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 A281617 #11 May 21 2021 16:19:18
%S A281617 0,0,0,0,1,0,1,0,2,1,3,0,5,2,6,3,9,3,14,7,16,10,23,12,32,20,37,28,52,
%T A281617 35,69,49,80,68,110,83,137,112,166,150,215,178,268,239,324,303,406,
%U A281617 365,504,472,604,584,747,708,917,888,1089,1085,1337,1311,1618,1606,1916,1954,2332,2334,2782,2829,3300,3407,3963
%N A281617 Expansion of Sum_{i = p*q, p prime, q prime} x^i/(1 - x^i) / Product_{j = p*q, p prime, q prime} (1 - x^j).
%C A281617 Total number of parts in all partitions of n into semiprimes (A001358).
%C A281617 Convolution of A086971 and A101048.
%H A281617 Alois P. Heinz, <a href="/A281617/b281617.txt">Table of n, a(n) for n = 0..10000</a>
%H A281617 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A281617 G.f.: Sum_{i = p*q, p prime, q prime} x^i/(1 - x^i) / Product_{j = p*q, p prime, q prime} (1 - x^j).
%F A281617 a(n) = Sum_{k>0} k * A344447(n,k). - _Alois P. Heinz_, May 19 2021
%e A281617 a(12) = 5 because we have [6, 6], [4, 4, 4] and 2 + 3 = 5.
%p A281617 h:= proc(n) option remember; `if`(n=0, 0,
%p A281617 `if`(numtheory[bigomega](n)=2, n, h(n-1)))
%p A281617 end:
%p A281617 b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, [0$2],
%p A281617 `if`(i>n, 0, (p-> p+[0, p[1]])(b(n-i, h(min(n-i, i)))))+b(n, h(i-1))))
%p A281617 end:
%p A281617 a:= n-> b(n, h(n))[2]:
%p A281617 seq(a(n), n=0..70); # _Alois P. Heinz_, May 19 2021
%t A281617 nmax = 70; Rest[CoefficientList[Series[Sum[Floor[PrimeOmega[i]/2] Floor[2/PrimeOmega[i]] x^i/(1 - x^i), {i, 2, nmax}]/Product[1 - Floor[PrimeOmega[j]/2] Floor[2/PrimeOmega[j]] x^j, {j, 2, nmax}], {x, 0, nmax}], x]]
%Y A281617 Cf. A001358, A084993, A086971, A101048, A344447.
%K A281617 nonn
%O A281617 0,9
%A A281617 _Ilya Gutkovskiy_, Jan 25 2017