A282568 Number of compositions (ordered partitions) of n into abundant numbers (A005101).

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

Author

Ilya Gutkovskiy, Feb 18 2017

Keywords

• nonn

Examples

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

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
• Index entries for sequences related to compositions

Crossrefs

Cf. A005101, A097798.

Programs

Mathematica

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

PARI

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

Formula

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