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A302236
Expansion of Product_{k>=1} (1 + x^prime(k))/(1 + x^k).
3
1, -1, 1, -1, 0, 0, -1, 1, -1, 0, 0, 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, -1, 1, 0, -1, 1, -2, 1, 0, 0, 2, -1, 0, 0, -1, 2, -1, -1, 1, -2, 1, 0, 0, 0, -2, -1, 2, 0, 0, 1, -3, 2, -1, 1, 2, -2, -1, -1, 1, 3, 0, -2, 1, -2, 0, 3, 0, 0, -2, -2, 5, 1, 1, -1, -4, 1, -1, 2, 4, -2
OFFSET
0,28
COMMENTS
The difference between the number of partitions of n into an even number of nonprime parts and the number of partitions of n into an odd number of nonprime parts.
Convolution of the sequences A000586 and A081362.
FORMULA
G.f.: Product_{k>=1} 1/(1 + x^A018252(k)).
MATHEMATICA
nmax = 80; CoefficientList[Series[Product[(1 + x^Prime[k])/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 80; CoefficientList[Series[Product[1/(1 + Boole[!PrimeQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
KEYWORD
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AUTHOR
Ilya Gutkovskiy, Apr 03 2018
STATUS
approved