A281501
Number of partitions of n^3 into distinct parts.
Original entry on oeis.org
1, 1, 6, 192, 16444, 3207086, 1258238720, 916112394270, 1168225267521350, 2496696209705056142, 8635565795744155161506, 46977052491046305327286932, 392416122247953159916295467008, 4931628582570689013431218105121792, 91603865924570978521516549662581412000
Offset: 0
a(2) = 6 because we have [8], [7, 1], [6, 2], [5, 3], [5, 2, 1] and [4, 3, 1].
A267709
Number of partitions of pentagonal numbers.
Original entry on oeis.org
1, 1, 7, 77, 1002, 14883, 239943, 4087968, 72533807, 1327710076, 24908858009, 476715857290, 9275102575355, 182973889854026, 3652430836071053, 73653287861850339, 1498478743590581081, 30724985147095051099, 634350763653787028583, 13177726323474524612308
Offset: 0
a(2) = 7, because second pentagonal number is a 5 and 5 can be partitioned in 7 distinct ways: 5, 4 + 1, 3 + 2, 3 + 1 + 1, 3 + 2 + 1, 2 + 1 + 1 + 1, 1 + 1 + 1 + 1 + 1.
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Table[PartitionsP[n ((3 n - 1)/2)], {n, 0, 19}]
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a(n)=numbpart(n*(3*n-1)/2) \\ Charles R Greathouse IV, Jul 26 2016
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from sympy.ntheory import npartitions
print([npartitions(n*(3*n - 1)//2) for n in range(51)]) # Indranil Ghosh, Apr 11 2017
A355728
Indices k of partition function where consecutive p(k) and p(k+1) are prime.
Original entry on oeis.org
2, 3, 4, 5, 1085
Offset: 1
5 is in the sequence because A000041(5) = 7 and A000041(6) = 11 are prime.
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for(k=1, 5000, if(ispseudoprime(numbpart(k))&&ispseudoprime(numbpart(k+1)), print1(k, ", ")))
A355956
Index k of partition function p such that p(k) is a member of a cousin prime pair.
Original entry on oeis.org
3, 5, 6, 13, 36, 157, 302, 546, 2502, 2732, 19439060
Offset: 1
5 is in the sequence because A000041(5) = 7 and 7 + 4 = 11 are cousin primes.
13 is in the sequence because A000041(13) = 101 and 101 - 4 = 97 are cousin primes.
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for(n=1, 10000, if(ispseudoprime(p=numbpart(n))&&(ispseudoprime(p-4)||ispseudoprime(p+4)), print1(n, ", ")))
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