A327800 Expansion of 1 / (1 + Sum_{i>=1, j>=1} x^(i*prime(j))).

1, 0, -1, -1, 0, 1, 0, 0, 1, 1, -2, -3, 0, 4, 2, -3, 0, 4, -1, -10, -5, 12, 13, -6, -12, 7, 9, -20, -28, 23, 57, 1, -59, -18, 51, -5, -93, 1, 176, 93, -189, -188, 131, 183, -191, -220, 370, 525, -347, -902, 44, 973, 64, -1071, 171, 1881, 156, -2974, -1537

Offset: 0

Author

Ilya Gutkovskiy, Sep 25 2019

Keywords

• sign

Crossrefs

Cf. A001221, A300671.

Programs

Mathematica

nmax = 58; CoefficientList[Series[1/(1 + Sum[x^Prime[k]/(1 - x^Prime[k]), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[PrimeNu[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 58}]

Formula

G.f.: 1 / (1 + Sum_{k>=1} x^prime(k) / (1 - x^prime(k))).

a(0) = 1; a(n) = -Sum_{k=1..n} A001221(k) * a(n-k).