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%I #9 Apr 25 2017 10:02:39
%S 1,0,0,1,0,1,0,1,1,1,1,1,2,1,2,1,3,2,2,3,3,3,3,4,4,5,4,6,6,6,7,7,9,8,
%T 9,10,11,12,11,14,14,16,15,18,19,19,21,22,25,25,27,28,32,32,34,36,40,
%U 41,42,47,49,52,53,57,62,63,67,71,76,79,82,88,93,98,100,108,114,118,124
%N Expansion of Product_{k>=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 distinct odd prime powers (1 excluded).
%H G. C. Greubel, <a href="/A280152/b280152.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 + floor(1/omega(2*k+1))*x^(2*k+1)).
%e a(16) = 3 because we have [13, 3], [11, 5], [9, 7].
%t nmax = 78; CoefficientList[Series[Product[1 + Floor[1/PrimeNu[2 k + 1]] x^(2 k + 1), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A001221, A054685, A061345, A246655, A280151.
%K nonn
%O 0,13
%A _Ilya Gutkovskiy_, Dec 27 2016
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