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%I #7 Aug 02 2019 12:59:35
%S 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 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 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 Number of partitions of n into odd semiprimes (A046315).
%H Amiram Eldar, <a href="/A280912/b280912.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F 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 a(39) = 3 because we have [39], [21, 9, 9] and [15, 15, 9].
%t 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]
%Y Cf. A001222, A001358, A046315, A099773, A101048, A112020.
%K nonn
%O 0,31
%A _Ilya Gutkovskiy_, Jan 10 2017
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