%I
%S 1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,2,2,1,2,2,2,4,4,2,3,4,4,5,6,5,5,6,7,9,
%T 10,10,12,11,11,15,16,15,17,18,19,23,26,25,27,30,33,37,38,39,46,50,52,
%U 57,59,61,71,77,78,84,91,97,107,114,120,131,139,147,163,172,180,197
%N Number of partitions of n into distinct parts with an even number of distinct prime divisors.
%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 partitioncounting sequences</a>
%F G.f.: Product_{k>=1} (1 + x^A030231(k)).
%e a(21) = 4 because we have [21], [20, 1], [15, 6] and [14, 6, 1].
%t nmax = 75; CoefficientList[Series[Product[1 + Boole[EvenQ[PrimeNu[k]]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A030231, A285798, A286220.
%K nonn
%O 0,16
%A _Ilya Gutkovskiy_, May 04 2017
