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A283761 Number of partitions of n into distinct multiplicatively perfect numbers (A007422). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 24 14:41 EST 2018. Contains 299623 sequences. (Running on oeis4.)