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%I A282568 #13 Oct 01 2018 21:08:24
%S A282568 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,
%T A282568 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,
%U A282568 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
%N A282568 Number of compositions (ordered partitions) of n into abundant numbers (A005101).
%H A282568 Antti Karttunen, <a href="/A282568/b282568.txt">Table of n, a(n) for n = 0..1221</a> (terms 0..200 from Indranil Ghosh)
%H A282568 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AbundantNumber.html">Abundant Number</a>
%H A282568 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A282568 G.f.: 1/(1 - Sum_{k>=1} x^A005101(k)).
%e A282568 a(30) = 3 because we have [30], [18, 12] and [12, 18].
%t A282568 nmax = 95; CoefficientList[Series[1/(1 - Sum[Boole[DivisorSigma[1, k] > 2 k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
%o A282568 (PARI) Vec(1/(1 - sum(k=1, 95, (sigma(k)>2*k)*x^k)) + O(x^95)) \\ _Indranil Ghosh_, Mar 15 2017
%Y A282568 Cf. A005101, A097798.
%K A282568 nonn
%O A282568 0,25
%A A282568 _Ilya Gutkovskiy_, Feb 18 2017

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