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%I #4 Dec 02 2020 20:59:09
%S 0,1,0,1,1,1,2,1,3,3,4,4,6,6,9,9,13,14,18,20,26,29,37,39,51,57,69,78,
%T 95,105,129,141,173,192,231,255,306,340,403,446,531,585,691,764,896,
%U 995,1160,1279,1493,1652,1911,2117,2443,2700,3109,3434,3941,4357,4983,5496,6277
%N Number of partitions of n into an odd number of nonprime parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F G.f.: (1/2) * (Product_{k>=1} (1 - x^prime(k)) / (1 - x^k) - Product_{k>=1} (1 + x^prime(k)) / (1 + x^k)).
%F a(n) = (A002095(n) - A302236(n)) / 2.
%e a(9) = 3 because we have [9], [4, 4, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1].
%t nmax = 60; CoefficientList[Series[(1/2) (Product[(1 - x^Prime[k])/(1 - x^k), {k, 1, nmax}] - Product[(1 + x^Prime[k])/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A002095, A018252, A027193, A184199, A302236, A339381, A339395.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Dec 02 2020
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