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 A280544 #8 Feb 16 2025 08:33:39
%S A280544 1,0,0,0,1,0,1,0,2,1,3,0,5,2,8,3,13,5,22,10,34,18,58,31,94,57,153,99,
%T A280544 254,172,417,302,685,523,1136,901,1872,1557,3097,2673,5133,4577,8505,
%U A280544 7843,14109,13380,23440,22816,38953,38855,64789,66053,107871,112190,179664,190369,299478,322683,499501,546548
%N A280544 Expansion of 1/(1 - Sum_{k>=2} (1 - floor(2/d(k)))*x^k), where d(k) is the number of divisors (A000005).
%C A280544 Number of compositions (ordered partitions) of n into composite parts (A002808).
%H A280544 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompositeNumber.html">Composite Number</a>
%H A280544 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A280544 G.f.: 1/(1 - Sum_{k>=2} (1 - floor(2/d(k)))*x^k).
%e A280544 a(10) = 3 because we have [10], [6, 4] and [4, 6].
%t A280544 nmax = 59; CoefficientList[Series[1/(1 - Sum[(1 - Floor[2/DivisorSigma[0, k]]) x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
%o A280544 (PARI) x='x+O('x^60); Vec(1/(1 - sum(k=2, 59, (1 - 2\numdiv(k))*x^k))) \\ _Indranil Ghosh_, Apr 03 2017
%Y A280544 Cf. A000005, A002808, A023360, A023895, A052284.
%K A280544 nonn
%O A280544 0,9
%A A280544 _Ilya Gutkovskiy_, Jan 05 2017