A328777 Product_{n>=1} (1 + x^n)^a(n) = 1 + Sum_{n>=1} x^prime(n).

0, 1, 1, 0, 0, 0, 1, 0, -1, -1, 2, 1, 0, -2, 0, 1, 3, -3, -1, -1, 4, -1, -1, -4, 6, 2, 2, -13, 4, 4, 13, -15, -5, -5, 30, -11, -7, -34, 42, 7, 16, -78, 27, 18, 95, -117, -21, -49, 223, -76, -40, -262, 326, 48, 135, -642, 242, 103, 752, -938, -105, -408, 1826, -732, -240

Offset: 1

Author

Ilya Gutkovskiy, Oct 27 2019

Keywords

• sign

Comments

Inverse weigh transform of A010051.

Crossrefs

Cf. A000040, A000586, A010051, A305871, A308298.

Programs

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; a[n_] := a[n] = Boole[PrimeQ[n]] - b[n, n - 1]; Array[a, 65]