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%I #9 Apr 23 2017 23:59:09
%S 1,0,0,1,0,1,1,1,1,2,2,2,3,3,4,4,5,6,7,8,9,10,12,14,15,18,20,23,26,29,
%T 33,37,42,46,53,58,66,74,81,91,101,113,124,139,153,169,188,207,228,
%U 252,278,304,336,369,405,444,487,533,583,640,697,763,832,908,990,1078,1175,1278
%N Expansion of Product_{k>=1} 1/(1 - floor(1/omega(2*k+1))*x^(2*k+1)), where omega() is the number of distinct prime factors (A001221).
%C Number of partitions of n into odd prime powers (1 excluded).
%H G. C. Greubel, <a href="/A280151/b280151.txt">Table of n, a(n) for n = 0..1000</a>
%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_{k>=1} 1/(1 - floor(1/omega(2*k+1))*x^(2*k+1)).
%e a(12) = 3 because we have [9, 3], [7, 5], [3, 3, 3, 3].
%t nmax = 67; CoefficientList[Series[Product[1/(1 - Floor[1/PrimeNu[2 k + 1]] x^(2 k + 1)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A001221, A018819, A023894, A061345, A246655, A280152.
%K nonn
%O 0,10
%A _Ilya Gutkovskiy_, Dec 27 2016
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