A282566 Number of compositions (ordered partitions) of n into deficient numbers (A005100).

1, 1, 2, 4, 8, 16, 31, 62, 123, 244, 484, 960, 1904, 3777, 7492, 14861, 29478, 58472, 115984, 230064, 456350, 905208, 1795554, 3561628, 7064780, 14013568, 27797058, 55137735, 109370201, 216944729, 430327593, 853589936, 1693165371, 3358531834, 6661922265, 13214467050, 26211974934, 51993593638, 103133540536

Offset

0,3

Links

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

Eric Weisstein's World of Mathematics, Deficient Number

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A005100(k)).

Example

a(3) = 4 because we have [3], [2, 1], [1, 2] and [1, 1, 1].

Mathematica

nmax = 38; 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, 38, (sigma(k)<2*k)*x^k)) + O(x^39)) \\ Indranil Ghosh, Mar 15 2017

Crossrefs

Cf. A005100, A097797.

Sequence in context: A003240 A378698 A280543 * A251706 A251711 A251741

Adjacent sequences: A282563 A282564 A282565 * A282567 A282568 A282569

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 18 2017

Status

approved