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%I #8 Dec 27 2016 13:23:40
%S 1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,
%T 1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,2,1,0,1,1,1,0,
%U 0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1
%N Expansion of Product_{k>=1} (1 + x^(prime(k)^2))*(1 + x^(prime(k)^3)).
%C Number of partitions of n into distinct parts that are squares of primes (A001248) or cubes of primes (A030078).
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} (1 + x^(prime(k)^2))*(1 + x^(prime(k)^3)).
%e a(61) = 2 because we have [49, 8, 4] and [25, 27, 9].
%t nmax = 120; CoefficientList[Series[Product[(1 + x^Prime[k]^2) (1 + x^Prime[k]^3), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000586, A001248, A030078, A106244, A111900, A111902, A131799, A168363, A280125.
%K nonn
%O 0,62
%A _Ilya Gutkovskiy_, Dec 26 2016
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