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%I #9 Aug 02 2019 13:02:13
%S 1,0,1,1,1,2,1,3,2,4,3,5,5,6,7,7,10,9,12,12,15,15,18,19,22,24,26,30,
%T 32,36,40,43,49,52,58,63,69,76,81,91,96,108,114,127,135,148,159,173,
%U 186,202,217,234,253,271,293,313,339,361,390,416,449,478,514,547,588,625,671,714,763,815,867
%N Number of partitions of n into distinct parts with an odd number of distinct prime divisors.
%H Amiram Eldar, <a href="/A286220/b286220.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} (1 + x^A030230(k)).
%e a(9) = 4 because we have [9], [7, 2], [5, 4] and [4, 3, 2].
%t nmax = 70; CoefficientList[Series[Product[1 + Boole[OddQ[PrimeNu[k]]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A030230, A285799, A286221.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, May 04 2017
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