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A285798 Number of partitions of n into parts with an even number of distinct prime divisors. 7

%I

%S 1,1,1,1,1,1,2,2,2,2,3,3,5,5,6,7,8,8,11,11,14,16,19,19,25,26,31,34,40,

%T 41,51,53,62,68,80,85,103,107,124,135,157,166,195,205,235,256,294,311,

%U 362,383,437,472,535,568,652,695,786,847,954,1016,1155,1231,1381,1486,1662,1774,1997,2130,2377,2557,2846

%N Number of partitions of n into parts with an even number of distinct prime divisors.

%H Alois P. Heinz, <a href="/A285798/b285798.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

%F G.f.: Product_{k>=1} 1/(1 - x^A030231(k)).

%e a(10) = 3 because we have [10], [6, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

%t nmax = 70; CoefficientList[Series[Product[1/(1 - Boole[EvenQ[PrimeNu[k]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A030231, A087153 (number of partitions into parts with an even number of divisors), A285799.

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, Apr 26 2017

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Last modified June 18 01:16 EDT 2021. Contains 345098 sequences. (Running on oeis4.)