A323881 Dirichlet inverse of A126760.

1, -1, -1, 0, -2, 1, -3, 0, 0, 2, -4, 0, -5, 3, 2, 0, -6, 0, -7, 0, 3, 4, -8, 0, -5, 5, 0, 0, -10, -2, -11, 0, 4, 6, 0, 0, -13, 7, 5, 0, -14, -3, -15, 0, 0, 8, -16, 0, -8, 5, 6, 0, -18, 0, -3, 0, 7, 10, -20, 0, -21, 11, 0, 0, -2, -4, -23, 0, 8, 0, -24, 0, -25, 13, 5, 0, -2, -5, -27, 0, 0, 14, -28, 0, -5, 15, 10, 0, -30, 0, -1, 0

Offset: 1

Author

Antti Karttunen, Feb 08 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A126760, A323882, A323883, A323886.

Programs

Mathematica

b[n_] := b[n] = Which[n == 0, 0, 0 < n < 4, 1, EvenQ[n], b[n/2], Mod[n, 3] == 0, b[n/3], Mod[n, 6] == 1, (n-1)/3 + 1, Mod[n, 6] == 5, (n-5)/3 + 2];
a[n_] := a[n] = If[n == 1, 1, -Sum[b[n/d] a[d], {d, Most@ Divisors[n]}]];
Array[a, 100] (* Jean-François Alcover, Feb 16 2020 *)

PARI

up_to = 20000;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1])*sumdiv(n, d, if(dA126760(n) = {n&&n\=3^valuation(n, 3)<A126760
v323881 = DirInverseCorrect(vector(up_to,n,A126760(n)));
A323881(n) = v323881[n];