A323766 Dirichlet convolution of the integer partition numbers A000041 with the number of divisors function A000005.

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

Author

Gus Wiseman, Jan 27 2019

Keywords

• nonn

Comments

Also the number of constant multiset partitions of constant multiset partitions of integer partitions of n.

Examples

			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))
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000005, A000041, A000837, A001970, A034729, A047968, A306017, A319066, A323764, A323765, A323774.

Programs

Mathematica

Table[If[n==0,1,Sum[PartitionsP[d]*DivisorSigma[0,n/d],{d,Divisors[n]}]],{n,0,30}]

PARI

a(n) = if (n==0, 1, sumdiv(n, d, numbpart(d)*numdiv(n/d))); \\ Michel Marcus, Jan 28 2019

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*n*sqrt(3)). - Vaclav Kotesovec, Jan 28 2019