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 A280912 #10 Feb 16 2025 08:33:39
%S A280912 1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,2,0,0,2,
%T A280912 1,1,2,0,0,3,1,0,3,1,1,3,1,0,4,2,2,5,1,1,5,3,1,6,3,2,8,2,1,7,5,4,9,4,
%U A280912 3,11,6,3,11,6,6,14,7,5,15,9,7,16,9,8,20,14,9,21,13,11,26,16,12,28,19,17,29,19,17,37,27
%N A280912 Number of partitions of n into odd semiprimes (A046315).
%H A280912 Amiram Eldar, <a href="/A280912/b280912.txt">Table of n, a(n) for n = 0..10000</a>
%H A280912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%H A280912 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A280912 G.f.: Product_{k>=1} 1/(1 - floor(bigomega(2*k+1)/2)*floor(2/bigomega(2*k+ 1))*x^(2*k+1)), where bigomega(k) is the number of prime divisors of k counted with multiplicity (A001222).
%e A280912 a(39) = 3 because we have [39], [21, 9, 9] and [15, 15, 9].
%t A280912 nmax = 100; CoefficientList[Series[Product[1/(1 - Floor[PrimeOmega[2 k + 1]/2] Floor[2/PrimeOmega[2 k + 1]] x^(2 k + 1)), {k, 1, nmax}], {x, 0, nmax}], x]
%t A280912 Join[{1},Table[Count[IntegerPartitions[n],_?(AllTrue[#,OddQ]&&Union[PrimeOmega[#]]=={2}&)],{n,110}]] (* _Harvey P. Dale_, Nov 11 2024 *)
%Y A280912 Cf. A001222, A001358, A046315, A099773, A101048, A112020.
%K A280912 nonn
%O A280912 0,31
%A A280912 _Ilya Gutkovskiy_, Jan 10 2017