%I #4 Nov 28 2020 09:12:05
%S 1,0,0,0,1,0,2,0,1,1,3,0,3,1,4,3,5,1,6,4,8,6,9,5,12,9,14,11,17,13,22,
%T 17,24,21,31,26,37,31,42,39,52,46,61,56,71,67,84,79,100,95,114,111,
%U 135,131,158,154,180,180,212,209,244,244,280,283,324,325,372,378,426,434,487
%N Number of partitions of n into prime parts where every part appears at least 2 times.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F G.f.: Product_{k>=1} (1 + x^(2*prime(k)) / (1 - x^prime(k))).
%e a(10) = 3 because we have [5, 5], [3, 3, 2, 2] and [2, 2, 2, 2, 2].
%t nmax = 70; CoefficientList[Series[Product[1 + x^(2 Prime[k])/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000040, A000607, A007690, A161077.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Nov 27 2020