378434", "A378435" ]
null
Antti Karttunen, Nov 26 2024
2024-11-26T17:14:21
oeisdata/seq/A378/A378435.seq
8749a7bfba4e7137bcbaf81ecf10a52e
A378436
Inverse Möbius transform of A033630, where A033630 is the number of partitions of n into distinct divisors of n.
[ "1", "2", "2", "3", "2", "5", "2", "4", "3", "4", "2", "9", "2", "4", "4", "5", "2", "9", "2", "7", "4", "4", "2", "16", "3", "4", "4", "7", "2", "12", "2", "6", "4", "4", "4", "21", "2", "4", "4", "12", "2", "11", "2", "6", "6", "4", "2", "28", "3", "6", "4", "6", "2", "14", "4", "11", "4", "4", "2", "53", "2", "4", "6", "7", "4", "11", "2", "6", "4", "8", "2", "60", "2", "4", "6", "6", "4", "10", "2", "20", "5", "4", "2", "43", "4", "4", "4", "9", "2", "41", "4", "6", "4", "4", "4", "51", "2", "6", "6", "12" ]
[ "nonn" ]
11
1
2
[ "A000005", "A005231", "A033630", "A099774", "A378436", "A378438" ]
null
Antti Karttunen, Nov 26 2024
2024-11-26T20:59:30
oeisdata/seq/A378/A378436.seq
3a1ed2cea71f517de67019a5cc74da05
A378437
Dirichlet inverse of A033630, where A033630 is the number of partitions of n into distinct divisors of n.
[ "1", "-1", "-1", "0", "-1", "0", "-1", "0", "0", "1", "-1", "0", "-1", "1", "1", "0", "-1", "0", "-1", "-1", "1", "1", "-1", "-2", "0", "1", "0", "-1", "-1", "-2", "-1", "0", "1", "1", "1", "-2", "-1", "1", "1", "-1", "-1", "-1", "-1", "0", "0", "1", "-1", "-2", "0", "0", "1", "0", "-1", "0", "1", "0", "1", "1", "-1", "-26", "-1", "1", "0", "0", "1", "-1", "-1", "0", "1", "-1", "-1", "-14", "-1", "1", "0", "0", "1", "0", "-1", "-1", "0", "1", "-1", "-19", "1", "1", "1", "-1", "-1", "-17", "1", "0", "1", "1", "1" ]
[ "sign" ]
7
1
24
[ "A033630", "A378437", "A378438" ]
null
Antti Karttunen, Nov 26 2024
2024-11-26T20:59:34
oeisdata/seq/A378/A378437.seq
bd1350be49abf5bee7d054366b2be246
A378438
Dirichlet inverse of A378436, where A378436 is the inverse Möbius transform of the number of partitions of n into distinct divisors of n.
[ "1", "-2", "-2", "1", "-2", "3", "-2", "0", "1", "4", "-2", "-1", "-2", "4", "4", "0", "-2", "-1", "-2", "-3", "4", "4", "-2", "-2", "1", "4", "0", "-3", "-2", "-8", "-2", "0", "4", "4", "4", "-2", "-2", "4", "4", "0", "-2", "-7", "-2", "-2", "-2", "4", "-2", "0", "1", "-2", "4", "-2", "-2", "0", "4", "1", "4", "4", "-2", "-21", "-2", "4", "-2", "0", "4", "-7", "-2", "-2", "4", "-8", "-2", "-10", "-2", "4", "-2", "-2", "4", "-6", "-2", "0", "0", "4", "-2", "-15", "4", "4", "4", "-1", "-2" ]
[ "sign" ]
7
1
2
[ "A008683", "A033630", "A378436", "A378437", "A378438" ]
null
Antti Karttunen, Nov 26 2024
2024-11-26T20:59:39
oeisdata/seq/A378/A378438.seq
81b045ad5a5c7a7ff7e93d4be87d6913
A378439
Möbius transform of A033630, where A033630 is the number of partitions of n into distinct divisors of n.
[ "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "3", "0", "0", "0", "1", "0", "2", "0", "0", "0", "0", "0", "4", "0", "0", "0", "2", "0", "1", "0", "0", "0", "0", "0", "5", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "29", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "21", "0", "0", "0", "0", "0", "0", "0", "3", "0", "0", "0", "21", "0", "0", "0", "1", "0", "19", "0", "0", "0", "0", "0", "11", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "12" ]
[ "nonn" ]
6
1
24
[ "A008683", "A033630", "A378439", "A378440" ]
null
Antti Karttunen, Nov 27 2024
2024-11-27T15:56:43
oeisdata/seq/A378/A378439.seq
52644d339e0649a36384bebcae28a509
A378440
Dirichlet inverse of Möbius transform of A033630, where A033630 is the number of partitions of n into distinct divisors of n.
[ "1", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "-3", "0", "0", "0", "-1", "0", "-2", "0", "0", "0", "0", "0", "-3", "0", "0", "0", "-2", "0", "-1", "0", "0", "0", "0", "0", "-5", "0", "0", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "-29", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "-19", "0", "0", "0", "0", "0", "0", "0", "-3", "0", "0", "0", "-21", "0", "0", "0", "-1", "0", "-19", "0", "0", "0", "0", "0", "-11", "0", "0", "0", "-1" ]
[ "sign" ]
8
1
24
[ "A033630", "A378437", "A378439", "A378440" ]
null
Antti Karttunen, Nov 27 2024
2024-11-27T15:56:47
oeisdata/seq/A378/A378440.seq
e0e0c764b35871995b204d532d55daf9
A378441
Fixed points of A378226, where A278226 is XOR-Moebius transform of A318457, and A318457(n) = n XOR (sigma(n)-n).
[ "1", "2", "3", "4", "5", "7", "8", "11", "13", "16", "17", "19", "23", "27", "29", "31", "32", "37", "41", "43", "47", "53", "59", "61", "64", "67", "71", "73", "79", "83", "89", "97", "101", "103", "107", "109", "113", "125", "127", "128", "131", "137", "139", "149", "151", "157", "163", "167", "173", "179", "181", "191", "193", "197", "199", "211", "223", "227", "229", "233", "239", "241", "243", "251", "256", "257", "263", "269", "271", "277", "281" ]
[ "nonn" ]
9
1
2
[ "A000040", "A001065", "A003987", "A318457", "A378226", "A378441" ]
null
Antti Karttunen, Nov 26 2024
2024-11-26T15:21:42
oeisdata/seq/A378/A378441.seq
5594e54c4b3db018410bca1dc8eeabe5
A378442
Characteristic function of stable numbers: a(n) = 1 if the distinct prime indices of n are pairwise indivisible, otherwise 0.
[ "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1" ]
[ "nonn" ]
7
1
null
[ "A000720", "A316476", "A327394", "A378442" ]
null
Antti Karttunen, Nov 27 2024
2024-11-27T15:56:39
oeisdata/seq/A378/A378442.seq
ca24eb1ff3a574b9a81bc26452c522a2
A378443
Inverse Möbius transform of A372573.
[ "1", "1", "1", "1", "2", "2", "2", "2", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "3", "3", "2", "2", "2", "2", "4", "2", "2", "2", "2", "4", "3", "2", "2", "2", "4", "2", "4", "2", "2", "2", "2", "2", "4", "3", "3", "2", "2", "2", "3", "4", "4", "2", "2", "2", "4", "2", "2", "2", "3", "4", "4", "2", "2", "2", "4", "2", "4", "2", "2", "3", "2", "4", "4", "2", "4", "2", "2", "2", "4", "4", "2", "2", "4", "2", "4", "4", "2", "2", "2", "4", "4", "2", "3", "2", "3", "2", "4", "2", "4", "4" ]
[ "nonn" ]
8
1
5
[ "A174273", "A339746", "A372573", "A378443", "A378444" ]
null
Antti Karttunen, Nov 27 2024
2024-11-27T17:56:10
oeisdata/seq/A378/A378443.seq
a7e2cb734d80ccc992a9c722fef17ec4
A378444
a(n) is the number of divisors d of n such that A083345(d) is even, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "2", "2", "1", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "3", "1", "1", "2", "2", "1", "2", "1", "2", "3", "1", "1", "3", "2", "2", "2", "2", "1", "2", "2", "2", "2", "1", "1", "4", "1", "1", "3", "2", "2", "2", "1", "2", "2", "2", "1", "3", "1", "1", "3", "2", "2", "2", "1", "3", "3", "1", "1", "4", "2", "1", "2", "2", "1", "3", "2", "2", "2", "1", "2", "3", "1", "2", "3", "3", "1", "2", "1", "2", "4" ]
[ "nonn" ]
7
1
9
[ "A000005", "A369001", "A369002", "A369257", "A378444", "A378445" ]
null
Antti Karttunen, Nov 27 2024
2024-11-27T17:56:14
oeisdata/seq/A378/A378444.seq
15b529944d3f45dfc6dfc03352e2482a
A378445
a(n) is the number of divisors d of n such that A083345(d) is odd, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).
[ "0", "1", "1", "2", "1", "3", "1", "3", "1", "3", "1", "4", "1", "3", "2", "3", "1", "4", "1", "4", "2", "3", "1", "6", "1", "3", "2", "4", "1", "6", "1", "4", "2", "3", "2", "6", "1", "3", "2", "6", "1", "6", "1", "4", "3", "3", "1", "7", "1", "4", "2", "4", "1", "6", "2", "6", "2", "3", "1", "8", "1", "3", "3", "5", "2", "6", "1", "4", "2", "6", "1", "9", "1", "3", "3", "4", "2", "6", "1", "7", "2", "3", "1", "8", "2", "3", "2", "6", "1", "9", "2", "4", "2", "3", "2", "9", "1", "4", "3", "6", "1", "6", "1", "6", "4" ]
[ "nonn" ]
7
1
4
[ "A000005", "A174273", "A369003", "A377874", "A378443", "A378444", "A378445" ]
null
Antti Karttunen, Nov 27 2024
2024-11-27T17:56:18
oeisdata/seq/A378/A378445.seq
08ef25211ea882d352cffaf726c5a751
A378446
Inverse Möbius transform of A083206, where A083206(n) is the number of ways of partitioning the divisors of n into two disjoint sets with equal sum.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "5", "0", "0", "0", "1", "0", "4", "0", "0", "0", "0", "0", "2", "0", "0", "0", "3", "0", "3", "0", "0", "0", "0", "0", "10", "0", "0", "0", "0", "0", "3", "0", "2", "0", "0", "0", "23", "0", "0", "0", "0", "0", "3", "0", "0", "0", "1", "0", "5", "0", "0", "0", "0", "0", "3", "0", "6", "0", "0", "0", "19", "0", "0", "0", "1", "0", "17", "0", "0", "0", "0", "0", "21", "0", "0", "0", "1", "0", "3", "0", "1", "0", "0", "0", "12" ]
[ "nonn" ]
6
1
12
[ "A083206", "A378446" ]
null
Antti Karttunen, Nov 28 2024
2024-11-28T10:49:58
oeisdata/seq/A378/A378446.seq
c9b196b73f224576579e2f5865419a5e
A378447
Difference between {the number of distinct sums of distinct divisors of n} and {the number of distinct sums of distinct proper divisors of n}.
[ "1", "2", "2", "4", "2", "6", "2", "8", "4", "8", "2", "12", "2", "8", "8", "16", "2", "18", "2", "20", "8", "8", "2", "24", "4", "8", "8", "28", "2", "30", "2", "32", "8", "8", "8", "36", "2", "8", "8", "40", "2", "42", "2", "32", "28", "8", "2", "48", "4", "32", "8", "32", "2", "54", "8", "56", "8", "8", "2", "60", "2", "8", "30", "64", "8", "66", "2", "32", "8", "70", "2", "72", "2", "8", "32", "32", "8", "78", "2", "80", "16", "8", "2", "84", "8", "8", "8", "88", "2", "90", "8", "32", "8", "8", "8" ]
[ "nonn" ]
7
1
2
[ "A119347", "A193279", "A378447" ]
null
Antti Karttunen, Nov 29 2024
2024-11-29T12:23:14
oeisdata/seq/A378/A378447.seq
a132692c5b266f8990c27059efa04252
A378448
Characteristic function of A064771: a(n) = 1 if there is exactly one subset of the proper divisors of n that sum to n, otherwise 0.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "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", "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", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn" ]
7
1
null
[ "A033630", "A064771", "A065205", "A065235", "A378448", "A378449" ]
null
Antti Karttunen, Nov 28 2024
2024-11-28T19:17:00
oeisdata/seq/A378/A378448.seq
6440bed90252936c2ff01920ea9337dc
A378449
Characteristic function of A083209: a(n) = 1 if there is exactly one subset of the divisors of n such that the complement has the same sum, otherwise 0.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "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", "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", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn" ]
14
1
null
[ "A083206", "A083209", "A179527", "A378448", "A378449", "A378598" ]
null
Antti Karttunen, Nov 28 2024
2024-12-03T11:45:36
oeisdata/seq/A378/A378449.seq
d1465d8f6216b04b3c7f556f910e819b
A378450
a(n) is the number of positive numbers k <= sigma(n) that are not a sum of any subset of distinct divisors of n.
[ "0", "0", "1", "0", "3", "0", "5", "0", "6", "3", "9", "0", "11", "9", "9", "0", "15", "0", "17", "0", "17", "21", "21", "0", "24", "27", "25", "0", "27", "0", "29", "0", "33", "39", "33", "0", "35", "45", "41", "0", "39", "0", "41", "21", "23", "57", "45", "0", "50", "30", "57", "35", "51", "0", "57", "0", "65", "75", "57", "0", "59", "81", "45", "0", "69", "0", "65", "63", "81", "2", "69", "0", "71", "99", "61", "77", "81", "0", "77", "0", "90", "111", "81", "0", "93", "117", "105" ]
[ "nonn" ]
21
1
5
[ "A000203", "A005153", "A030057", "A119347", "A237287", "A237289", "A322860", "A378450" ]
null
Antti Karttunen, Nov 29 2024
2024-11-29T12:23:02
oeisdata/seq/A378/A378450.seq
3c499a69fe20718c6feaaf04df138cdd
A378451
Dirichlet inverse of A119347, where A119347(n) is the number of distinct sums of distinct divisors of n.
[ "1", "-3", "-3", "2", "-3", "6", "-3", "0", "2", "3", "-3", "5", "-3", "3", "3", "0", "-3", "-6", "-3", "9", "3", "3", "-3", "-12", "2", "3", "0", "-5", "-3", "18", "-3", "0", "3", "3", "3", "13", "-3", "3", "3", "3", "-3", "-6", "-3", "-12", "-4", "3", "-3", "4", "2", "-12", "3", "-12", "-3", "-6", "3", "57", "3", "3", "-3", "-15", "-3", "3", "-8", "0", "3", "-54", "-3", "-12", "3", "-34", "-3", "-39", "-3", "3", "-12", "-12", "3", "-78", "-3", "-24", "0", "3", "-3", "157", "3", "3", "3" ]
[ "sign" ]
6
1
2
[ "A119347", "A378451" ]
null
Antti Karttunen, Nov 29 2024
2024-11-29T15:09:34
oeisdata/seq/A378/A378451.seq
e99d0e38cb968a1108237dbe75d71c81
A378452
Dirichlet inverse of A007875, where A007875(n) = phi(2^omega(n)).
[ "1", "-1", "-1", "0", "-1", "0", "-1", "0", "0", "0", "-1", "1", "-1", "0", "0", "0", "-1", "1", "-1", "1", "0", "0", "-1", "0", "0", "0", "0", "1", "-1", "2", "-1", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "-1", "2", "-1", "1", "1", "0", "-1", "0", "0", "1", "0", "1", "-1", "0", "0", "0", "0", "0", "-1", "0", "-1", "0", "1", "0", "0", "2", "-1", "1", "0", "2", "-1", "-1", "-1", "0", "1", "1", "0", "2", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "-1", "0", "0", "1", "0", "0", "0", "0", "-1", "1", "1", "0" ]
[ "sign" ]
7
1
30
[ "A007875", "A378452", "A378453" ]
null
Antti Karttunen, Nov 29 2024
2024-11-29T21:04:46
oeisdata/seq/A378/A378452.seq
98082719841d52ec0e50c37e73e77bf5
A378453
Dirichlet inverse of A018892, where A018892(n) = (tau(n^2)+1)/2.
[ "1", "-2", "-2", "1", "-2", "3", "-2", "0", "1", "3", "-2", "0", "-2", "3", "3", "0", "-2", "0", "-2", "0", "3", "3", "-2", "-1", "1", "3", "0", "0", "-2", "-2", "-2", "0", "3", "3", "3", "-2", "-2", "3", "3", "-1", "-2", "-2", "-2", "0", "0", "3", "-2", "0", "1", "0", "3", "0", "-2", "-1", "3", "-1", "3", "3", "-2", "-3", "-2", "3", "0", "0", "3", "-2", "-2", "0", "3", "-2", "-2", "0", "-2", "3", "0", "0", "3", "-2", "-2", "0", "0", "3", "-2", "-3", "3", "3", "3", "-1", "-2", "-3", "3", "0", "3", "3", "3" ]
[ "sign" ]
7
1
2
[ "A008683", "A018892", "A378452", "A378453" ]
null
Antti Karttunen, Nov 29 2024
2024-11-29T21:04:50
oeisdata/seq/A378/A378453.seq
701c123c0305f340b70fe3a373f08aea
A378454
Characteristic function of A267124, primitive practical numbers
[ "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "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", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn" ]
8
1
null
[ "A005153", "A008966", "A267124", "A322860", "A378454" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T21:59:53
oeisdata/seq/A378/A378454.seq
0fd323c7b9361018e0d14583597250c8
A378455
Total number of coronal tilings of a width one length n straight polyiamond central frame with a specific hexiamond tile.
[ "1272", "2644", "2684", "3141", "3144", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185", "3184", "3185" ]
[ "nonn", "easy" ]
23
1
1
null
null
Craig Knecht, Nov 26 2024
2025-02-11T07:46:40
oeisdata/seq/A378/A378455.seq
d28b7e810c479052b44f9c132a9b8f97
A378456
Number of composite numbers between consecutive nonprime prime powers (exclusive).
[ "1", "0", "4", "5", "1", "2", "12", "11", "12", "31", "3", "1", "32", "59", "11", "25", "46", "13", "125", "14", "80", "88", "94", "103", "52", "261", "35", "267", "147", "172", "120", "9", "9", "163", "355", "279", "313", "207", "329", "347", "376", "108", "257", "805", "283", "262", "25", "917", "242", "1081", "702", "365", "752", "389", "251", "535", "1679", "877", "447" ]
[ "nonn" ]
8
1
3
[ "A000015", "A000040", "A000961", "A001223", "A002808", "A024619", "A031218", "A046933", "A053607", "A053706", "A053707", "A057820", "A065890", "A067871", "A076259", "A078147", "A080101", "A236575", "A243348", "A246655", "A276781", "A345531", "A361102", "A366833", "A377057", "A377281", "A377282", "A377286", "A377287", "A377288", "A378373", "A378456" ]
null
Gus Wiseman, Nov 30 2024
2024-12-02T15:38:39
oeisdata/seq/A378/A378456.seq
6b1a0ace39e545d175807262fbb78d21
A378457
Difference between n and the greatest prime power <= n, allowing 1.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "2", "0", "0", "1", "0", "1", "2", "3", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "1", "2", "3", "4", "0", "1", "2", "3", "0", "1", "0", "1", "2", "3", "0", "1", "0", "1", "2", "3", "0", "1", "2", "3", "4", "5", "0", "1", "0", "1", "2", "0", "1", "2", "0", "1", "2", "3", "0", "1", "0", "1", "2", "3", "4", "5", "0", "1", "0", "1", "0", "1", "2", "3", "4" ]
[ "nonn" ]
9
1
15
[ "A000015", "A000040", "A000961", "A001223", "A001597", "A007917", "A007918", "A007920", "A010051", "A013632", "A024619", "A031218", "A053607", "A057820", "A064722", "A065514", "A069584", "A070321", "A074984", "A080101", "A081676", "A151800", "A179278", "A246655", "A276781", "A304521", "A361102", "A366833", "A375708", "A375735", "A377051", "A377054", "A377057", "A377281", "A377282", "A377289", "A377468", "A378033", "A378357", "A378363", "A378366", "A378367", "A378370", "A378371", "A378457" ]
null
Gus Wiseman, Nov 29 2024
2024-12-02T18:11:16
oeisdata/seq/A378/A378457.seq
5c1b8cf98b43674cada8eb25e3df3a93
A378458
Squarefree numbers k such that k + 1 is squarefree but k + 2 is not.
[ "2", "6", "10", "14", "22", "30", "34", "38", "42", "46", "58", "61", "66", "70", "73", "78", "82", "86", "94", "102", "106", "110", "114", "118", "122", "130", "133", "138", "142", "145", "154", "158", "166", "173", "178", "182", "186", "190", "194", "202", "205", "210", "214", "218", "222", "226", "230", "238", "246", "254", "258", "262", "266", "273", "277", "282" ]
[ "nonn" ]
10
1
1
[ "A000961", "A006549", "A007674", "A007675", "A013929", "A057820", "A065474", "A067535", "A073247", "A081221", "A120327", "A179384", "A206256", "A236575", "A373415", "A377046", "A378033", "A378039", "A378086", "A378369", "A378373", "A378458" ]
null
Gus Wiseman, Dec 02 2024
2024-12-06T11:29:04
oeisdata/seq/A378/A378458.seq
c419f2597269952af9f11e0bfcb7ed51
A378459
a(n) is the least k such that the concatenation of 2^n-1 and 2^k-1 is prime, or -1 if there is no such k.
[ "1", "1", "1", "1", "1", "1", "3", "1", "2", "13", "3", "11", "5", "5", "2", "1", "6", "1", "3", "1", "25", "5", "9", "7", "6", "3", "11", "3", "2", "17", "2", "99", "31", "15", "3", "19", "6", "9", "1", "1", "5", "23", "9", "1", "11", "15", "5", "11", "26", "9", "2", "35", "17", "43", "17", "61", "11", "21", "13", "139", "3", "13", "25", "17", "14", "1", "2", "21", "19", "9", "3", "5", "6", "177", "41", "39", "2", "73", "22", "9", "31", "3", "2", "89", "179", "21" ]
[ "nonn", "base" ]
12
1
7
[ "A378288", "A378459" ]
null
Robert Israel, Nov 26 2024
2024-12-05T10:47:04
oeisdata/seq/A378/A378459.seq
845fb1b2eace444fd15ec34db06b6d41
A378460
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(2*n+k-1,n-k).
[ "1", "2", "14", "107", "854", "6997", "58337", "492459", "4195910", "36008585", "310797519", "2695146412", "23462692889", "204927930573", "1794924637121", "15759722754487", "138667548834150", "1222405694908165", "10793913082306739", "95452822514557693", "845239550997448559", "7493699336086875984" ]
[ "nonn" ]
11
0
2
[ "A009723", "A378460", "A378461", "A378465" ]
null
Seiichi Manyama, Nov 27 2024
2024-11-27T07:11:52
oeisdata/seq/A378/A378460.seq
90dbd048bbfb27c6778b4ac1824de765
A378461
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(2*n+2*k-1,n-k).
[ "1", "2", "16", "137", "1216", "11057", "102229", "956601", "9032680", "85893860", "821402341", "7891371303", "76105710253", "736364519399", "7144586617597", "69487754788517", "677259385478616", "6613163312601491", "64681617534027028", "633569272646345064", "6214190349161222941", "61023489213944162889" ]
[ "nonn" ]
7
0
2
[ "A009723", "A378460", "A378461", "A378466" ]
null
Seiichi Manyama, Nov 27 2024
2024-11-27T08:06:06
oeisdata/seq/A378/A378461.seq
85805f53e299e41471bc877a7e681aa3
A378462
a(n) = Sum_{k=0..floor(n/2)} binomial(n+k-1,k) * binomial(2*n+k-1,n-2*k).
[ "1", "1", "5", "28", "157", "891", "5126", "29814", "174869", "1032481", "6128795", "36541220", "218672950", "1312712519", "7901609196", "47673716238", "288226881669", "1745734656930", "10590673033931", "64342403492274", "391414638274987", "2383907483199039", "14534764399148966", "88705912126094358" ]
[ "nonn" ]
6
0
3
[ "A002002", "A213684", "A378462", "A378467" ]
null
Seiichi Manyama, Nov 27 2024
2024-11-27T08:06:49
oeisdata/seq/A378/A378462.seq
48addd036930913eb45a68adaf31b79b
A378463
a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(2*n-k-1,n-3*k).
[ "1", "1", "3", "13", "59", "266", "1203", "5489", "25259", "117022", "545038", "2549592", "11970035", "56372460", "266194295", "1259910113", "5975382699", "28390616727", "135108035502", "643891031826", "3072604703774", "14679493913048", "70206875750168", "336103001918788", "1610476039036259", "7723148579525441" ]
[ "nonn" ]
8
0
3
[ "A054515", "A370624", "A378463", "A378464" ]
null
Seiichi Manyama, Nov 27 2024
2024-11-27T08:06:37
oeisdata/seq/A378/A378463.seq
244d97044f6983a8de5cb14a4009a90c
A378464
a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(2*n-1,n-3*k).
[ "1", "1", "3", "13", "63", "306", "1473", "7085", "34239", "166459", "813618", "3994200", "19678233", "97239130", "481740885", "2392004853", "11900655999", "59312062026", "296071376307", "1479998924447", "7407613846698", "37118966710076", "186195636158436", "934889598483048", "4698229684691913", "23629859054461331" ]
[ "nonn" ]
7
0
3
[ "A367413", "A370624", "A378463", "A378464" ]
null
Seiichi Manyama, Nov 27 2024
2024-11-27T08:06:31
oeisdata/seq/A378/A378464.seq
90340e6648c4a6ae58cb9b5735b665f6
A378465
Expansion of (1/x) * Series_Reversion( x * (1 - x - x/(1 - x)) ).
[ "1", "2", "9", "51", "324", "2206", "15737", "116098", "878495", "6780544", "53175176", "422508607", "3394004192", "27518168434", "224899980185", "1850830170355", "15324273361220", "127562500961502", "1066940307951747", "8962213871074848", "75572666059970392", "639485384767169924", "5428457500063304272" ]
[ "nonn" ]
11
0
2
[ "A151374", "A378460", "A378465", "A378466" ]
null
Seiichi Manyama, Nov 27 2024
2024-11-27T07:11:57
oeisdata/seq/A378/A378465.seq
fe18e7308993679bfbc8f69b093d37cd
A378466
Expansion of (1/x) * Series_Reversion( x * (1 - x - x/(1 - x)^2) ).
[ "1", "2", "10", "63", "444", "3351", "26490", "216523", "1815080", "15519271", "134817972", "1186570526", "10557959696", "94817735251", "858333997230", "7823946906726", "71751021314438", "661541649024816", "6128551736153622", "57018343512420580", "532529776531703666", "4991007108135966433" ]
[ "nonn" ]
10
0
2
[ "A151374", "A378461", "A378465", "A378466" ]
null
Seiichi Manyama, Nov 27 2024
2024-11-27T08:06:20
oeisdata/seq/A378/A378466.seq
cc54e7966e06a5c746a75dd3a34af3a1
A378467
Expansion of (1/x) * Series_Reversion( x * (1 - x - x^2/(1 - x)^2) ).
[ "1", "1", "3", "12", "53", "249", "1223", "6207", "32296", "171355", "923583", "5042840", "27834231", "155052721", "870594423", "4921968177", "27995045409", "160080985928", "919731472614", "5306779508096", "30737417720495", "178654274650097", "1041678247875531", "6091298104643577", "35714017347725474" ]
[ "nonn" ]
10
0
3
[ "A001002", "A001003", "A378462", "A378467" ]
null
Seiichi Manyama, Nov 27 2024
2024-11-27T08:06:14
oeisdata/seq/A378/A378467.seq
b73b1be899811f893f1d20c489d5520c
A378468
Coefficients in expansion of (1/E_4)^3.
[ "1", "-720", "339120", "-132039360", "46081214640", "-14974899930720", "4627836408778560", "-1377759164154871680", "398508058352289409200", "-112648427646194257313040", "31252327416307233967209120", "-8536592939398421710286859840", "2301363255613811638678456000320", "-613491781086725734777586106900960" ]
[ "sign" ]
7
0
2
[ "A001943", "A004009", "A287933", "A378468", "A378469" ]
null
Vaclav Kotesovec, Nov 27 2024
2024-11-27T10:04:55
oeisdata/seq/A378/A378468.seq
ce2d49d5762e940aa67a1c4e85818600
A378469
Coefficients in expansion of (1/E_4)^4.
[ "1", "-960", "567360", "-266138880", "108735481920", "-40500351480960", "14114830665358080", "-4678563821426250240", "1491145606587529742400", "-460511820740945555286720", "138585483759128030100927360", "-40812342463218781348220286720", "11800049457060387849887324117760", "-3358272262154871467174772417214080" ]
[ "sign" ]
7
0
2
[ "A001943", "A004009", "A287933", "A289247", "A289319", "A289566", "A295815", "A378468", "A378469" ]
null
Vaclav Kotesovec, Nov 27 2024
2024-11-27T10:04:59
oeisdata/seq/A378/A378469.seq
422955ae8289b6cef31fd0d47f2fa077
A378470
a(n) is the smallest number k for which the width pattern of the symmetric representation of sigma(k), SRS(k), consists of two unimodal parts of maximum width n.
[ "3", "78", "10728", "28920", "53752896", "4157280", "278628512256", "90323520", "1658908800", "21499810560", "7487812494923563008", "13005699840", "155267279705546496147456", "111451576596480", "8599694054400", "468208581120", "4172630516011611848266349543424", "5202323481600", "21630916595004029113587563614961664", "67421367982080" ]
[ "nonn" ]
7
1
1
[ "A003056", "A082662", "A162247", "A235791", "A237270", "A237591", "A237593", "A239929", "A250071", "A341969", "A370206", "A378470" ]
null
Hartmut F. W. Hoft, Nov 27 2024
2024-12-12T23:25:36
oeisdata/seq/A378/A378470.seq
5ad20eff2f86938be76bb6dd560bfe5b
A378471
Numbers m whose symmetric representation of sigma(m), SRS(m), has at least 2 parts the first of which has width 1.
[ "3", "5", "7", "9", "10", "11", "13", "14", "15", "17", "19", "21", "22", "23", "25", "26", "27", "29", "31", "33", "34", "35", "37", "38", "39", "41", "43", "44", "45", "46", "47", "49", "50", "51", "52", "53", "55", "57", "58", "59", "61", "62", "63", "65", "67", "68", "69", "70", "71", "73", "74", "75", "76", "77", "79", "81", "82", "83", "85", "86", "87", "89", "91", "92", "93", "94", "95", "97", "98", "99", "101", "103", "105" ]
[ "nonn" ]
11
1
1
[ "A000079", "A005408", "A091999", "A235791", "A237287", "A237591", "A237593", "A238524", "A246956", "A270298", "A270301", "A341969", "A370206", "A377654", "A378471" ]
null
Hartmut F. W. Hoft, Nov 27 2024
2024-12-12T23:28:44
oeisdata/seq/A378/A378471.seq
c39b3449ed2ac0e66af862fa94ac0208
A378472
Position of start of first run of exactly n zeros in the base-2 representation of Pi, or -1 if no such run exists.
[ "17", "1", "26", "7", "109", "135", "96", "189", "2610", "902", "4267", "36139", "17317", "8375", "479166", "11791", "112954", "436893", "1286743", "726844", "5572140", "27456324", "2005750", "42248747", "200643872", "547151636", "171498580", "469458286", "1222711767", "2151391703", "1407238214" ]
[ "nonn", "base", "more" ]
50
1
1
[ "A004601", "A175945", "A178708", "A233836", "A378472" ]
null
James S. DeArmon, Nov 27 2024
2024-12-23T14:04:37
oeisdata/seq/A378/A378472.seq
72cb522c0ca9e91605b62086616c305f
A378473
The number of n-colorings of the vertices of the truncated octahedron up to rotation and reflection.
[ "0", "1", "355048", "5886817533", "5864336054656", "1241773051013125", "98716454926955496", "3991277735434713913", "98382652674879674368", "1661801013342756245961", "20833333958666683585000", "205202766952229526577141", "1656184328295547539616128", "11308349424395689922231053" ]
[ "nonn" ]
17
0
3
[ "A000332", "A060530", "A128766", "A199406", "A252704", "A252705", "A274900", "A337963", "A378473", "A378474", "A378475", "A378476", "A378477", "A378478" ]
null
Peter Kagey, Nov 27 2024
2024-12-01T03:40:37
oeisdata/seq/A378/A378473.seq
92013bbc1bd92662a4ffe8e4929fbc2f
A378474
The number of n-colorings of the vertices of the truncated cuboctahedron up to rotation and reflection.
[ "0", "1", "5864068667776", "1661800897546646288751", "1650586719047285117763813376", "74014868308343792955106160546875", "467755368903219944377426648894114176", "764653504526960946768130306131125170501", "464598858302721315450530067459906444722176" ]
[ "nonn", "easy" ]
18
0
3
[ "A000332", "A060530", "A128766", "A199406", "A252704", "A252705", "A274900", "A337963", "A378473", "A378474", "A378475", "A378476", "A378477", "A378478" ]
null
Peter Kagey, Nov 27 2024
2024-12-01T03:40:33
oeisdata/seq/A378/A378474.seq
238d15eb07f24a80b9bbf49bd3bee2fb
A378475
The number of n-colorings of the vertices of the snub cube up to rotation.
[ "0", "1", "700688", "11768099013", "11728130343936", "2483526957328125", "197432556580265616", "7982551312716034313", "196765270145344012288", "3323601794975613468921", "41666666667041700250000", "410405528159827444816781", "3312368633477962187301888", "22616698765607508420521013" ]
[ "nonn" ]
21
0
3
[ "A000332", "A060530", "A128766", "A199406", "A252704", "A252705", "A274900", "A337963", "A378473", "A378474", "A378475", "A378476", "A378477", "A378478" ]
null
Peter Kagey, Nov 27 2024
2024-12-09T05:27:56
oeisdata/seq/A378/A378475.seq
70dd53a50c486040089978697245e900
A378476
The number of n-colorings of the vertices of the truncated dodecahedron up to rotation and reflection.
[ "0", "1", "9607679885269312", "353259652293727442874919719", "11076899964874301400431118585745408", "7228014483236696229750911410649667971875", "407280649839077145745380578110103790290896704", "4233515506163528044351709372473136729199352546645" ]
[ "nonn", "easy", "changed" ]
16
0
3
[ "A000332", "A060530", "A128766", "A199406", "A252704", "A252705", "A274900", "A337963", "A378473", "A378474", "A378475", "A378476", "A378477", "A378478" ]
null
Peter Kagey, Nov 27 2024
2025-04-16T12:44:29
oeisdata/seq/A378/A378476.seq
111accfe5090796664f94c357051b0fd
A378477
The number of n-colorings of the vertices of the truncated icosidodecahedron up to rotation and reflection.
[ "0", "1", "11076899964874299238703297447907328", "14975085832620260086776498590197757887552760437584786915", "14723725539819869413194145839524321308612931385268246121155792029614080", "6269303204385533375833261531851976948366440371233447120478861810030555725146484375" ]
[ "nonn" ]
10
0
3
[ "A000332", "A060530", "A128766", "A199406", "A252704", "A252705", "A274900", "A337963", "A378473", "A378474", "A378475", "A378476", "A378477", "A378478" ]
null
Peter Kagey, Nov 27 2024
2024-11-30T12:53:56
oeisdata/seq/A378/A378477.seq
14f397657a2911806609a21c6f6f6bf0
A378478
The number of n-colorings of the vertices of the snub dodecahedron up to rotation.
[ "0", "1", "19215358678900736", "706519304586988199183738259", "22153799929748598169960860333637632", "14456028966473392453665534687042333984375", "814561299678154291488767806377392301451223040", "8467031012327056088703142262372040966699399765293" ]
[ "nonn" ]
8
0
3
[ "A000332", "A060530", "A128766", "A199406", "A252704", "A252705", "A274900", "A337963", "A378473", "A378474", "A378475", "A378476", "A378477", "A378478" ]
null
Peter Kagey, Nov 27 2024
2024-11-30T12:54:06
oeisdata/seq/A378/A378478.seq
aa97d1595050f4b0dac57113639fa14d
A378479
Numbers k such that in base 2 the k-th composite is a substring of the k-th prime.
[ "16", "17", "98", "210", "654", "3386", "3387", "3388", "3389", "3392", "3395", "3397", "3398", "3401", "3504", "4806", "22401", "27997", "30930", "75126", "109303", "119466", "119467", "221344", "265167", "391691", "412566", "772432", "949072", "1451888", "2456497", "2739020", "2963199", "4942623", "4942624", "4942631", "4942632", "4942634", "4942636", "4942637", "4942638" ]
[ "nonn", "base" ]
13
1
1
[ "A000040", "A002808", "A175349", "A378479" ]
null
Robert Israel, Nov 28 2024
2024-12-03T12:23:40
oeisdata/seq/A378/A378479.seq
7dc1df9377a9a46e0ac4435d1ea6066e
A378480
Products of 3 distinct primes numbers (or sphenics) that are deficient.
[ "105", "110", "130", "154", "165", "170", "182", "190", "195", "230", "231", "238", "255", "266", "273", "285", "286", "290", "310", "322", "345", "357", "370", "374", "385", "399", "406", "410", "418", "429", "430", "434", "435", "442", "455", "465", "470", "483", "494", "506", "518", "530", "555", "561", "574", "590", "595", "598", "602", "609", "610", "615", "627", "638", "645", "646", "651", "658", "663", "665" ]
[ "nonn" ]
7
1
1
[ "A005100", "A007304", "A378480" ]
null
Massimo Kofler, Nov 28 2024
2024-12-01T11:39:13
oeisdata/seq/A378/A378480.seq
29fae0b3e65385ecbffc53a6310e3cae
A378481
Integers k such that A378414(k) == k (mod A066417(k))
[ "33", "77", "153", "372", "1540", "2300", "2692", "2736", "7812", "8721", "12593", "26025", "26481", "27972", "39321", "64009", "104409", "175441", "325180", "335616", "422593", "455625", "564376", "575040", "756460", "800073", "1104521", "2180545", "2304332", "3502665", "3691968", "5130909", "5515121", "9331441", "9546265" ]
[ "nonn", "easy" ]
4
1
1
[ "A000217", "A066417", "A232538", "A378414", "A378481" ]
null
Paolo P. Lava, Nov 28 2024
2024-12-16T14:31:44
oeisdata/seq/A378/A378481.seq
e198822776ab36f73d9332716d83e72b
A378482
Decimal expansion of 1/(8*log(2)*A005597), where A005597 is the twin prime constant C_2.
[ "2", "7", "3", "1", "7", "0", "7", "2", "2", "3", "6", "2", "6", "3", "8", "3", "9", "7", "4", "7", "1", "0", "6", "6", "0", "1", "4", "3", "1", "6", "5", "5", "1", "5", "1", "4", "7", "9", "1", "2", "9", "7", "3", "6", "9", "3", "6", "5", "7", "0", "1", "6", "3", "9", "5", "1", "3", "9", "8", "5", "3", "5", "0", "7", "4", "3", "0", "0", "3", "2", "4", "9", "1", "7", "5", "0", "5", "5", "9", "8", "5", "8", "3", "2", "6", "8", "4", "7", "8", "6", "6", "5", "4", "6", "5", "0", "5", "8", "8", "6" ]
[ "nonn", "cons" ]
12
0
1
[ "A002162", "A005597", "A069205", "A378482" ]
null
Stefano Spezia, Nov 28 2024
2025-02-15T09:47:14
oeisdata/seq/A378/A378482.seq
e6b4e4ee3bbf163c1e1dcde9f28b22f3
A378483
Expansion of (Sum_{k>=0} binomial(3*k,k) * x^k)^3.
[ "1", "9", "72", "549", "4077", "29772", "214884", "1537677", "10930923", "77298849", "544300992", "3819184236", "26718251868", "186440019192", "1298115301356", "9020928853341", "62582406445287", "433509545320731", "2998884192348888", "20720206275346269", "143005275737941437", "986000187782876976" ]
[ "nonn" ]
10
0
2
[ "A000302", "A005809", "A378483", "A378484" ]
null
Seiichi Manyama, Nov 28 2024
2024-11-28T09:04:39
oeisdata/seq/A378/A378483.seq
bfdbdf068fa5bdc49d4cebebe4d2b49f
A378484
Expansion of (Sum_{k>=0} binomial(4*k,k) * x^k)^4.
[ "1", "16", "208", "2480", "28176", "310336", "3344688", "35472672", "371570320", "3853862080", "39650662720", "405221752112", "4117879215472", "41643345090240", "419362920305952", "4207604570770752", "42079232716865424", "419609034657373120", "4173470598366784960", "41413032430984848832", "410071444666659404352" ]
[ "nonn" ]
19
0
2
[ "A000302", "A005810", "A078995", "A378483", "A378484" ]
null
Seiichi Manyama, Nov 28 2024
2024-11-28T10:49:39
oeisdata/seq/A378/A378484.seq
b1bf6497c200af3db48a6abed7a54ac8
A378485
Decimal expansion of Product_{p prime} (1 + 1/p^(5/4) + 1/p^(3/2) + 1/p^(7/4)).
[ "9", "6", "6", "9", "4", "7", "5", "4", "8", "4", "3", "8", "2", "3", "6", "8", "1", "0", "6", "5", "0", "0", "6", "6", "6", "9", "4", "3", "2", "0", "0", "8", "1", "7", "9", "3", "8", "0", "9", "2", "7", "2", "4", "8", "4", "4", "4", "7", "6", "3", "8", "8", "8", "7", "0", "7", "8", "4", "6", "2", "6", "5", "7", "1", "3", "9", "3", "3", "9", "3", "8", "6", "8", "1", "2", "5", "1", "9", "3", "5", "5", "6", "1", "1", "1", "9", "6", "3", "1", "4", "2", "8", "4", "0", "3", "0", "3", "3", "4", "1" ]
[ "nonn", "cons" ]
6
1
1
[ "A090699", "A362974", "A362975", "A362976", "A378485", "A378486", "A378487" ]
null
Stefano Spezia, Nov 28 2024
2024-11-29T09:38:47
oeisdata/seq/A378/A378485.seq
4029331d79f1afb1fbbe01f1174a0223
A378486
Decimal expansion of Product_{p prime} (1 + 1/p^(6/5) + 1/p^(7/5) + 1/p^(8/5) + 1/p^(9/5)).
[ "1", "9", "4", "4", "5", "5", "7", "6", "0", "8", "3", "9", "0", "0", "5", "7", "1", "1", "3", "9", "0", "8", "0", "0", "8", "9", "3", "2", "8", "9", "9", "1", "3", "5", "4", "6", "4", "7", "1", "1", "9", "5", "0", "5", "0", "7", "5", "4", "8", "5", "7", "0", "8", "0", "2", "7", "3", "0", "8", "9", "8", "6", "3", "0", "3", "5", "8", "9", "5", "9", "6", "1", "5", "4", "2", "5", "0", "2", "5", "5", "8", "8", "6", "7", "0", "4", "9", "7", "6", "3", "2", "5", "6", "6", "2", "9", "7", "7", "3", "5" ]
[ "nonn", "cons" ]
5
2
2
[ "A090699", "A362974", "A362975", "A362976", "A378485", "A378486", "A378487" ]
null
Stefano Spezia, Nov 28 2024
2024-11-29T09:38:58
oeisdata/seq/A378/A378486.seq
21ba533f4a08bec42ff055cda4f29d6d
A378487
Decimal expansion of Product_{p prime} (1 + 1/p^(6/5) + 1/p^(7/5) - 1/p^2 - 1/p^(11/5) - 1/p^(12/5)) (negated).
[ "1", "6", "9", "7", "8", "7", "8", "1", "4", "8", "3", "4", "3", "5", "2", "4", "3", "9", "9", "2", "7", "9", "9", "7", "0", "6", "2", "6", "1", "4", "0", "3", "1", "3", "3", "2", "3", "4", "1", "2", "5", "8", "7", "3", "3", "4", "2", "9", "5", "9", "5", "4", "0", "4", "6", "7", "5", "1", "4", "1", "2", "5", "6", "6", "4", "9", "0", "8", "1", "4", "6", "0", "9", "6", "5", "7", "0", "6", "1", "6", "9", "0", "5", "5", "4", "3", "0", "4", "7", "2", "7", "4", "9", "3", "8", "6", "3", "1", "1", "8" ]
[ "nonn", "cons" ]
9
2
2
[ "A090699", "A362974", "A362975", "A362976", "A378485", "A378486", "A378487" ]
null
Stefano Spezia, Nov 28 2024
2024-11-29T09:39:23
oeisdata/seq/A378/A378487.seq
a3e284431f344cb10db5f60e177f5c3e
A378488
Table T(n,k) read by rows where in the n-th row the k-th column is the permutation rank of the k-th solution to the n-queens problem in a n X n board.
[ "0", "0", "0", "10", "13", "10", "13", "36", "44", "50", "69", "75", "83", "106", "109", "186", "346", "373", "533", "186", "346", "373", "533", "980", "1032", "1090", "1108", "1188", "1244", "1399", "1515", "1519", "1905", "1956", "2074", "2090", "2197", "2210", "2390", "2649", "2829", "2842", "2949", "2965", "3083", "3134", "3520", "3524", "3640", "3795", "3851" ]
[ "nonn", "tabf" ]
6
1
4
[ "A000170", "A378488" ]
null
Darío Clavijo, Nov 28 2024
2024-12-12T23:15:21
oeisdata/seq/A378/A378488.seq
a93ee86a5e94fc5a17dd5c04804c0390
A378489
Intersection of A000028 and A028260.
[ "4", "9", "16", "24", "25", "40", "49", "54", "56", "60", "81", "84", "88", "90", "96", "104", "121", "126", "132", "135", "136", "140", "150", "152", "156", "160", "169", "184", "189", "198", "204", "220", "224", "228", "232", "234", "240", "248", "250", "256", "260", "276", "289", "294", "296", "297", "306", "308", "315", "328", "336", "340", "342", "344", "348", "350" ]
[ "nonn" ]
12
1
1
[ "A000028", "A028260", "A066427", "A378489", "A378494" ]
null
Paolo Xausa, Nov 28 2024, following a suggestion from Peter Munn.
2024-11-30T12:58:36
oeisdata/seq/A378/A378489.seq
ebf247c3f2b2142b5f72750f0e422128
A378490
Least prime p such that p^(2^n) + 2^(2^n) is prime.
[ "3", "3", "3", "13", "89", "29", "37", "113", "113", "13", "1151", "43", "53", "5503" ]
[ "nonn", "more" ]
19
0
1
[ "A001146", "A132260", "A157764", "A375215", "A378490" ]
null
Jean-Marc Rebert, Nov 28 2024
2024-12-12T23:30:28
oeisdata/seq/A378/A378490.seq
753e2bc51a2ac2b25d1631dc5f10e3e1
A378491
Numbers k such that (in base 10) the k-th composite is a substring of the k-th prime.
[ "5738", "20393", "20397", "20532", "28566", "305037", "511920", "151810713", "27746745416", "60097588222" ]
[ "nonn", "base", "more" ]
14
1
1
[ "A000040", "A002808", "A378479", "A378491" ]
null
Robert Israel, Nov 28 2024
2024-12-09T17:48:32
oeisdata/seq/A378/A378491.seq
b786fb346d47e51e74745ffc1f80c487
A378492
Squares where larger digits have larger multiplicity.
[ "0", "1", "4", "9", "144", "441", "1444", "29929", "55225", "166464", "255025", "299209", "633616", "646416", "767376", "4999696", "9696996", "34433424", "228281881", "414041104", "414488881", "424442404", "536663556", "969699600", "1649496996", "1929229929", "2636206336", "2666999449", "2929299129", "2996029696", "4664343616" ]
[ "nonn", "base" ]
27
1
3
[ "A000290", "A018884", "A052046", "A235718", "A378492", "A378498" ]
null
Erich Friedman, Nov 28 2024
2024-12-01T14:32:57
oeisdata/seq/A378/A378492.seq
82fb1dc6be1dcd89def84906e4ae2e49
A378493
Dot product of the first n primes and the first n triangular numbers.
[ "2", "11", "41", "111", "276", "549", "1025", "1709", "2744", "4339", "6385", "9271", "13002", "17517", "23157", "30365", "39392", "49823", "62553", "77463", "94326", "114313", "137221", "163921", "195446", "230897", "269831", "313273", "360688", "413233", "476225", "545393", "622250", "704955", "798825", "899391", "1009762" ]
[ "nonn" ]
16
1
1
[ "A000040", "A000217", "A166486", "A196421", "A378493" ]
null
Harvey P. Dale, Nov 28 2024
2024-12-12T17:51:53
oeisdata/seq/A378/A378493.seq
947c7e8a4ab652bdcba548f77eb750ed
A378494
Intersection of A000379 and A026424.
[ "8", "12", "18", "20", "27", "28", "32", "44", "45", "48", "50", "52", "63", "68", "75", "76", "80", "92", "98", "99", "112", "116", "117", "120", "124", "125", "147", "148", "153", "162", "164", "168", "171", "172", "175", "176", "188", "207", "208", "212", "236", "242", "243", "244", "245", "261", "264", "268", "270", "272", "275", "279", "280", "284", "292", "304", "312", "316" ]
[ "nonn" ]
11
1
1
[ "A000379", "A026424", "A187042", "A378489", "A378494" ]
null
Paolo Xausa, Nov 28 2024, following a suggestion from Peter Munn.
2024-11-30T12:58:51
oeisdata/seq/A378/A378494.seq
1e7019363d5c2e3562084c598183950e
A378495
Triangle read by rows: T(n,k) is the number of derangements in S_n with no k-cycles. 1 <= k <= n.
[ "0", "0", "0", "0", "2", "0", "0", "6", "9", "3", "0", "24", "24", "44", "20", "0", "160", "225", "175", "265", "145", "0", "1140", "1224", "1434", "1350", "1854", "1134", "0", "8988", "11025", "12313", "12145", "11473", "14833", "9793", "0", "80864", "93456", "100232", "106280", "113336", "107576", "133496", "93176", "0", "809856", "965601", "1057761", "1141425", "1108161", "1162161", "1108161", "1334961", "972081" ]
[ "nonn", "tabl" ]
68
1
5
[ "A000166", "A038205", "A122974", "A238474", "A378495" ]
null
Peter Kagey, Nov 29 2024
2024-11-30T12:54:12
oeisdata/seq/A378/A378495.seq
929296d18d1288dca0262c21465d90eb
A378496
Inverse of permutation in A380856.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "10", "9", "11", "12", "14", "13", "15", "16", "20", "17", "21", "18", "22", "19", "23", "24", "28", "25", "29", "26", "30", "27", "31", "32", "33", "40", "41", "34", "35", "42", "43", "36", "37", "44", "45", "38", "39", "46", "47", "48", "49", "56", "57", "50", "51", "58", "59", "52", "53", "60", "61", "54", "55", "62", "63", "64", "65", "66", "67" ]
[ "nonn", "look" ]
24
0
3
[ "A001477", "A378496", "A380856" ]
null
Alois P. Heinz, Feb 14 2025
2025-02-18T12:36:23
oeisdata/seq/A378/A378496.seq
edb1a9bda05f6d99f83739d46e1d2644
A378497
a(n) is the number whose base-4 digits are 1 followed by the first n-1 terms of the periodic sequence with initial period 2,0,3.
[ "1", "6", "24", "99", "398", "1592", "6371", "25486", "101944", "407779", "1631118", "6524472", "26097891", "104391566", "417566264", "1670265059", "6681060238", "26724240952", "106896963811", "427587855246", "1710351420984", "6841405683939", "27365622735758", "109462490943032", "437849963772131" ]
[ "nonn", "base", "easy" ]
35
1
2
[ "A037618", "A037667", "A037688", "A378497", "A378499", "A378502" ]
null
Jonathan Shadrach Gilbert, Nov 28 2024
2025-03-31T01:47:26
oeisdata/seq/A378/A378497.seq
478cf14d52d51ec119128b2c4da23403
A378498
Squares where larger digits have smaller multiplicity.
[ "1", "4", "9", "100", "121", "225", "400", "484", "676", "900", "10000", "11881", "40000", "44944", "69696", "90000", "111556", "202500", "220900", "225625", "232324", "261121", "265225", "300304", "442225", "444889", "695556", "1000000", "1002001", "1020100", "1210000", "2250000", "2295225", "4000000", "4008004", "4080400", "4840000", "5112121", "6760000", "8008900", "9000000" ]
[ "nonn", "base" ]
18
1
2
[ "A000290", "A018884", "A052046", "A235718", "A378492", "A378498" ]
null
Erich Friedman, Nov 28 2024
2024-11-29T21:04:23
oeisdata/seq/A378/A378498.seq
88b7d209762e9bf0a05032372f83c0e3
A378499
a(n) is the number whose base-4 digits are 1 followed by the first n-1 terms of the periodic sequence with initial period 0,3,2.
[ "1", "4", "19", "78", "312", "1251", "5006", "20024", "80099", "320398", "1281592", "5126371", "20505486", "82021944", "328087779", "1312351118", "5249404472", "20997617891", "83990471566", "335961886264", "1343847545059", "5375390180238", "21501560720952", "86006242883811", "344024971535246" ]
[ "nonn", "base", "easy" ]
24
1
2
[ "A037618", "A037667", "A037681", "A378497", "A378499", "A378502" ]
null
Jonathan Shadrach Gilbert, Nov 28 2024
2024-12-21T00:19:48
oeisdata/seq/A378/A378499.seq
58b0dad46c6f3475b7f59571a2799560
A378500
a(1) = 2, then a(n) = a(n-1) - 2 for n even, a(n) = a(n-1) + 3 for n an odd prime or odd prime power, and a(n) = a(n-1) + 2 otherwise.
[ "2", "0", "3", "1", "4", "2", "5", "3", "6", "4", "7", "5", "8", "6", "8", "6", "9", "7", "10", "8", "10", "8", "11", "9", "12", "10", "13", "11", "14", "12", "15", "13", "15", "13", "15", "13", "16", "14", "16", "14", "17", "15", "18", "16", "18", "16", "19", "17", "20", "18", "20", "18", "21", "19", "21", "19", "21", "19", "22", "20", "23", "21", "23", "21", "23", "21", "24", "22", "24", "22", "25" ]
[ "nonn" ]
39
1
1
null
null
Bill McEachen, Nov 30 2024
2024-12-06T16:28:19
oeisdata/seq/A378/A378500.seq
616600d90e995d926eded6b0fb80e3a3