A328970 Numbers k such that the coefficient of x^k in the expansion of Product_{j>=1} (1 - x^j) / (1 - x^prime(j)) is zero.

2, 3, 9, 11, 12, 14, 17, 18, 19, 20, 28, 44, 47, 51, 52, 55, 56, 58, 59, 62, 64, 65, 69, 80, 81, 82, 83, 87, 91, 92, 94, 96, 99, 105, 106, 107, 113, 118, 119, 126, 127, 131, 147, 155, 157, 160, 161, 162, 164, 178, 179, 180, 215, 218, 224, 227, 257, 259, 269, 295

Offset: 1

Author

Ilya Gutkovskiy, Nov 01 2019

Keywords

• nonn

Comments

Numbers k such that number of partitions of k into an even number of distinct nonprime parts equals number of partitions of k into an odd number of distinct nonprime parts.

Positions of 0's in A302234.

Crossrefs

Cf. A002095, A018252, A090864, A096258, A302234.

Programs

Mathematica

a[j_] := a[j] = If[j == 0, 1, -Sum[Sum[Boole[!PrimeQ[d]] d, {d, Divisors[k]}] a[j - k], {k, 1, j}]/j]; Select[Range[300], a[#] == 0 &]
Flatten[Position[nmax = 300; Rest[CoefficientList[Series[Product[(1 - x^j)/(1 - x^Prime[j]), {j, 1, nmax}], {x, 0, nmax}], x]], 0]]