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christopher
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oeis

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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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A382789
The number of prime factors of Euler phi of the n-th primorial number, counted with multiplicity.
[ "0", "0", "1", "3", "5", "7", "10", "14", "17", "19", "22", "25", "29", "33", "36", "38", "41", "43", "47", "50", "53", "58", "61", "63", "67", "73", "77", "80", "82", "87", "92", "96", "99", "103", "106", "109", "113", "117", "122", "124", "127", "129", "134", "137", "144", "148", "152", "156", "159", "161", "165", "169", "172", "178", "182", "190", "192", "195", "200", "204" ]
[ "nonn", "easy" ]
7
0
4
[ "A000010", "A001222", "A002110", "A023508", "A055768", "A055769", "A382789" ]
null
Amiram Eldar, Apr 05 2025
2025-04-05T09:10:10
oeisdata/seq/A382/A382789.seq
c2566bd13d8e8415785d7f8c45e5b413
A382790
a(n) is the (2^n)-th powerful number.
[ "1", "4", "9", "32", "121", "392", "1352", "5000", "18432", "69192", "265837", "1024144", "3968064", "15523600", "60972500", "240413400", "950612224", "3767130288", "14959246864", "59495990724", "236902199076", "944193944097", "3765996039168", "15029799230264", "60010866324576", "239700225078125", "957712290743329" ]
[ "nonn", "changed" ]
12
0
2
[ "A001694", "A062762", "A090699", "A376092", "A382790" ]
null
Amiram Eldar, Apr 05 2025
2025-04-15T11:58:39
oeisdata/seq/A382/A382790.seq
3e4e40a0f973f33aebb016c11beafaf4
A382791
Carmichael numbers with exactly 3 prime factors, p*q*r, such that p-1, q-1 and r-1 have an equal 2-adic valuation.
[ "8911", "29341", "314821", "410041", "1024651", "1152271", "5481451", "10267951", "14913991", "15247621", "36765901", "64377991", "67902031", "133800661", "139952671", "178482151", "188516329", "299736181", "362569201", "368113411", "395044651", "532758241", "579606301", "612816751", "620169409", "625482001", "652969351" ]
[ "nonn" ]
9
1
1
[ "A002997", "A007814", "A087788", "A329799", "A382791" ]
null
Amiram Eldar, Apr 05 2025
2025-04-05T09:10:49
oeisdata/seq/A382/A382791.seq
c5e5a9992dea6c80f2ebd41824957ef4
A382792
a(n) = Sum_{k=0..n} (Stirling1(n,k) * k!)^2.
[ "1", "1", "5", "76", "2392", "126676", "10057204", "1114096320", "163918005696", "30894047577216", "7254176241285504", "2075722128162164736", "710883208780304954112", "287061726161439955116288", "134961239570613490548986112", "73079781978184515947237031936", "45150931601954398539342470578176" ]
[ "nonn" ]
16
0
3
[ "A006252", "A007840", "A047796", "A048144", "A379821", "A382792", "A382794" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-05T16:09:44
oeisdata/seq/A382/A382792.seq
5dffef11d84abce61635cc7605d92b92
A382793
a(n) = Sum_{k=0..n} (-1)^k * (Stirling2(n,k) * k!)^2.
[ "1", "-1", "3", "-1", "-525", "21599", "-575757", "-11712961", "4147828275", "-478419026401", "27474795508083", "3849481231073279", "-1772585499434165325", "366912253456842693599", "-26525609280231515934477", "-17189616925094873258825281", "10414911263566240831226298675", "-3136992122810471155294591778401" ]
[ "sign" ]
5
0
3
[ "A047797", "A048144", "A192552", "A382793" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-05T10:24:32
oeisdata/seq/A382/A382793.seq
0f21af10ba94996b5972f2b99cef6df7
A382794
a(n) = Sum_{k=0..n} Stirling1(n,k) * Stirling2(n,k) * (k!)^2.
[ "1", "1", "3", "2", "-418", "-14676", "-234344", "18565056", "2659703616", "169046742960", "-6539356064736", "-4061128974843744", "-672969012637199040", "-19289566159655581440", "27323548725052131528960", "10157639436460221570630144", "1433264952547826545065237504", "-520046813680980959472490690560" ]
[ "sign" ]
6
0
3
[ "A000670", "A006252", "A047792", "A048144", "A064618", "A192554", "A192564", "A382792", "A382794" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-05T10:24:29
oeisdata/seq/A382/A382794.seq
69fed55eda2da0ab8bb1875228463953
A382795
Number of minimum total dominating sets in the n-odd graph.
[ "0", "3", "10", "3570", "52920" ]
[ "nonn", "more" ]
4
1
2
null
null
Eric W. Weisstein, Apr 05 2025
2025-04-05T09:10:01
oeisdata/seq/A382/A382795.seq
5ac4cdab73596d3dc82aa5ee5470bc93
A382796
Numbers that can be represented as the sum of two distinct Ulam numbers in more than one way.
[ "5", "7", "9", "10", "12", "14", "15", "17", "19", "20", "21", "22", "24", "27", "29", "30", "31", "32", "34", "37", "39", "40", "41", "42", "44", "46", "49", "50", "51", "52", "54", "55", "56", "58", "59", "60", "61", "63", "64", "65", "66", "68", "70", "71", "73", "74", "75", "76", "78", "79", "80", "81", "83", "84", "85", "86", "88", "89", "90", "91", "93", "95", "98", "100", "101" ]
[ "nonn" ]
10
1
1
[ "A002858", "A033629", "A138892", "A382796" ]
null
Shyam Sunder Gupta, Apr 05 2025
2025-04-06T15:00:52
oeisdata/seq/A382/A382796.seq
0b97d060dac370945bfb1d6fe7ca1cb0
A382797
Odd Ulam numbers.
[ "1", "3", "11", "13", "47", "53", "57", "69", "77", "87", "97", "99", "131", "145", "155", "175", "177", "189", "197", "209", "219", "221", "241", "243", "253", "273", "309", "319", "339", "341", "363", "409", "429", "431", "441", "451", "483", "485", "497", "585", "605", "607", "627", "673", "685", "695", "739", "751", "781", "783", "847", "849", "861", "891" ]
[ "nonn" ]
12
1
2
[ "A002858", "A005408", "A382797" ]
null
Shyam Sunder Gupta, Apr 05 2025
2025-04-06T15:01:23
oeisdata/seq/A382/A382797.seq
66f6d19c888921d6d23e384c5490621e
A382798
Even Ulam numbers.
[ "2", "4", "6", "8", "16", "18", "26", "28", "36", "38", "48", "62", "72", "82", "102", "106", "114", "126", "138", "148", "180", "182", "206", "236", "238", "258", "260", "282", "316", "324", "356", "358", "370", "382", "390", "400", "402", "412", "414", "434", "456", "502", "522", "524", "544", "546", "566", "568", "602", "612", "624", "646", "668", "688", "690" ]
[ "nonn" ]
11
1
1
[ "A002858", "A005843", "A382798" ]
null
Shyam Sunder Gupta, Apr 05 2025
2025-04-06T15:01:34
oeisdata/seq/A382/A382798.seq
1fcd1f711f6ce57ca2d1b04df730908d
A382799
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (1 - log(1-x) * log(1-y))^2.
[ "1", "0", "0", "0", "2", "0", "0", "2", "2", "0", "0", "4", "14", "4", "0", "0", "12", "40", "40", "12", "0", "0", "48", "144", "260", "144", "48", "0", "0", "240", "648", "1284", "1284", "648", "240", "0", "0", "1440", "3528", "6936", "9588", "6936", "3528", "1440", "0", "0", "10080", "22608", "42744", "65928", "65928", "42744", "22608", "10080", "0", "0", "80640", "166896", "300240", "476808", "581952", "476808", "300240", "166896", "80640", "0" ]
[ "nonn", "tabl" ]
12
0
5
[ "A379821", "A382734", "A382799", "A382800", "A382801", "A382804" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T16:10:01
oeisdata/seq/A382/A382799.seq
546673794533efca1758854f2daa0099
A382800
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (1 - log(1-x) * log(1-y))^3.
[ "1", "0", "0", "0", "3", "0", "0", "3", "3", "0", "0", "6", "27", "6", "0", "0", "18", "78", "78", "18", "0", "0", "72", "282", "588", "282", "72", "0", "0", "360", "1272", "2988", "2988", "1272", "360", "0", "0", "2160", "6936", "16344", "24612", "16344", "6936", "2160", "0", "0", "15120", "44496", "101448", "175632", "175632", "101448", "44496", "15120", "0" ]
[ "nonn", "tabl" ]
13
0
5
[ "A379821", "A382735", "A382799", "A382800", "A382802", "A382806" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T16:09:57
oeisdata/seq/A382/A382800.seq
2323130a644a87822a720f595f1cbab0
A382801
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/2) * (1 / (1 - log(1-x) * log(1-y))^2 - 1).
[ "1", "1", "1", "2", "7", "2", "6", "20", "20", "6", "24", "72", "130", "72", "24", "120", "324", "642", "642", "324", "120", "720", "1764", "3468", "4794", "3468", "1764", "720", "5040", "11304", "21372", "32964", "32964", "21372", "11304", "5040", "40320", "83448", "150120", "238404", "290976", "238404", "150120", "83448", "40320" ]
[ "nonn", "tabl" ]
14
1
4
[ "A382740", "A382799", "A382801" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T23:17:14
oeisdata/seq/A382/A382801.seq
011b1d98eb23517f5ae0d41409253c95
A382802
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/3) * (1 / (1 - log(1-x) * log(1-y))^3 - 1).
[ "1", "1", "1", "2", "9", "2", "6", "26", "26", "6", "24", "94", "196", "94", "24", "120", "424", "996", "996", "424", "120", "720", "2312", "5448", "8204", "5448", "2312", "720", "5040", "14832", "33816", "58544", "58544", "33816", "14832", "5040", "40320", "109584", "238656", "431632", "556376", "431632", "238656", "109584", "40320" ]
[ "nonn", "tabl" ]
16
1
4
[ "A382741", "A382800", "A382802" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T23:17:20
oeisdata/seq/A382/A382802.seq
6882964a02cc16788fc9d6bd554c5b38
A382803
Positive integers m such that phi(m) and phi(m+1) are both powers of 2.
[ "1", "2", "3", "4", "5", "15", "16", "255", "256", "65535", "65536", "4294967295" ]
[ "nonn", "hard", "new" ]
41
1
2
[ "A000010", "A000215", "A003401", "A019434", "A051179", "A382519", "A382803" ]
null
Caleb Stanford, Apr 05 2025
2025-04-18T21:29:29
oeisdata/seq/A382/A382803.seq
4dfdee03cdfe0eea12bafed5d51961a4
A382804
a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling1(n,k)^2.
[ "1", "2", "14", "260", "9588", "581952", "52096512", "6423520896", "1041005447424", "214260350714496", "54547409318781312", "16820040059243046144", "6175245603727007034624", "2661063379044058584861696", "1329787781176741647226481664", "762665713456216694195942866944" ]
[ "nonn" ]
14
0
2
[ "A382737", "A382792", "A382799", "A382804", "A382806" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T16:09:35
oeisdata/seq/A382/A382804.seq
8720814927f72dfd3a3893d63957b14b
A382805
a(n) = Sum_{k=0..n} (-1)^(n-k) * (Stirling1(n,k) * k!)^2.
[ "1", "1", "3", "4", "-272", "-8524", "-96596", "9634752", "983055168", "36429411456", "-4303305703296", "-1051644384152064", "-89651253435644160", "10632887072757561600", "5599203549778990667520", "914684633796830925275136", "-89559567563652079025946624", "-104514775371103880549281775616" ]
[ "sign" ]
4
0
3
[ "A006252", "A007840", "A047796", "A048144", "A192554", "A320502", "A382792", "A382793", "A382805" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-06T14:56:50
oeisdata/seq/A382/A382805.seq
dc99617f175f826a5f374546bf0b1702
A382806
a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+2,2) * Stirling1(n,k)^2.
[ "1", "3", "27", "588", "24612", "1669128", "165049224", "22269896064", "3918921022656", "870149951146944", "237662482188210624", "78249086559726140160", "30547324837444471084800", "13946361918619108837939200", "7359961832428044552536217600", "4444946383758589481684168540160" ]
[ "nonn" ]
9
0
2
[ "A382738", "A382792", "A382800", "A382804", "A382806" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-05T16:09:31
oeisdata/seq/A382/A382806.seq
fd4a27d1e0aeb9f3d9652fb57fa5ae9e
A382807
a(n) = Sum_{k=0..n} (Stirling1(n,k) * k!)^3.
[ "1", "1", "7", "8", "-22400", "-3821176", "733375592", "1324952888832", "521577465629184", "-1322687167356985344", "-3493561791052460040192", "83811280007607865122816", "33603928402796871413168222208", "112696506862115060894313558528000", "-389416384673353674591900391305326592" ]
[ "sign" ]
5
0
3
[ "A006252", "A242280", "A382792", "A382807", "A382808" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-06T14:57:01
oeisdata/seq/A382/A382807.seq
ec9c4e9f5a7e8ff6799810c8d39198ce
A382808
a(n) = Sum_{k=0..n} (|Stirling1(n,k)| * k!)^3.
[ "1", "1", "9", "440", "71344", "25826824", "17321581592", "19304140340736", "33142988156751360", "82906630912116006912", "289508760665893747703808", "1364207202603804952193826816", "8438589244471363680258331914240", "66972265137135031645961782287814656", "668922701586813036491303458870218731520" ]
[ "nonn" ]
7
0
3
[ "A007840", "A242280", "A382792", "A382807", "A382808" ]
null
Ilya Gutkovskiy, Apr 05 2025
2025-04-06T05:52:03
oeisdata/seq/A382/A382808.seq
445fce080d911cd74b83b87767a6716c
A382809
a(n) = (6*n + 1)*(12*n + 1)*(18*n + 1).
[ "1", "1729", "12025", "38665", "89425", "172081", "294409", "464185", "689185", "977185", "1335961", "1773289", "2296945", "2914705", "3634345", "4463641", "5410369", "6482305", "7687225", "9032905", "10527121", "12177649", "13992265", "15978745", "18144865", "20498401", "23047129", "25798825", "28761265", "31942225", "35349481" ]
[ "nonn", "easy" ]
12
0
2
[ "A002476", "A002997", "A016921", "A017533", "A033502", "A046025", "A068228", "A161705", "A382809" ]
null
Stefano Spezia, Apr 05 2025
2025-04-06T06:17:50
oeisdata/seq/A382/A382809.seq
99b2bf436e34123711b03fee3c133e22
A382810
Primes p such that p + 6, p + 10 and p + 16 are also primes.
[ "7", "13", "31", "37", "73", "97", "157", "223", "373", "433", "1087", "1291", "1423", "1483", "1543", "1861", "1987", "2341", "2383", "2677", "2683", "3313", "3607", "4441", "4507", "4783", "4993", "5641", "5851", "6037", "6961", "7237", "7867", "8731", "9613", "9733", "10723", "13093", "13681", "14143", "14731", "16057", "16411", "16921", "17377" ]
[ "nonn", "changed" ]
18
1
1
[ "A000040", "A001223", "A023200", "A031924", "A033451", "A078852", "A078856", "A078858", "A382810" ]
null
Alexander Yutkin, Apr 05 2025
2025-04-25T15:14:29
oeisdata/seq/A382/A382810.seq
5583920ef139b00af4da4523bcf387e0
A382811
Integers k such that d*2^k - 1 is prime for some divisor d of k.
[ "2", "3", "4", "5", "6", "7", "10", "12", "13", "16", "17", "18", "19", "21", "28", "30", "31", "36", "42", "46", "54", "60", "61", "63", "75", "81", "88", "89", "99", "102", "104", "106", "107", "108", "115", "123", "126", "127", "132", "133", "204", "214", "216", "225", "249", "264", "270", "286", "304", "306", "324", "330", "342", "352", "362", "384", "390" ]
[ "nonn", "new" ]
40
1
1
[ "A000043", "A002234", "A382811" ]
null
Juri-Stepan Gerasimov, Apr 15 2025
2025-04-25T15:56:15
oeisdata/seq/A382/A382811.seq
9620fdfebf0db627acb00962fb38a264
A382812
Numerator of the n-th partial sum of the squares of the harmonic numbers.
[ "1", "13", "119", "1577", "3233", "8867", "141563", "2844129", "28119709", "335676251", "3968696491", "55023970333", "758025067309", "799020611041", "1676892996083", "59597395635137", "351844709221043", "2314823924364859", "9114392136427625", "628176680098075", "216039223801697", "5117413095318143", "363066107054194281", "27957386425926920257" ]
[ "nonn", "frac", "changed" ]
33
1
2
[ "A001008", "A002805", "A027611", "A027612", "A382812", "A382813" ]
null
Gary Detlefs, Apr 05 2025
2025-04-25T17:15:55
oeisdata/seq/A382/A382812.seq
a8b49701b29af538f17cf35d4fd0262d
A382813
Denominator of the n-th partial sum of the squares of the harmonic numbers.
[ "1", "4", "18", "144", "200", "400", "4900", "78400", "635040", "6350400", "64033200", "768398400", "9275666400", "8657288640", "16232416200", "519437318400", "2779951574400", "16679709446400", "60213751101504", "3823095308032", "1216439416192", "26761667156224", "1769615240705312", "127412297330782464", "3062795608913040000" ]
[ "nonn", "frac", "changed" ]
29
1
2
[ "A001008", "A002805", "A027611", "A027612", "A382812", "A382813" ]
null
Gary Detlefs, Apr 05 2025
2025-04-25T17:15:32
oeisdata/seq/A382/A382813.seq
7daf1e47786f577e3dfc666ad01bfad6
A382814
Number of nachos that the first player gets when playing the "Fibonachos" game starting with n nachos.
[ "1", "1", "2", "3", "3", "4", "3", "4", "4", "5", "6", "8", "8", "9", "9", "9", "10", "10", "12", "8", "9", "9", "10", "11", "11", "12", "11", "12", "12", "13", "14", "16", "21", "21", "22", "22", "22", "23", "23", "25", "25", "26", "26", "26", "25", "26", "26", "27", "28", "28", "29", "28", "33", "21", "22", "22", "23", "24", "24", "25", "24", "25", "25", "26", "27", "29", "29", "30", "30", "30" ]
[ "nonn" ]
10
1
3
[ "A000045", "A280521", "A382814" ]
null
Peter Kagey, Apr 05 2025
2025-04-12T12:38:46
oeisdata/seq/A382/A382814.seq
c5af6fe02fde0ade8bc0eb903b4aaf2a
A382816
a(n) = number of occurrences of n in A008949.
[ "1", "1", "2", "1", "1", "2", "2", "1", "1", "2", "1", "1", "1", "2", "3", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "2", "1", "2", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "2", "3", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn" ]
13
2
3
[ "A007318", "A008949", "A382816", "A382817" ]
null
Clark Kimberling, Apr 07 2025
2025-04-13T11:47:20
oeisdata/seq/A382/A382816.seq
036378d16591fd1757c4435100853370
A382817
a(n) = number of primes among the partial sums of row n of Pascal's triangle (A007318).
[ "0", "1", "1", "1", "2", "1", "1", "2", "2", "0", "2", "1", "3", "2", "3", "2", "3", "1", "1", "2", "1", "1", "2", "2", "1", "1", "2", "3", "3", "0", "2", "7", "2", "0", "0", "1", "1", "0", "0", "0", "2", "0", "1", "1", "1", "0", "1", "3", "1", "0", "1", "1", "1", "1", "1", "1", "5", "3", "3", "2", "3", "2", "3", "3", "10", "0", "1", "0", "1", "0", "2", "2", "2", "0", "0", "1", "1", "0", "2", "1", "1", "1", "2", "1", "2", "0" ]
[ "nonn" ]
21
0
5
[ "A007318", "A008949", "A258483", "A382816", "A382817" ]
null
Clark Kimberling, Apr 07 2025
2025-04-13T11:49:16
oeisdata/seq/A382/A382817.seq
7b7baacec76265792616d52f249fad5b
A382818
Square array A(n,k), n > 0, k > 0, read by downward antidiagonals: A(n,k) is the number of columns in all k-compositions of n.
[ "1", "2", "3", "3", "11", "8", "4", "24", "52", "20", "5", "42", "163", "227", "48", "6", "65", "372", "1017", "944", "112", "7", "93", "710", "3019", "6030", "3800", "256", "8", "126", "1208", "7095", "23256", "34563", "14944", "576", "9", "164", "1897", "14340", "67251", "173076", "193392", "57748", "1280", "10", "207", "2808", "26082", "161394", "615630", "1256936", "1062756", "220128", "2816" ]
[ "nonn", "easy", "tabl" ]
14
1
2
[ "A001792", "A005475", "A145839", "A181289", "A181290", "A382818", "A382820" ]
null
John Tyler Rascoe, Apr 05 2025
2025-04-06T08:45:19
oeisdata/seq/A382/A382818.seq
ae59a6f833a7515c215075ca308291a1
A382819
Number of Grassmannian permutations on [n] of order dividing 3.
[ "1", "1", "1", "3", "5", "7", "12", "17", "22", "31", "40", "49", "63", "77", "91", "111", "131", "151", "178", "205", "232", "267", "302", "337", "381", "425", "469", "523", "577", "631", "696", "761", "826", "903", "980", "1057", "1147", "1237", "1327", "1431", "1535", "1639", "1758", "1877", "1996", "2131", "2266", "2401", "2553", "2705", "2857", "3027", "3197", "3367", "3556", "3745", "3934" ]
[ "nonn", "easy" ]
24
0
4
[ "A000325", "A001470", "A382819" ]
null
Aaron Geary, Apr 05 2025
2025-04-12T16:29:04
oeisdata/seq/A382/A382819.seq
e964c2131e6a311c7dba36dba733743a
A382820
Number of columns in all n-compositions of n.
[ "1", "11", "163", "3019", "67251", "1753877", "52468711", "1772042699", "66708748963", "2770212058261", "125812351808551", "6203908746628501", "330108021642012407", "18853083403505443593", "1150352428059538611663", "74685045367715777653195", "5140745255774277374241411", "373950591013899715795929605" ]
[ "nonn", "easy" ]
7
1
2
[ "A001792", "A145839", "A181289", "A181290", "A382818", "A382820" ]
null
John Tyler Rascoe, Apr 05 2025
2025-04-06T08:45:09
oeisdata/seq/A382/A382820.seq
2dab59feb7a46c1f91d45673e3a46952
A382821
Decimal expansion of (3/2) * (log(3) - 1).
[ "1", "4", "7", "9", "1", "8", "4", "3", "3", "0", "0", "2", "1", "6", "4", "5", "3", "7", "0", "9", "2", "8", "6", "7", "8", "5", "5", "3", "8", "3", "7", "8", "8", "5", "5", "6", "9", "7", "1", "2", "3", "5", "8", "3", "6", "7", "3", "4", "1", "2", "4", "1", "7", "7", "6", "0", "2", "0", "4", "1", "5", "0", "0", "4", "5", "6", "2", "4", "1", "4", "3", "9", "8", "2", "7", "9", "1", "3", "4", "5", "0", "3", "1", "0", "4", "2", "3" ]
[ "nonn", "cons" ]
13
0
2
[ "A016627", "A016631", "A093064", "A145425", "A382821" ]
null
Sean A. Irvine, Apr 05 2025
2025-04-08T04:47:03
oeisdata/seq/A382/A382821.seq
f5b89bed3fe4b635598240472a271470
A382822
If a(n-1) is odd, then a(n) is the smallest even integer not yet in the sequence; if a(n-1) is even, then a(n) = a(n-1)/2 if this number is not in the sequence, otherwise a(n) = 3*a(n-1)/2; a(1)=1.
[ "1", "2", "3", "4", "6", "9", "8", "12", "18", "27", "10", "5", "14", "7", "16", "24", "36", "54", "81", "20", "30", "15", "22", "11", "26", "13", "28", "42", "21", "32", "48", "72", "108", "162", "243", "34", "17", "38", "19", "40", "60", "90", "45", "44", "66", "33", "46", "23", "50", "25", "52", "78", "39", "56", "84", "126", "63", "58", "29", "62", "31", "64", "96", "144", "216", "324", "486", "729", "68", "102", "51", "70", "35", "74", "37", "76", "114", "57" ]
[ "nonn", "new" ]
30
1
2
[ "A350877", "A382822" ]
null
Enrique Navarrete, Apr 15 2025
2025-04-23T10:21:41
oeisdata/seq/A382/A382822.seq
0d358682cbc6fa89e3797450984d3444
A382823
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y)) ).
[ "1", "1", "1", "2", "2", "2", "6", "5", "5", "6", "24", "17", "17", "17", "24", "120", "74", "69", "69", "74", "120", "720", "394", "338", "337", "338", "394", "720", "5040", "2484", "1962", "1894", "1894", "1962", "2484", "5040", "40320", "18108", "13228", "12194", "12152", "12194", "13228", "18108", "40320", "362880", "149904", "101812", "89160", "87320", "87320", "89160", "101812", "149904", "362880" ]
[ "nonn", "tabl" ]
17
0
4
[ "A000142", "A000774", "A099594", "A379821", "A382823", "A382824", "A382825", "A382826" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-06T03:48:25
oeisdata/seq/A382/A382823.seq
a146359be84965d8c800a0ae263a2525
A382824
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y))^2 ).
[ "1", "1", "1", "2", "3", "2", "6", "8", "8", "6", "24", "28", "34", "28", "24", "120", "124", "150", "150", "124", "120", "720", "668", "768", "854", "768", "668", "720", "5040", "4248", "4584", "5204", "5204", "4584", "4248", "5040", "40320", "31176", "31512", "35188", "37556", "35188", "31512", "31176", "40320", "362880", "259488", "246072", "265896", "290380", "290380", "265896", "246072", "259488", "362880" ]
[ "nonn", "tabl" ]
12
0
4
[ "A382823", "A382824", "A382825", "A382827" ]
null
Seiichi Manyama, Apr 05 2025
2025-04-06T08:46:34
oeisdata/seq/A382/A382824.seq
27cda19c4822be4fe48e563a0e29d8b1
A382825
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y))^3 ).
[ "1", "1", "1", "2", "4", "2", "6", "11", "11", "6", "24", "39", "55", "39", "24", "120", "174", "255", "255", "174", "120", "720", "942", "1338", "1623", "1338", "942", "720", "5040", "6012", "8106", "10434", "10434", "8106", "6012", "5040", "40320", "44244", "56292", "72762", "82116", "72762", "56292", "44244", "40320", "362880", "369072", "442860", "560988", "668580", "668580", "560988", "442860", "369072", "362880" ]
[ "nonn", "tabl" ]
11
0
4
[ "A382673", "A382800", "A382823", "A382824", "A382825", "A382828" ]
null
Seiichi Manyama, Apr 06 2025
2025-04-06T08:46:30
oeisdata/seq/A382/A382825.seq
b93426ccc1644cbd983ecbcd8659bf7f
A382826
a(n) = Sum_{k=0..n} (k! * Stirling1(n+1,k+1))^2.
[ "1", "2", "17", "337", "12152", "696076", "58136500", "6673107316", "1008077743552", "193915431216576", "46281189562936704", "13420575661095930240", "4647502230640182602496", "1894412230202331489632256", "897850527136410029486517504", "489578762044356075253626875136" ]
[ "nonn" ]
10
0
2
[ "A048163", "A382792", "A382823", "A382826" ]
null
Seiichi Manyama, Apr 06 2025
2025-04-06T05:07:30
oeisdata/seq/A382/A382826.seq
fee619a1d77b57ff255875b335179ee2
A382827
a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling1(n+1,k+1)^2.
[ "1", "3", "34", "854", "37556", "2546852", "246113904", "32104625520", "5433891955968", "1157778241057152", "303197684900579712", "95717977509042032256", "35847800701044816248064", "15713483696924130220098816", "7969364997624587289470810112", "4630203661005094483980386924544" ]
[ "nonn" ]
8
0
2
[ "A092552", "A382804", "A382824", "A382827" ]
null
Seiichi Manyama, Apr 06 2025
2025-04-06T05:08:54
oeisdata/seq/A382/A382827.seq
b152cfd4ac3f1b08c18e3bbc23bfcb5b
A382828
a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+2,2) * Stirling1(n+1,k+1)^2.
[ "1", "4", "55", "1623", "82116", "6302028", "680105112", "98011315608", "18163969766592", "4205977241171328", "1189459906531372224", "403300593144673493184", "161454763431242385682176", "75337361633768810384542464", "40524573487904551618353921024", "24890567631479746511661428751360" ]
[ "nonn" ]
10
0
2
[ "A382676", "A382806", "A382825", "A382828" ]
null
Seiichi Manyama, Apr 06 2025
2025-04-06T05:06:06
oeisdata/seq/A382/A382828.seq
1b743e427e9d5646a4671fbf99392b1b
A382829
Number of distinct rank vectors of distributive lattices of height n.
[ "1", "1", "2", "5", "15", "51", "197", "864", "4325", "24922" ]
[ "nonn", "more" ]
5
0
3
[ "A000112", "A006982", "A382829" ]
null
Ludovic Schwob, Apr 06 2025
2025-04-12T12:00:06
oeisdata/seq/A382/A382829.seq
74c0b1f432522bad7631cde4d4bb8f39
A382830
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * |Stirling1(n,k)| * k!.
[ "1", "1", "8", "102", "1804", "40890", "1131108", "36948240", "1391945616", "59411849040", "2833582748160", "149347596487056", "8620256620495584", "540775669746661440", "36636074309252234880", "2665704585421541790720", "207329122282259073044736", "17165075378189396045777280", "1507206260097615729874083840" ]
[ "nonn" ]
6
0
3
[ "A007840", "A052801", "A277759", "A305919", "A354122", "A354123", "A382830" ]
null
Ilya Gutkovskiy, Apr 06 2025
2025-04-06T14:57:13
oeisdata/seq/A382/A382830.seq
e3bb07dee0c45e068b59d0fb4ca44d10
A382831
Achilles numbers such that the three numbers before it and the three numbers after it are squarefree.
[ "108", "392", "432", "500", "968", "1800", "1944", "2592", "2700", "3200", "3456", "4000", "4500", "5400", "8712", "8788", "9000", "10368", "10584", "10800", "13068", "13500", "14112", "14792", "16200", "18000", "18432", "20808", "21168", "21600", "21632", "24696", "25088", "25992", "26136", "27436", "31104", "33800", "34992", "37044", "38088", "38988" ]
[ "nonn" ]
10
1
1
[ "A005117", "A052486", "A068088", "A373689", "A382831" ]
null
Massimo Kofler, Apr 06 2025
2025-04-12T11:58:47
oeisdata/seq/A382/A382831.seq
1817652096999cc5e9b97b95997a0a91
A382832
Least k such that there exist two distinct subsets of {0, ..., k-1} with the same sum of m-th powers for 0 <= m <= n.
[ "2", "4", "7", "12", "16", "23", "31" ]
[ "nonn", "hard", "more" ]
9
0
1
[ "A382382", "A382832", "A382833" ]
null
Pontus von Brömssen, Apr 10 2025
2025-04-12T09:42:45
oeisdata/seq/A382/A382832.seq
a7a1687f487320cbbfc335b478e6a365
A382833
Square array read by antidiagonals: T(n,k) is the number of distinct sum-of-powers vectors (Sum_{x in X} x^m, 0 <= m <= k) for subsets X of {0, ..., n-1}; n, k >= 0.
[ "1", "1", "2", "1", "2", "3", "1", "2", "4", "4", "1", "2", "4", "8", "5", "1", "2", "4", "8", "15", "6", "1", "2", "4", "8", "16", "26", "7", "1", "2", "4", "8", "16", "32", "42", "8", "1", "2", "4", "8", "16", "32", "64", "64", "9", "1", "2", "4", "8", "16", "32", "64", "126", "93", "10", "1", "2", "4", "8", "16", "32", "64", "128", "247", "130", "11", "1", "2", "4", "8", "16", "32", "64", "128", "256", "476", "176", "12" ]
[ "nonn", "tabl" ]
4
0
3
[ "A000027", "A000125", "A382383", "A382832", "A382833" ]
null
Pontus von Brömssen, Apr 10 2025
2025-04-12T12:46:57
oeisdata/seq/A382/A382833.seq
208fb592c0089bb4c7f9746bab2fe955
A382834
Smallest number k > P(n) - prime(n+1)^2 which is coprime to P(n), where P(n)= A002110(n) are the primorials.
[ "-5", "-17", "-17", "97", "2143", "29747", "510151", "9699167", "223092031", "6469692277", "200560488763", "7420738133141", "304250263525363", "13082761331667823", "614889782588488607", "32589158477190041261", "1922760350154212635351", "117288381359406970978787", "7858321551080267055874051" ]
[ "sign", "easy", "new" ]
53
1
1
[ "A002110", "A034386", "A054270", "A064819", "A382834" ]
null
Jakub Buczak, Apr 06 2025
2025-04-17T19:25:09
oeisdata/seq/A382/A382834.seq
94e4fd99fafadfba6600b88850937b43
A382835
Array read by ascending antidiagonals: A(n,k) = (6*n + 1)*(12*n + 1)*Product_{i=0..k-2} (9*2^i*n + 1) with k >= 2.
[ "1", "91", "1", "325", "1729", "1", "703", "12025", "63973", "1", "1225", "38665", "877825", "4670029", "1", "1891", "89425", "4214485", "127284625", "677154205", "1", "2701", "172081", "12966625", "914543245", "36785256625", "195697565245", "1", "3655", "294409", "31146661", "3747354625", "395997225085", "21225093072625", "112917495146365", "1" ]
[ "nonn", "tabl" ]
11
0
2
[ "A000012", "A002997", "A318646", "A382809", "A382835", "A382836" ]
null
Stefano Spezia, Apr 06 2025
2025-04-12T12:31:25
oeisdata/seq/A382/A382835.seq
ef6fb8a61b4e4bb261e1e47476d93a47
A382836
Antidiagonal sums of A382835.
[ "1", "92", "2055", "76702", "5587745", "808744632", "233410506523", "134542364243426", "155011115348112933", "357100810407398252476", "1645189596276664815781823", "15158968746195230959317963654", "279359806252976896009489630292137", "10296791416488914892304807658835547904", "759072247447684071473777552807296660596387" ]
[ "nonn" ]
6
0
2
[ "A382835", "A382836" ]
null
Stefano Spezia, Apr 06 2025
2025-04-12T12:31:33
oeisdata/seq/A382/A382836.seq
8493cc289f97e0d60122f4547e2a5017
A382837
Numbers k such that k - A071324(k) > A000010(k).
[ "60", "70", "84", "120", "140", "154", "168", "180", "200", "210", "220", "240", "252", "260", "264", "280", "286", "300", "312", "336", "340", "350", "360", "374", "390", "396", "408", "418", "420", "442", "456", "468", "480", "490", "494", "504", "510", "520", "528", "540", "560", "570", "588", "598", "600", "624", "630", "646", "660", "672", "680", "700" ]
[ "nonn" ]
34
1
1
[ "A000010", "A071324", "A382837" ]
null
Shreyansh Jaiswal, Apr 06 2025
2025-04-13T16:26:46
oeisdata/seq/A382/A382837.seq
dbee8c1175e0f737dfe8e438d1a9e0fe
A382838
a(n) is the least k such that there are exactly n solutions in positive integers to the equation x^3 + y^2 = k^2.
[ "1", "3", "15", "105", "665", "1155", "9240", "68265", "200640", "54285", "434280", "3474240", "19120920", "1430715", "451605", "38629305", "3612840", "28902720", "97546680", "154900515", "451605000", "1239204120", "2633760360", "12193335000", "21070082880", "28902720000" ]
[ "nonn", "more" ]
14
0
2
[ "A382338", "A382838" ]
null
Robert Israel, Apr 06 2025
2025-04-12T12:19:33
oeisdata/seq/A382/A382838.seq
8d3bec47a6bf3ff58ef817d007cdd6ed
A382839
Number of dense binary relations on {1,...,n}.
[ "1", "2", "7", "114", "9602", "3962940", "7516789560", "62622777447552" ]
[ "nonn", "more" ]
20
0
2
[ "A382693", "A382839" ]
null
Mark Bowron, Apr 06 2025
2025-04-13T19:02:35
oeisdata/seq/A382/A382839.seq
d55163527ad416651c023b8d8123ac50
A382840
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * Stirling1(n,k) * k!.
[ "1", "1", "4", "30", "316", "4290", "71268", "1400112", "31750416", "816215760", "23455342560", "745073660496", "25924233481056", "980518650296640", "40054724743501440", "1757539560656401920", "82439565962427760896", "4116529729771939393920", "218017561353648160158720", "12206586491422209675532800" ]
[ "nonn" ]
6
0
3
[ "A006252", "A305919", "A308565", "A317280", "A354120", "A354121", "A382830", "A382840" ]
null
Ilya Gutkovskiy, Apr 06 2025
2025-04-10T03:25:44
oeisdata/seq/A382/A382840.seq
e385612abf954961a31ce2eb5fa97357
A382841
a(n) = Sum_{k=0..floor(n/2)} (binomial(n,k) * binomial(n-k,k))^2.
[ "1", "1", "5", "37", "181", "1301", "9401", "65465", "498037", "3796021", "29221705", "230396585", "1828448425", "14651160265", "118544522045", "965075143037", "7907605360757", "65162569952245", "539515760866889", "4486877961224297", "37463151704756281", "313909383754331801", "2638892573249746445", "22249830926517611917" ]
[ "nonn", "changed" ]
15
0
3
[ "A000984", "A002426", "A005259", "A005260", "A051286", "A089627", "A181546", "A275027", "A277247", "A382841", "A382842" ]
null
Ilya Gutkovskiy, Apr 06 2025
2025-04-15T15:10:08
oeisdata/seq/A382/A382841.seq
a6aac9e2f8b7519fab0602e0abe59255
A382842
a(n) = Sum_{k=0..floor(n/2)} (binomial(n,k) * binomial(n-k,k))^3.
[ "1", "1", "9", "217", "1945", "35001", "764001", "12079089", "250222617", "5424133465", "107360983009", "2358751625649", "52540471866961", "1147794435985393", "26151265459123065", "600227875293254217", "13779170435209475097", "322302377797126709913", "7582484532013652243169", "179184911648568670363185", "4275721755296040840336945" ]
[ "nonn" ]
11
0
3
[ "A000172", "A002426", "A069865", "A089627", "A092813", "A181545", "A382841", "A382842" ]
null
Ilya Gutkovskiy, Apr 06 2025
2025-04-09T05:05:52
oeisdata/seq/A382/A382842.seq
d8de80ffb5e764be0fb106e72a70eb45
A382843
Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers.
[ "-1", "0", "1", "1", "0", "1", "1", "0", "1", "3", "4", "5", "5", "12", "13", "9", "40", "41", "15", "112", "113", "25", "312", "313", "41", "840", "841", "67", "2244", "2245", "109", "5940", "5941", "177", "15664", "15665", "287", "41184", "41185", "465", "108112", "108113", "753", "283504", "283505", "1219", "742980", "742981", "1973", "1946364", "1946365", "3193", "5097624", "5097625", "5167", "13348944", "13348945" ]
[ "sign", "easy", "tabf" ]
16
0
10
[ "A000045", "A001595", "A095122", "A382843", "A382844", "A382845" ]
null
Miguel-Ángel Pérez García-Ortega, Apr 06 2025
2025-04-13T16:12:33
oeisdata/seq/A382/A382843.seq
b6302773672b9614cdcfc664e6e01434
A382844
Area of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers.
[ "0", "0", "0", "6", "30", "180", "840", "3900", "17220", "75174", "323730", "1386264", "5909904", "25136040", "106739256", "452846310", "1920088086", "8138356716", "34486996824", "146121685380", "619066205340", "2622628707270", "11110214972010", "47065148576496", "199375154768160", "844577145104400", "3577713520710960" ]
[ "nonn", "easy" ]
12
0
4
[ "A000045", "A095122", "A382843", "A382844", "A382845" ]
null
Miguel-Ángel Pérez García-Ortega, Apr 06 2025
2025-04-13T16:12:15
oeisdata/seq/A382/A382844.seq
808021e63348f6528f1bf72438c08bac
A382845
Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers.
[ "-1", "1", "1", "7", "17", "49", "127", "337", "881", "2311", "6049", "15841", "41471", "108577", "284257", "744199", "1948337", "5100817", "13354111", "34961521", "91530449", "239629831", "627359041", "1642447297", "4299982847", "11257501249", "29472520897", "77160061447", "202007663441", "528862928881", "1384581123199" ]
[ "sign", "easy" ]
11
0
4
[ "A000045", "A007598", "A080097", "A095122", "A382843", "A382844", "A382845" ]
null
Miguel-Ángel Pérez García-Ortega, Apr 06 2025
2025-04-13T16:11:56
oeisdata/seq/A382/A382845.seq
ceca6d31a08aaf94e29de71cc17875b3
A382846
Decimal expansion of 4 - Pi^2/4 - 2*log(2).
[ "1", "4", "6", "3", "0", "4", "5", "3", "8", "6", "0", "7", "7", "6", "9", "7", "2", "6", "4", "5", "6", "9", "1", "3", "0", "0", "7", "1", "1", "4", "6", "0", "9", "0", "8", "0", "0", "2", "0", "5", "7", "4", "8", "7", "9", "4", "6", "9", "2", "9", "1", "8", "3", "5", "1", "5", "5", "3", "0", "2", "6", "3", "6", "9", "5", "8", "2", "0", "1", "5", "5", "0", "4", "5", "5", "8", "0", "9", "2", "5", "8", "0", "3", "7", "8", "2", "9" ]
[ "nonn", "cons" ]
5
0
2
[ "A016627", "A091476", "A382846" ]
null
Sean A. Irvine, Apr 06 2025
2025-04-06T16:51:23
oeisdata/seq/A382/A382846.seq
8beb986e50acb4e9d72d4f9f71f547dc
A382847
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * (Stirling2(n,k) * k!)^2.
[ "1", "1", "14", "579", "48044", "6647405", "1379024730", "400315753159", "154879704709784", "77018569697097009", "47863427797633958630", "36348262891572161261963", "33119479438137288670256964", "35660343372397246917403353013", "44791475616825872944740798413234", "64911462519379469821754507087299215" ]
[ "nonn" ]
11
0
3
[ "A048144", "A305919", "A382737", "A382738", "A382739", "A382847", "A382853" ]
null
Ilya Gutkovskiy, Apr 06 2025
2025-04-08T12:23:51
oeisdata/seq/A382/A382847.seq
ea55946fea71030d2fdbf64d8be35c4e
A382848
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k)^2 * binomial(n+k,k).
[ "1", "1", "-5", "-35", "-29", "751", "3991", "-4115", "-137885", "-495269", "2114245", "25786795", "50109775", "-627370925", "-4643568305", "-495798035", "157753390435", "768269873875", "-1851203127335", "-35924154988865", "-107001450483779", "763444753890721", "7510024190977105", "8899910747771995" ]
[ "sign" ]
7
0
3
[ "A005258", "A026641", "A126869", "A245086", "A382848", "A382849" ]
null
Ilya Gutkovskiy, Apr 06 2025
2025-04-09T05:40:11
oeisdata/seq/A382/A382848.seq
9d290a0c62c85bc48f72734865f85995
A382849
a(n) = Sum_{k=0..n} (-1)^(n-k) * (binomial(n,k) * binomial(n+k,k))^2.
[ "1", "3", "1", "-357", "-6999", "-62997", "444529", "27783003", "508019689", "3206511003", "-89889084999", "-3274278527517", "-49395223500999", "-66079827133317", "16197028704290001", "433384098559415643", "4988878584849669609", "-35687369703800052357", "-2815548294132454060151", "-58942279760573467233357" ]
[ "sign" ]
6
0
2
[ "A005258", "A005259", "A126869", "A176335", "A228304", "A382848", "A382849" ]
null
Ilya Gutkovskiy, Apr 06 2025
2025-04-09T05:40:07
oeisdata/seq/A382/A382849.seq
d78731ba1d042eaf650452a6b2b974df
A382850
a(n) = least k such that binomial(n, k) > binomial(n - 1, h) for 0 <= h <= n - 1.
[ "1", "1", "1", "2", "2", "2", "3", "3", "4", "4", "4", "5", "5", "6", "6", "7", "7", "7", "8", "8", "9", "9", "10", "10", "10", "11", "11", "12", "12", "13", "13", "14", "14", "15", "15", "15", "16", "16", "17", "17", "18", "18", "19", "19", "19", "20", "20", "21", "21", "22", "22", "23", "23", "24", "24", "25", "25", "25", "26", "26", "27", "27", "28", "28", "29", "29", "30", "30", "31", "31" ]
[ "nonn", "new" ]
21
2
4
[ "A001405", "A007318", "A382850", "A382851" ]
null
Clark Kimberling, Apr 07 2025
2025-04-18T21:03:39
oeisdata/seq/A382/A382850.seq
2aae4a068e7a90c2f116873b156f41ab
A382851
a(n) = least number in row n of Pascal's triangle that exceeds every number in row n-1.
[ "2", "3", "4", "10", "15", "21", "56", "84", "210", "330", "495", "1287", "2002", "5005", "8008", "19448", "31824", "50388", "125970", "203490", "497420", "817190", "1961256", "3268760", "5311735", "13037895", "21474180", "51895935", "86493225", "206253075", "347373600", "818809200", "1391975640", "3247943160", "5567902560" ]
[ "nonn", "new" ]
8
2
1
[ "A007318", "A382850", "A382851" ]
null
Clark Kimberling, Apr 13 2025
2025-04-18T21:03:55
oeisdata/seq/A382/A382851.seq
edc2e936bf6a917a89ce03defd3dccef
A382853
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * (k! * Stirling1(n,k))^2.
[ "1", "1", "14", "588", "51064", "7542780", "1688795184", "532244030976", "224335607135616", "121793234373123840", "82750681453274478720", "68773648886955417943296", "68628724852793337500166144", "80970628401965472953705395200", "111490683570184861858636405923840", "177177650274516448010905794637332480" ]
[ "nonn" ]
15
0
3
[ "A382792", "A382804", "A382806", "A382853" ]
null
Seiichi Manyama, Apr 06 2025
2025-04-07T09:26:19
oeisdata/seq/A382/A382853.seq
22377001af020daaa9fcc31092fc5bd4
A382854
Decimal expansion of (1-log(2))/2.
[ "1", "5", "3", "4", "2", "6", "4", "0", "9", "7", "2", "0", "0", "2", "7", "3", "4", "5", "2", "9", "1", "3", "8", "3", "9", "3", "9", "2", "7", "0", "9", "1", "1", "7", "1", "5", "9", "6", "2", "2", "4", "9", "9", "3", "2", "8", "1", "9", "8", "7", "2", "3", "7", "2", "9", "3", "9", "6", "5", "9", "9", "9", "5", "2", "5", "3", "3", "0", "3", "1", "8", "9", "0", "1", "5", "1", "5", "2", "6", "4", "2", "1", "9", "7", "0", "6", "8" ]
[ "nonn", "cons" ]
13
0
2
[ "A187832", "A372858", "A382854", "A382884" ]
null
Sean A. Irvine, Apr 06 2025
2025-04-07T16:51:26
oeisdata/seq/A382/A382854.seq
47df28116da2f59652bc68c9d58b86f6
A382855
Number of minimum connected dominating sets in the n-diagonal intersection graph.
[ "3", "1", "40", "54", "1862", "32" ]
[ "nonn", "more" ]
15
3
1
null
null
Eric W. Weisstein, Apr 07 2025
2025-04-07T11:07:08
oeisdata/seq/A382/A382855.seq
61800f8b8e9854252964ecaf19a7bc88
A382856
Numbers whose prime indices do not have a mode of 1.
[ "1", "3", "5", "7", "9", "11", "13", "15", "17", "18", "19", "21", "23", "25", "27", "29", "31", "33", "35", "37", "39", "41", "43", "45", "47", "49", "50", "51", "53", "54", "55", "57", "59", "61", "63", "65", "67", "69", "71", "73", "75", "77", "79", "81", "83", "85", "87", "89", "90", "91", "93", "95", "97", "98", "99", "101", "103", "105", "107", "108", "109", "111", "113", "115" ]
[ "nonn" ]
9
1
2
[ "A000265", "A001222", "A002865", "A007814", "A024556", "A051903", "A056239", "A091602", "A106529", "A112798", "A116598", "A240312", "A241131", "A327473", "A327476", "A356862", "A359178", "A360013", "A360014", "A360015", "A362605", "A362611", "A362613", "A362614", "A363486", "A364061", "A364062", "A364158", "A364159", "A381437", "A381542", "A382526", "A382856" ]
null
Gus Wiseman, Apr 07 2025
2025-04-07T09:26:41
oeisdata/seq/A382/A382856.seq
7252946763687136705f46ee7ad160b6
A382857
Number of ways to permute the prime indices of n so that the run-lengths are all equal.
[ "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "2", "2", "1", "0", "1", "2", "1", "1", "1", "6", "1", "1", "2", "2", "2", "4", "1", "2", "2", "0", "1", "6", "1", "1", "1", "2", "1", "0", "1", "1", "2", "1", "1", "0", "2", "0", "2", "2", "1", "6", "1", "2", "1", "1", "2", "6", "1", "1", "2", "6", "1", "1", "1", "2", "1", "1", "2", "6", "1", "0", "1", "2", "1", "6", "2", "2" ]
[ "nonn", "changed" ]
10
0
7
[ "A000720", "A000961", "A001221", "A001222", "A003242", "A003963", "A005811", "A008480", "A044813", "A047966", "A056239", "A112798", "A164707", "A181821", "A238130", "A238279", "A239455", "A304442", "A328592", "A329738", "A335407", "A351201", "A351293", "A351294", "A351295", "A353744", "A353833", "A382771", "A382773", "A382774", "A382857", "A382858", "A382876", "A382877", "A382878", "A382879", "A383089", "A383112" ]
null
Gus Wiseman, Apr 09 2025
2025-04-21T10:47:15
oeisdata/seq/A382/A382857.seq
f491c907235eb4bb40ddf47c6a199df2
A382858
Number of ways to permute a multiset whose multiplicities are the prime indices of n so that the run-lengths are all equal.
[ "1", "1", "1", "2", "1", "1", "1", "6", "4", "0", "1", "6", "1", "0", "1", "24", "1", "12", "1", "2", "1", "0", "1", "36", "4", "0", "36", "0", "1", "10", "1", "120", "0", "0", "1", "84", "1", "0", "0", "24", "1", "3", "1", "0", "38", "0", "1", "240", "6", "18", "0", "0", "1", "246", "0", "6", "0", "0", "1", "96", "1", "0", "30", "720", "1", "0", "1", "0", "0", "14", "1", "660", "1", "0", "74", "0", "1", "0", "1" ]
[ "nonn" ]
6
1
4
[ "A000720", "A000961", "A001221", "A001222", "A003242", "A003963", "A044813", "A047966", "A048767", "A056239", "A098859", "A112798", "A140690", "A181821", "A182854", "A238130", "A304442", "A305936", "A329738", "A329739", "A335125", "A335407", "A351202", "A351291", "A351596", "A353744", "A353833", "A382771", "A382772", "A382773", "A382774", "A382857", "A382858", "A382878", "A382879", "A382912", "A382913", "A382914", "A382915" ]
null
Gus Wiseman, Apr 09 2025
2025-04-10T23:22:30
oeisdata/seq/A382/A382858.seq
513606d48b461dd6f7fc62790dd6ca73
A382859
a(n) = Sum_{k=0..n} binomial(n,k) * binomial((n-1)*(k+1),n-k).
[ "1", "1", "5", "37", "345", "3851", "49468", "713931", "11391985", "198523495", "3741919446", "75702725440", "1633591960883", "37404262517506", "904734768056239", "23030071358784701", "614912094171482849", "17172036245893988575", "500281954849350450946", "15170753984617328108901" ]
[ "nonn", "easy" ]
17
0
3
[ "A121673", "A121674", "A121675", "A381425", "A382859" ]
null
Seiichi Manyama, Apr 07 2025
2025-04-09T09:57:09
oeisdata/seq/A382/A382859.seq
c12db201602fc641841794315a1da89c
A382860
Number of odd Ulam numbers <= 10^n.
[ "2", "12", "60", "398", "3780", "36868", "368904", "3696883", "36977302", "369860633" ]
[ "nonn", "more" ]
8
1
1
[ "A002858", "A307331", "A382797", "A382860", "A382861" ]
null
Shyam Sunder Gupta, Apr 07 2025
2025-04-13T16:14:15
oeisdata/seq/A382/A382860.seq
413a832b0c3a4440fca99bd18271c4b6
A382861
Number of even Ulam numbers <= 10^n.
[ "4", "14", "65", "429", "3804", "37216", "371464", "3702470", "36999540", "369917405" ]
[ "nonn", "more" ]
7
1
1
[ "A002858", "A307331", "A382798", "A382860", "A382861" ]
null
Shyam Sunder Gupta, Apr 07 2025
2025-04-13T16:14:51
oeisdata/seq/A382/A382861.seq
93cda639c485205590db571c24a10bcc
A382862
Prime numbers whose congruence speed of tetration equals 1.
[ "2", "3", "11", "13", "17", "19", "23", "29", "31", "37", "41", "47", "53", "59", "61", "67", "71", "73", "79", "83", "89", "97", "103", "109", "113", "127", "131", "137", "139", "163", "167", "173", "179", "181", "191", "197", "211", "223", "227", "229", "233", "239", "241", "263", "269", "271", "277", "281", "283", "311", "313", "317", "331", "337", "347", "353", "359" ]
[ "nonn", "base", "new" ]
38
1
1
[ "A000040", "A317905", "A321131", "A373387", "A382862" ]
null
Marco Ripà and Gabriele Di Pietro, Apr 13 2025
2025-04-24T13:33:09
oeisdata/seq/A382/A382862.seq
3c5e294efcc659702c79ef90ad2a4fe4
A382863
a(2*k-1) and a(2*k) are a pair of prime numbers where 9*a(2*k-1) and 8*a(2*k) are neighboring integers.
[ "17", "19", "47", "53", "79", "89", "97", "109", "113", "127", "223", "251", "239", "269", "241", "271", "337", "379", "353", "397", "383", "431", "433", "487", "463", "521", "607", "683", "673", "757", "719", "809", "863", "971", "881", "991", "1087", "1223", "1153", "1297", "1279", "1439", "1297", "1459", "1327", "1493", "1361", "1531", "1423", "1601" ]
[ "nonn", "tabf" ]
7
1
1
null
null
Steven Lu, Apr 07 2025
2025-04-13T16:17:11
oeisdata/seq/A382/A382863.seq
409c3beb54a86f367cc91f3e355252f4
A382864
Triangle read by rows: T(n,k) = T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).
[ "1", "0", "1", "0", "1", "0", "1", "1", "0", "1", "1", "0", "1", "2", "0", "1", "2", "1", "0", "1", "3", "1", "0", "1", "3", "2", "0", "1", "4", "3", "0", "1", "4", "4", "1", "0", "1", "5", "5", "1", "0", "1", "5", "7", "2", "0", "1", "6", "8", "3", "0", "1", "6", "10", "5", "0", "1", "7", "12", "6", "1", "0", "1", "7", "14", "9", "1", "0", "1", "8", "16", "11", "2", "0", "1", "8", "19", "15", "3", "0", "1", "9", "21", "18", "5", "0", "1", "9", "24", "23", "7" ]
[ "nonn", "tabf" ]
23
0
14
[ "A000007", "A000009", "A000012", "A003056", "A004526", "A008284", "A026810", "A026811", "A026812", "A026813", "A026814", "A026815", "A026816", "A069905", "A291954", "A291960", "A291968", "A292047", "A292049", "A382864" ]
null
Seiichi Manyama, Apr 07 2025
2025-04-07T09:26:29
oeisdata/seq/A382/A382864.seq
36a69eee9ef43f988815e5dabaa0fff2
A382868
a(1) = 1, a(2) = 2. For n > 2 a(n) is the smallest novel number divisible by the smallest prime p which divides a(n-1) but does not divide a(n-2). If no such prime exists a(n) is the least novel k such that gcd(k, a(n-1)) > 1.
[ "1", "2", "4", "6", "3", "9", "12", "8", "10", "5", "15", "18", "14", "7", "21", "24", "16", "20", "25", "30", "22", "11", "33", "27", "36", "26", "13", "39", "42", "28", "32", "34", "17", "51", "45", "35", "49", "56", "38", "19", "57", "48", "40", "50", "44", "55", "60", "46", "23", "69", "54", "52", "65", "70", "58", "29", "87", "63", "77", "66", "62", "31", "93", "72", "64", "68", "85", "75" ]
[ "nonn", "changed" ]
18
1
2
[ "A064413", "A382868" ]
null
David James Sycamore, Apr 07 2025
2025-04-20T09:00:35
oeisdata/seq/A382/A382868.seq
a62a0a9844b7b001fd56f63ba9348c49
A382869
Numbers k >= 1 such that A018804(k) is a Fibonacci number (A000045).
[ "1", "2", "3", "4", "7", "9", "11", "1751", "2031", "45012", "105772", "1266256", "1490601", "1774525" ]
[ "nonn", "more" ]
10
1
2
[ "A000045", "A005382", "A018804", "A382869" ]
null
Ctibor O. Zizka, Apr 07 2025
2025-04-13T16:19:53
oeisdata/seq/A382/A382869.seq
412104cddadffe78519296b4074cb779
A382870
Minimum period of an optimum covering of the set of integers by translates of its subset with diameter no greater than n, maximized over such subsets.
[ "1", "2", "4", "5", "8", "8", "13", "13", "27", "27", "45", "53", "66", "109", "129", "147", "147", "170", "192", "250", "286", "317" ]
[ "nonn", "more" ]
5
0
2
null
null
Andrey Zabolotskiy, Apr 07 2025
2025-04-07T10:06:49
oeisdata/seq/A382/A382870.seq
6ffca38a47e7c19d9e829852c1204f6e
A382871
Number of ways to partition distinct prime numbers into two disjoint sets such that the sum of each set equals n.
[ "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "1", "1", "1", "2", "3", "3", "2", "3", "4", "6", "2", "5", "0", "5", "9", "7", "14", "8", "6", "10", "9", "21", "19", "11", "18", "15", "29", "34", "35", "34", "24", "31", "51", "55", "48", "76", "34", "60", "93", "89", "97", "91", "76", "83", "156", "164", "189", "145", "157", "172", "186", "283", "276", "218", "242", "280", "405", "433", "476", "446" ]
[ "nonn" ]
34
0
19
[ "A000607", "A108796", "A382871", "A382954" ]
null
Seiichi Manyama, Apr 09 2025
2025-04-10T08:34:33
oeisdata/seq/A382/A382871.seq
fd4b48ed68c60606fac108399d41551c
A382872
For n >= 1, a(n) is the number of divisors (A000005) of the Pillai's arithmetical function: Sum_{k=1..n} gcd(k, n) (A018804).
[ "1", "2", "2", "4", "3", "4", "2", "6", "4", "4", "4", "8", "3", "4", "6", "10", "4", "6", "2", "12", "4", "6", "6", "9", "4", "6", "5", "8", "4", "8", "2", "10", "8", "6", "6", "16", "2", "4", "4", "18", "5", "8", "4", "16", "8", "8", "4", "20", "4", "8", "8", "12", "8", "6", "8", "12", "4", "6", "6", "24", "3", "4", "8", "9", "9", "12", "4", "16", "9", "8", "4", "24", "4", "4", "6", "8", "8", "8", "2", "20" ]
[ "nonn" ]
11
1
2
[ "A000005", "A005408", "A018804", "A065091", "A382872" ]
null
Ctibor O. Zizka, Apr 07 2025
2025-04-13T16:20:02
oeisdata/seq/A382/A382872.seq
8212b5ed9434d2b13a03ae0211d4741b
A382873
a(n) = A019565(A014311(n)).
[ "30", "42", "70", "105", "66", "110", "165", "154", "231", "385", "78", "130", "195", "182", "273", "455", "286", "429", "715", "1001", "102", "170", "255", "238", "357", "595", "374", "561", "935", "1309", "442", "663", "1105", "1547", "2431", "114", "190", "285", "266", "399", "665", "418", "627", "1045", "1463", "494", "741", "1235", "1729", "2717", "646" ]
[ "nonn" ]
10
1
1
[ "A007304", "A014311", "A019565", "A382873" ]
null
Chai Wah Wu, Apr 07 2025
2025-04-10T07:06:29
oeisdata/seq/A382/A382873.seq
d5746a998182d4d87547da2b4debbdee
A382874
Expansion of g.f. 2-hypergeom([3/2,7/2],[-1/2],4*x).
[ "1", "42", "1890", "32340", "378378", "3567564", "29201172", "216164520", "1484052570", "9607866268", "59342703420", "352648983960", "2029131058500", "11360419371000", "62125264788840", "332868702695760", "1751865025825530", "9075126224864700", "46353422502086700", "233788539957892920" ]
[ "nonn" ]
18
0
2
[ "A001700", "A002421", "A002423", "A002457", "A382874" ]
null
Karol A. Penson, Apr 07 2025
2025-04-08T13:59:50
oeisdata/seq/A382/A382874.seq
a39466eb32fd4dc3d53888ff2d00e449
A382875
Numbers which are a multiple of 2^k - 1 for some k > 1.
[ "0", "3", "6", "7", "9", "12", "14", "15", "18", "21", "24", "27", "28", "30", "31", "33", "35", "36", "39", "42", "45", "48", "49", "51", "54", "56", "57", "60", "62", "63", "66", "69", "70", "72", "75", "77", "78", "81", "84", "87", "90", "91", "93", "96", "98", "99", "102", "105", "108", "111", "112", "114", "117", "119", "120", "123", "124", "126", "127", "129", "132", "133", "135", "138", "140" ]
[ "nonn" ]
5
1
2
[ "A000225", "A001477", "A161788", "A161789", "A161790", "A382875" ]
null
Stefano Spezia, Apr 07 2025
2025-04-12T12:33:18
oeisdata/seq/A382/A382875.seq
29ce964764aaa5e8d618ac5b17712472
A382876
Number of ways to permute the prime indices of n so that the run-sums are all different.
[ "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "0", "1", "2", "2", "1", "1", "2", "1", "2", "2", "2", "1", "2", "1", "2", "1", "2", "1", "6", "1", "1", "2", "2", "2", "2", "1", "2", "2", "2", "1", "6", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "2", "4", "2", "2", "1", "0", "1", "2", "0", "1", "2", "6", "1", "2", "2", "6", "1", "4", "1", "2", "2", "2", "2", "6", "1", "2", "1", "2", "1", "0", "2", "2", "2" ]
[ "nonn", "changed" ]
22
1
6
[ "A000720", "A000961", "A001221", "A001222", "A044813", "A056239", "A098859", "A112798", "A130091", "A304442", "A329738", "A329739", "A351013", "A351202", "A351596", "A353832", "A353837", "A353838", "A353847", "A353848", "A353850", "A353851", "A353852", "A353932", "A354580", "A354584", "A381636", "A382076", "A382771", "A382857", "A382876", "A382877", "A382879", "A383100" ]
null
Gus Wiseman, Apr 12 2025
2025-04-27T09:09:03
oeisdata/seq/A382/A382876.seq
ba0f1d58d9f8b3cf4e86c4173b8c3a18
A382877
Number of ways to permute the prime indices of n so that the run-sums are all equal.
[ "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "2", "1", "0", "0", "1", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "2", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "2", "1", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0" ]
[ "nonn", "new" ]
7
1
12
[ "A000720", "A000961", "A001221", "A001222", "A044813", "A056239", "A112798", "A130091", "A304442", "A329738", "A329739", "A351596", "A353832", "A353833", "A353837", "A353838", "A353847", "A353848", "A353850", "A353851", "A353852", "A353932", "A354584", "A381871", "A382076", "A382771", "A382857", "A382876", "A382877", "A382879", "A383015", "A383098", "A383099", "A383100", "A383110" ]
null
Gus Wiseman, Apr 14 2025
2025-04-17T23:21:24
oeisdata/seq/A382/A382877.seq
a2a8ab15e137039321a2f42a5510bc5f
A382878
Set of positions of first appearances in A382857 (permutations of prime indices with equal run-lengths).
[ "1", "6", "24", "30", "36", "180", "210", "360", "420", "720", "1080", "1260", "1800", "2160", "2310", "2520", "3600", "4620", "5040", "5400", "6300", "7560", "10800", "12600", "13860", "15120", "21600", "25200", "25920", "27000", "27720", "30030", "32400", "37800", "44100", "45360", "46656", "50400", "54000", "55440", "60060", "60480", "64800" ]
[ "nonn" ]
6
1
2
[ "A000720", "A001221", "A001222", "A003242", "A044813", "A048767", "A056239", "A098859", "A112798", "A130091", "A140690", "A238130", "A239455", "A305936", "A329738", "A329739", "A351013", "A351202", "A351293", "A351294", "A351295", "A351596", "A353744", "A381432", "A381433", "A382771", "A382772", "A382773", "A382857", "A382858", "A382876", "A382878", "A382879" ]
null
Gus Wiseman, Apr 09 2025
2025-04-10T23:17:13
oeisdata/seq/A382/A382878.seq
a1c9e52fcf00ccc7a1f544b98d940374
A382879
Positions of 0 in A382857 (permutations of prime indices with equal run-lengths).
[ "24", "40", "48", "54", "56", "80", "88", "96", "104", "112", "135", "136", "152", "160", "162", "176", "184", "189", "192", "208", "224", "232", "240", "248", "250", "272", "288", "296", "297", "304", "320", "328", "336", "344", "351", "352", "368", "375", "376", "384", "405", "416", "424", "448", "459", "464", "472", "480", "486", "488", "496", "513", "528", "536" ]
[ "nonn", "changed" ]
8
1
1
[ "A000720", "A000961", "A001221", "A001222", "A003242", "A005811", "A008480", "A047966", "A056239", "A112798", "A130091", "A164707", "A238279", "A239455", "A297770", "A304442", "A328592", "A329739", "A351201", "A351290", "A351291", "A351293", "A351294", "A351295", "A351596", "A353744", "A353833", "A382773", "A382857", "A382858", "A382876", "A382877", "A382878", "A382879", "A382914", "A382915", "A383013", "A383100" ]
null
Gus Wiseman, Apr 09 2025
2025-04-21T10:47:08
oeisdata/seq/A382/A382879.seq
75c68f53c557f8b3c0226c67435ddb2b
A382880
Symmetric triangle read by rows refining A109113.
[ "1", "1", "1", "6", "6", "1", "1", "11", "33", "33", "11", "1", "1", "16", "85", "189", "189", "85", "16", "1", "1", "21", "162", "590", "1107", "1107", "590", "162", "21", "1", "1", "26", "264", "1361", "3919", "6588", "6588", "3919", "1361", "264", "26", "1", "1", "31", "391", "2627", "10400", "25484", "39663", "39663", "25484", "10400", "2627", "391", "31", "1" ]
[ "nonn", "tabf" ]
13
0
4
[ "A109113", "A382880" ]
null
F. Chapoton, Apr 07 2025
2025-04-12T12:48:15
oeisdata/seq/A382/A382880.seq
dbdc38c5716f32ab4a72aa4904f13e4a
A382882
Triangle read by rows: T(n, k) = k^ord(n, k) where ord(n, k) is the p-adic order if n and k >= 2, 1 if k = 1, and 0^n if k = 0.
[ "0", "1", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "4", "1", "4", "1", "1", "1", "1", "1", "5", "1", "1", "2", "3", "1", "1", "6", "1", "1", "1", "1", "1", "1", "1", "7", "1", "1", "8", "1", "4", "1", "1", "1", "8", "1", "1", "1", "9", "1", "1", "1", "1", "1", "9", "1", "1", "2", "1", "1", "5", "1", "1", "1", "1", "10", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "11", "1", "1", "4", "3", "4", "1", "6", "1", "1", "1", "1", "1", "12" ]
[ "nonn", "tabl" ]
7
0
6
[ "A286563", "A364813", "A381886", "A382882" ]
null
Peter Luschny, Apr 07 2025
2025-04-08T08:49:13
oeisdata/seq/A382/A382882.seq
245808845c2484a1f0fce4dce12cf3fb
A382884
Decimal expansion of 1/6 + Pi/(12*sqrt(3)) - log(3)/4.
[ "0", "4", "3", "1", "6", "3", "5", "4", "1", "5", "1", "9", "1", "5", "7", "3", "9", "8", "0", "3", "4", "0", "2", "8", "5", "4", "5", "5", "7", "2", "8", "8", "1", "5", "5", "1", "5", "2", "8", "4", "6", "6", "2", "1", "4", "5", "5", "2", "0", "4", "1", "0", "1", "8", "3", "6", "3", "8", "1", "6", "8", "2", "7", "8", "7", "2", "9", "7", "0", "0", "2", "5", "1", "2", "2", "5", "4", "3", "9", "1", "5", "2", "5", "5", "2", "7", "3" ]
[ "nonn", "cons" ]
12
0
2
[ "A187832", "A382854", "A382884" ]
null
Sean A. Irvine, Apr 07 2025
2025-04-08T15:44:17
oeisdata/seq/A382/A382884.seq
3f92207367d3a9b6f892a2d4d32fb4da
A382885
G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x) * A(x) )^3.
[ "1", "3", "18", "121", "900", "7110", "58598", "498153", "4336533", "38463732", "346368351", "3158325168", "29102914959", "270582713670", "2535191045652", "23913087584045", "226892934532149", "2164080724942155", "20737076963936828", "199542537271568802", "1927347504059464995", "18679645863925666721" ]
[ "nonn" ]
22
0
2
[ "A052709", "A365178", "A371483", "A371576", "A382885" ]
null
Seiichi Manyama, Apr 08 2025
2025-04-08T08:47:26
oeisdata/seq/A382/A382885.seq
e6ee5e094d45845b4d672031ee59be46
A382886
G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^2 * A(x) )^3.
[ "1", "3", "21", "154", "1248", "10710", "95751", "882297", "8320812", "79927938", "779303829", "7692585186", "76726084742", "772066751871", "7828529324175", "79908510600542", "820435635949686", "8467306916189517", "87791572491261912", "914032693961190414", "9552050623400554164", "100162810727306404897" ]
[ "nonn" ]
24
0
2
[ "A073155", "A378786", "A382406", "A382886", "A382893" ]
null
Seiichi Manyama, Apr 08 2025
2025-04-08T08:47:21
oeisdata/seq/A382/A382886.seq
f9dbafddf816be9984072b050e70c4e8
A382887
Numbers k such that (k*2^d + 1)*(d*2^k + 1) is semiprime for some divisor d of k.
[ "1", "2", "8", "12", "30", "51", "63", "141", "201", "209", "534", "4713", "5795", "6611", "7050", "18496", "24105", "32292", "32469", "52782", "59656", "80190", "90825" ]
[ "nonn", "more", "new" ]
25
1
2
[ "A001358", "A002064", "A005849", "A382646", "A382887" ]
null
Juri-Stepan Gerasimov, Apr 07 2025
2025-04-16T05:42:04
oeisdata/seq/A382/A382887.seq
7b449d80085602b29ccdd461d7e2254f
A382888
The squarefree kernel of the n-th cubefree number.
[ "1", "2", "3", "2", "5", "6", "7", "3", "10", "11", "6", "13", "14", "15", "17", "6", "19", "10", "21", "22", "23", "5", "26", "14", "29", "30", "31", "33", "34", "35", "6", "37", "38", "39", "41", "42", "43", "22", "15", "46", "47", "7", "10", "51", "26", "53", "55", "57", "58", "59", "30", "61", "62", "21", "65", "66", "67", "34", "69", "70", "71", "73", "74", "15", "38", "77", "78", "79", "82" ]
[ "nonn", "easy" ]
9
1
2
[ "A002117", "A004709", "A005117", "A007947", "A371188", "A382888", "A382889", "A382890", "A382891" ]
null
Amiram Eldar, Apr 07 2025
2025-04-08T12:49:59
oeisdata/seq/A382/A382888.seq
be1cdf8b4dcfcdc4720351a81905b263
A382889
The largest square dividing the n-th cubefree number.
[ "1", "1", "1", "4", "1", "1", "1", "9", "1", "1", "4", "1", "1", "1", "1", "9", "1", "4", "1", "1", "1", "25", "1", "4", "1", "1", "1", "1", "1", "1", "36", "1", "1", "1", "1", "1", "1", "4", "9", "1", "1", "49", "25", "1", "4", "1", "1", "1", "1", "1", "4", "1", "1", "9", "1", "1", "1", "4", "1", "1", "1", "1", "1", "25", "4", "1", "1", "1", "1", "1", "4", "1", "1", "1", "1", "9", "1", "4", "1", "1", "1", "1", "49", "9", "100" ]
[ "nonn", "easy" ]
9
1
4
[ "A002117", "A004709", "A008833", "A057521", "A062503", "A371188", "A382888", "A382889", "A382890", "A382891" ]
null
Amiram Eldar, Apr 07 2025
2025-04-08T12:23:31
oeisdata/seq/A382/A382889.seq
18d0248904bf043c076382a5d1551353
A382890
The square root of the largest square dividing the n-th cubefree number.
[ "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "2", "1", "1", "1", "1", "3", "1", "2", "1", "1", "1", "5", "1", "2", "1", "1", "1", "1", "1", "1", "6", "1", "1", "1", "1", "1", "1", "2", "3", "1", "1", "7", "5", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "3", "1", "1", "1", "2", "1", "1", "1", "1", "1", "5", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "3", "1", "2", "1", "1", "1", "1", "7", "3", "10", "1", "1" ]
[ "nonn", "easy" ]
9
1
4
[ "A000188", "A004709", "A005117", "A057521", "A371188", "A382888", "A382889", "A382890", "A382891" ]
null
Amiram Eldar, Apr 07 2025
2025-04-08T13:02:18
oeisdata/seq/A382/A382890.seq
508c4ec54c89295fb725085d1b8d21d7
A382891
The powerfree part of the n-th cubefree number.
[ "1", "2", "3", "1", "5", "6", "7", "1", "10", "11", "3", "13", "14", "15", "17", "2", "19", "5", "21", "22", "23", "1", "26", "7", "29", "30", "31", "33", "34", "35", "1", "37", "38", "39", "41", "42", "43", "11", "5", "46", "47", "1", "2", "51", "13", "53", "55", "57", "58", "59", "15", "61", "62", "7", "65", "66", "67", "17", "69", "70", "71", "73", "74", "3", "19", "77", "78", "79", "82", "83" ]
[ "nonn", "easy" ]
9
1
2
[ "A002117", "A004709", "A005117", "A007913", "A055231", "A371188", "A382888", "A382889", "A382890", "A382891" ]
null
Amiram Eldar, Apr 07 2025
2025-04-08T12:23:22
oeisdata/seq/A382/A382891.seq
9c6d2bd0f989c930a739ac55030322cb
A382892
G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^3 * A(x) )^3.
[ "1", "3", "24", "190", "1659", "15309", "146986", "1453536", "14704917", "151479031", "1583533308", "16756882194", "179149227231", "1932144798513", "20996553430206", "229678298803028", "2527034248221849", "27947027713469307", "310494250880357488", "3463870813896354726", "38787008808135775299" ]
[ "nonn" ]
10
0
2
[ "A360076", "A366272", "A382614", "A382892", "A382894" ]
null
Seiichi Manyama, Apr 08 2025
2025-04-08T08:47:17
oeisdata/seq/A382/A382892.seq
75edcba1ab8e6af65dbd18a41d112973
A382893
G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^2 * A(x) )^2.
[ "1", "2", "11", "60", "365", "2350", "15767", "109048", "771993", "5567066", "40751267", "302018484", "2261763205", "17088919814", "130108591407", "997225521136", "7688232599089", "59581977618098", "463890112373563", "3626778446099756", "28461425971969693", "224114796803735774", "1770236735807921863" ]
[ "nonn" ]
9
0
2
[ "A073155", "A366221", "A382886", "A382893" ]
null
Seiichi Manyama, Apr 08 2025
2025-04-08T08:47:13
oeisdata/seq/A382/A382893.seq
cd8aad5a815d05a1617cf7a1b7a31a4e
A382894
G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^3 * A(x) )^2.
[ "1", "2", "13", "78", "520", "3664", "26859", "202808", "1566693", "12323982", "98381841", "795023284", "6490951398", "53462144788", "443683640945", "3706539244272", "31144893093298", "263052053436600", "2231992880546400", "19016760502183968", "162629329186013523", "1395500273826639540" ]
[ "nonn" ]
9
0
2
[ "A360076", "A366200", "A382613", "A382892", "A382894" ]
null
Seiichi Manyama, Apr 08 2025
2025-04-08T08:47:09
oeisdata/seq/A382/A382894.seq
7c9c29ea3d13bd9445ff5ec7a79b6b1f
A382895
Divide n successively by its nonzero digits from most to least significant, updating the result at each step and skipping any digit that doesn't divide the current value exactly.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "10", "11", "6", "13", "14", "3", "16", "17", "18", "19", "10", "21", "11", "23", "3", "5", "13", "27", "14", "29", "10", "31", "16", "11", "34", "7", "2", "37", "38", "13", "10", "41", "21", "43", "11", "9", "46", "47", "12", "49", "10", "51", "26", "53", "54", "11", "56", "57", "58", "59", "10", "61", "31", "21", "16", "13", "11", "67", "68", "69", "10", "71", "36", "73", "74", "15" ]
[ "nonn", "easy", "base" ]
15
1
10
[ "A051801", "A382895", "A382897" ]
null
Seiichi Manyama, Apr 08 2025
2025-04-08T08:46:19
oeisdata/seq/A382/A382895.seq
836dbaa9af328609c8aee543b5eeef9c