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%I #7 Apr 03 2017 20:37:22
%S 1,0,0,0,1,0,0,0,2,1,0,0,2,1,0,0,4,2,1,0,4,2,1,0,6,5,2,2,6,5,2,2,10,8,
%T 5,4,12,8,5,4,16,14,8,9,18,16,8,9,24,23,15,14,30,25,18,14,36,36,26,25,
%U 42,42,29,28,52,54,42,40,65,60,50,43,78,78,65,63,93,92,73,72,110,117,96,94,135,133,114,103,158,166,145
%N Expansion of Product_{p prime, k>=2} 1/(1 - x^(p^k)).
%C Number of partitions of n into proper prime powers (A246547).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePower.html">Prime Power</a>
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{p prime, k>=2} 1/(1 - x^(p^k)).
%e a(16) = 4 because we have [16], [8, 8], [8, 4, 4] and [4, 4, 4, 4].
%t nmax = 90; CoefficientList[Series[Product[1/(1 - Sign[PrimeOmega[k] - 1] Floor[1/PrimeNu[k]] x^k), {k, 2, nmax}], {x, 0, nmax}], x]
%o (PARI) x='x+O('x^68); Vec(prod(k=2, 67, 1/(1 - sign(bigomega(k) - 1) * (1\omega(k)) * x^k))) \\ _Indranil Ghosh_, Apr 03 2017
%Y Cf. A023893, A023894, A246547.
%K nonn
%O 0,9
%A _Ilya Gutkovskiy_, Jan 06 2017
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