A341698 a(1) = a(2) = 1; a(n+1) = -Sum_{d|n, d < n} a(n/d) * a(d).

1, 1, -1, 1, -2, 2, 0, 0, -2, 1, 3, -3, 1, -1, 1, -5, 4, -4, 12, -12, 14, -14, 8, -8, 10, -14, 12, -16, 18, -18, 26, -26, 36, -30, 22, -22, 24, -24, 0, 2, 20, -20, -10, 10, 12, -18, 2, -2, 14, -14, -2, 10, 16, -16, -8, 20, 14, 10, -46, 46, -52, 52, -104, 132, -70, 74, -186, 186, -134, 150

Offset: 1

Author

Ilya Gutkovskiy, Feb 17 2021

Keywords

• sign

Crossrefs

Cf. A038044, A325303, A341697.

Programs

Mathematica

a[1] = a[2] = 1; a[n_] := a[n] = -Sum[If[d < (n - 1), a[(n - 1)/d] a[d], 0], {d, Divisors[n - 1]}]; Table[a[n], {n, 70}]

PARI

A341698(n) = if(n<3, 1, sumdiv(n-1,d,if(d<(n-1), -A341698((n-1)/d)*A341698(d), 0))); \\ Antti Karttunen, Feb 17 2021