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A323766
Dirichlet convolution of the integer partition numbers A000041 with the number of divisors function A000005.
5
1, 1, 4, 5, 12, 9, 25, 17, 42, 39, 64, 58, 132, 103, 173, 200, 303, 299, 491, 492, 756, 832, 1122, 1257, 1858, 1975, 2646, 3083, 4057, 4567, 6118, 6844, 8913, 10265, 12912, 14931, 19089, 21639, 27003, 31397, 38830, 44585, 55138, 63263, 77371, 89585, 108076
OFFSET
0,3
COMMENTS
Also the number of constant multiset partitions of constant multiset partitions of integer partitions of n.
LINKS
FORMULA
a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*n*sqrt(3)). - Vaclav Kotesovec, Jan 28 2019
EXAMPLE
The a(6) = 25 constant multiset partitions of constant multiset partitions of integer partitions of 6:
((6))
((52))
((42))
((33))
((3)(3))
((3))((3))
((411))
((321))
((222))
((2)(2)(2))
((2))((2))((2))
((3111))
((2211))
((21)(21))
((21))((21))
((21111))
((111111))
((111)(111))
((11)(11)(11))
((111))((111))
((11))((11))((11))
((1)(1)(1)(1)(1)(1))
((1)(1)(1))((1)(1)(1))
((1)(1))((1)(1))((1)(1))
((1))((1))((1))((1))((1))((1))
MATHEMATICA
Table[If[n==0, 1, Sum[PartitionsP[d]*DivisorSigma[0, n/d], {d, Divisors[n]}]], {n, 0, 30}]
PROG
(PARI) a(n) = if (n==0, 1, sumdiv(n, d, numbpart(d)*numdiv(n/d))); \\ Michel Marcus, Jan 28 2019
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 27 2019
STATUS
approved