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A282568 Number of compositions (ordered partitions) of n into abundant numbers (A005101). 1
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 5, 0, 2, 0, 2, 0, 8, 0, 5, 0, 0, 0, 13, 0, 8, 0, 5, 0, 21, 0, 16, 0, 5, 0, 37, 0, 26, 0, 14, 0, 55, 0, 48, 0, 24, 0, 99, 0, 82, 0, 48, 0, 154, 0, 150, 0, 85, 0, 265, 0, 248, 0, 163, 0, 433, 0, 450, 0, 290 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,25

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..200

Eric Weisstein's World of Mathematics, Abundant Number

Index entries for sequences related to compositions

FORMULA

G.f.: 1/(1 - Sum_{k>=1} x^A005101(k)).

EXAMPLE

a(30) = 3 because we have [30], [18, 12] and [12, 18].

MATHEMATICA

nmax = 95; CoefficientList[Series[1/(1 - Sum[Boole[DivisorSigma[1, k] > 2 k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

PROG

(PARI) Vec(1/(1 - sum(k=1, 95, (sigma(k)>2*k)*x^k)) + O(x^95)) \\ Indranil Ghosh, Mar 15 2017

CROSSREFS

Cf. A005101, A097798.

Sequence in context: A047764 A022883 A284270 * A028833 A024943 A005929

Adjacent sequences:  A282565 A282566 A282567 * A282569 A282570 A282571

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 18 2017

STATUS

approved

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Last modified February 23 23:15 EST 2018. Contains 299595 sequences. (Running on oeis4.)