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A282569 Number of compositions (ordered partitions) of n into multiplicatively perfect numbers (A007422). 1
1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 10, 13, 17, 22, 31, 44, 63, 88, 122, 166, 227, 312, 433, 601, 836, 1159, 1604, 2214, 3056, 4220, 5837, 8079, 11188, 15486, 21424, 29624, 40961, 56641, 78344, 108379, 149940, 207427, 286933, 396880, 548943, 759273, 1050234, 1452740, 2009545, 2779745, 3845085, 5318633, 7356839 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..52.

Eric Weisstein's World of Mathematics, Multiplicative Perfect Number

Index entries for sequences related to compositions

FORMULA

G.f.: 1/(1 - Sum_{k>=1} x^A007422(k)).

EXAMPLE

a(8) = 5 because we have [8], [6, 1, 1], [1, 6, 1], [1, 1, 6] and [1, 1, 1, 1, 1, 1, 1, 1].

MATHEMATICA

nmax = 52; CoefficientList[Series[1/(1 - Sum[Boole[Sqrt[k]^DivisorSigma[0, k]/k == k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A007422, A236473.

Sequence in context: A253170 A177332 A318155 * A213213 A319470 A115001

Adjacent sequences:  A282566 A282567 A282568 * A282570 A282571 A282572

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 18 2017

STATUS

approved

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Last modified October 15 13:36 EDT 2018. Contains 316236 sequences. (Running on oeis4.)