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 A280238 #9 Feb 16 2025 08:33:38
%S A280238 1,0,0,0,1,0,1,0,1,1,3,0,2,2,6,3,6,3,11,10,16,10,23,23,40,34,52,52,93,
%T A280238 94,130,133,209,234,330,352,488,570,804,909,1198,1405,1918,2283,2980,
%U A280238 3512,4622,5636,7340,8811,11321,13864,17937,21957,27936,34262,43857,54290,68915,84940,107685,133811,169615,210375,265305
%N A280238 Expansion of 1/(1 - Sum_{k>=2} floor(bigomega(k)/2)*floor(2/bigomega(k))*x^k), where bigomega(k) is the number of prime divisors of k counted with multiplicity (A001222).
%C A280238 Number of compositions (ordered partitions) into semiprimes (A001358).
%H A280238 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%H A280238 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A280238 G.f.: 1/(1 - Sum_{k>=2} floor(bigomega(k)/2)*floor(2/bigomega(k))*x^k).
%e A280238 a(10) = 3 because we have [4, 6], [6, 4] and [10].
%t A280238 nmax = 44; CoefficientList[Series[1/(1 - Sum[Floor[PrimeOmega[k]/2] Floor[2/PrimeOmega[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
%Y A280238 Cf. A001222, A001358, A023360, A101048.
%K A280238 nonn
%O A280238 0,11
%A A280238 _Ilya Gutkovskiy_, Dec 29 2016