This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A282566 #10 Feb 16 2025 08:33:41
%S A282566 1,1,2,4,8,16,31,62,123,244,484,960,1904,3777,7492,14861,29478,58472,
%T A282566 115984,230064,456350,905208,1795554,3561628,7064780,14013568,
%U A282566 27797058,55137735,109370201,216944729,430327593,853589936,1693165371,3358531834,6661922265,13214467050,26211974934,51993593638,103133540536
%N A282566 Number of compositions (ordered partitions) of n into deficient numbers (A005100).
%H A282566 Indranil Ghosh, <a href="/A282566/b282566.txt">Table of n, a(n) for n = 0..200</a>
%H A282566 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DeficientNumber.html">Deficient Number</a>
%H A282566 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A282566 G.f.: 1/(1 - Sum_{k>=1} x^A005100(k)).
%e A282566 a(3) = 4 because we have [3], [2, 1], [1, 2] and [1, 1, 1].
%t A282566 nmax = 38; CoefficientList[Series[1/(1 - Sum[Boole[DivisorSigma[1, k] < 2 k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
%o A282566 (PARI) Vec(1/(1 - sum(k=1, 38, (sigma(k)<2*k)*x^k)) + O(x^39)) \\ _Indranil Ghosh_, Mar 15 2017
%Y A282566 Cf. A005100, A097797.
%K A282566 nonn
%O A282566 0,3
%A A282566 _Ilya Gutkovskiy_, Feb 18 2017