A283761 Number of partitions of n into distinct multiplicatively perfect numbers (A007422).

1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 2, 3, 2, 1, 1, 1, 1, 3, 4, 3, 3, 3, 2, 3, 4, 5, 5, 4, 5, 6, 5, 7, 9, 8, 7, 8, 9, 10, 11, 12, 12, 12, 13, 14, 16, 18, 18, 18, 17, 18, 22, 24, 26, 28, 27, 27, 29, 32, 36, 38, 38, 40, 42, 43, 46, 50, 54, 57, 60, 61, 62, 67, 71, 74, 79, 83, 88, 90, 94, 102, 106, 108

Offset: 0

Author

Ilya Gutkovskiy, Mar 16 2017

Keywords

• nonn

Examples

			a(15) = 3 because we have [15], [14, 1] and [8, 6, 1].
		

Links

• Eric Weisstein's World of Mathematics, Multiplicative Perfect Number
• Index entries for related partition-counting sequences

Crossrefs

Cf. A007422, A236473.

Programs

Mathematica

nmax = 85; CoefficientList[Series[Product[1 + Boole[Sqrt[k]^DivisorSigma[0, k]/k == k] x^k, {k, 1, nmax}], {x, 0, nmax}], x]

PARI

a(k) = k==1 || numdiv(k) == 4;
Vec(prod(k=1, 85, 1 + a(k)*x^k) + O(x^86)) \\ Indranil Ghosh and modified by Michel Marcus, Mar 17 2017

Formula

G.f.: Product_{k>=1} (1 + x^A007422(k)).