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 A282135 #7 Feb 16 2025 08:33:40
%S A282135 0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,3,4,6,6,3,9,9,12,12,6,10,15,18,16,12,
%T A282135 12,21,27,27,21,18,24,30,36,36,25,27,36,49,48,36,36,51,51,54,57,66,63,
%U A282135 42,57,75,72,66,51,69,78,79,90,102,73,75,84,117,126,84,75,105,123,121,114,120,124,102,117,156,156,129
%N A282135 Expansion of (Sum_{k = p*q, p prime, q prime} x^k)^3.
%C A282135 Number of ways to write n as an ordered sum of three semiprimes (A001358).
%C A282135 Conjecture: a(n) > 0 for n > 15.
%H A282135 Ilya Gutkovskiy, <a href="/A282135/a282135.pdf">Extended graphical example</a>
%H A282135 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%F A282135 G.f.: (Sum_{k = p*q, p prime, q prime} x^k)^3.
%e A282135 a(14) = 3 because we have [6, 4, 4], [4, 6, 4] and [4, 4, 6].
%t A282135 nmax = 83; Rest[CoefficientList[Series[Sum[Floor[PrimeOmega[k]/2] Floor[2/PrimeOmega[k]] x^k, {k, 2, nmax}]^3, {x, 0, nmax}], x]]
%Y A282135 Cf. A001358, A098238, A199331.
%K A282135 nonn
%O A282135 1,14
%A A282135 _Ilya Gutkovskiy_, Feb 06 2017