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%I #5 Jul 29 2017 19:27:55
%S 1,0,1,1,1,2,3,3,5,5,8,9,12,15,19,23,29,35,43,52,64,77,93,111,134,158,
%T 190,225,266,315,372,435,514,599,703,819,955,1110,1290,1493,1732,1998,
%U 2309,2659,3062,3518,4040,4630,5305,6063,6931,7907,9015,10265,11680,13268,15070,17087,19366,21923,24799
%N Number of partitions of n into parts that contain primes to odd powers only (A002035).
%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} 1/(1 - x^A002035(k)).
%e a(7) = 3 because we have [7], [5, 2] and [3, 2, 2].
%t nmax = 60; CoefficientList[Series[Product[1/(1 - Boole[And @@ OddQ /@ FactorInteger[k][[All, 2]]] x^k), {k, 2, nmax}], {x, 0, nmax}], x]
%Y Cf. A002035, A290370.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Jul 28 2017
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