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

0,15

Links

Table of n, a(n) for n=0..85.

Eric Weisstein's World of Mathematics, Multiplicative Perfect Number

Index entries for related partition-counting sequences

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007422, A236473.

Sequence in context: A174985 A008406 A039735 * A171457 A129385 A217983

Adjacent sequences: A283758 A283759 A283760 * A283762 A283763 A283764

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 16 2017

Status

approved