%I #20 Jan 29 2017 01:39:42

%S 0,0,0,1,0,0,0,2,1,0,0,3,2,0,0,4,3,2,0,5,4,3,0,6,6,4,3,7,8,5,4,8,10,8,

%T 5,13,12,10,6,15,14,12,10,17,21,14,12,19,25,18,14,25,29,27,16,28,33,

%U 33,21,31,42,38,31,34,47,43,38,41,52,54,43,53,57,62,51,62,67,69,64,68,82,76,74,78,94,89,82,93

%N Expansion of Sum_{k>=1} x^(prime(k)^2)/(1 - x^(prime(k)^2)) / Product_{k>=1} (1 - x^(prime(k)^2)).

%C Total number of parts in all partitions of n into squares of primes (A001248).

%C Convolution of A056170 and A090677.

%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>

%F G.f.: Sum_{k>=1} x^(prime(k)^2)/(1 - x^(prime(k)^2)) / Product_{k>=1} (1 - x^(prime(k)^2)).

%e a(25) = 6 because we have [25], [9, 4, 4, 4, 4] and 1 + 5 = 6.

%t nmax = 88; Rest[CoefficientList[Series[Sum[x^Prime[k]^2/(1 - x^Prime[k]^2), {k, 1, nmax}]/Product[1 - x^Prime[k]^2, {k, 1, nmax}], {x, 0, nmax}], x]]

%Y Cf. A001248, A056170, A084993, A090677, A281541.

%K nonn

%O 1,8

%A _Ilya Gutkovskiy_, Jan 27 2017