A302234 - OEIS

%I #5 Apr 03 2018 15:11:49

%S 1,-1,0,0,-1,1,-1,1,-1,0,1,0,0,1,0,-1,1,0,0,0,0,-1,1,-1,1,-2,1,-1,0,1,

%T -1,1,-2,2,-1,-1,2,-1,-1,2,-2,2,-1,1,0,-1,1,0,1,-2,2,0,0,2,-1,0,0,1,0,

%U 0,1,-2,0,-1,0,0,-2,2,-3,0,2,-2,1,-1,1,-2,1,-1,-1,1

%N Expansion of Product_{k>=1} (1 - x^k)/(1 - x^prime(k)).

%C The difference between the number of partitions of n into an even number of distinct nonprime parts and the number of partitions of n into an odd number of distinct nonprime parts.

%C Convolution of the sequences A000607 and A010815.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F G.f.: Product_{k>=1} (1 - x^A018252(k)).

%t nmax = 80; CoefficientList[Series[Product[(1 - x^k)/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]

%t nmax = 80; CoefficientList[Series[Product[(1 - Boole[!PrimeQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000607, A002095, A010815, A018252, A046675, A096258, A302236.

%K sign

%O 0,26

%A _Ilya Gutkovskiy_, Apr 03 2018