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A282568
Number of compositions (ordered partitions) of n into abundant numbers (A005101).
2
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
OFFSET
0,25
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..1221 (terms 0..200 from Indranil Ghosh)
Eric Weisstein's World of Mathematics, Abundant Number
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
Sequence in context: A022883 A284270 A337542 * A028833 A024943 A325787
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 18 2017
STATUS
approved