%I #5 Dec 02 2020 20:59:03

%S 1,0,1,0,1,1,1,2,2,3,4,4,6,7,8,10,13,14,19,20,26,29,36,40,51,56,70,76,

%T 96,105,129,143,172,192,231,254,308,339,402,447,529,586,691,764,896,

%U 993,1159,1281,1493,1652,1912,2114,2445,2699,3110,3436,3939,4356,4982,5497,6280

%N Number of partitions of n into an even 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 [8, 1], [6, 1, 1, 1] and [4, 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, A027187, A184198, A302236, A339380, A339396.

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Dec 02 2020