A347090 Dirichlet inverse of A332844.

1, -3, -4, 1, -6, 12, -8, 3, 2, 18, -12, -4, -14, 24, 24, -2, -18, -6, -20, -6, 32, 36, -24, -12, 4, 42, 4, -8, -30, -72, -32, 0, 48, 54, 48, 2, -38, 60, 56, -18, -42, -96, -44, -12, -12, 72, -48, 8, 6, -12, 72, -14, -54, -12, 72, -24, 80, 90, -60, 24, -62, 96, -16, 0, 84, -144, -68, -18, 96, -144, -72, 6, -74, 114

Offset: 1

Author

Antti Karttunen, Aug 18 2021

Keywords

• sign
• mult
• look

Comments

Multiplicative because A332844 is.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A332844, A347091.

Programs

PARI

up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA332844(n) = sumdiv(n,d, issquare(n/d) * sigma(d));
v347090 = DirInverseCorrect(vector(up_to,n,A332844(n)));
A347090(n) = v347090[n];

Formula

a(1) = 1; a(n) = -Sum_{d|n, dA332844(n/d) * a(d).

a(n) = A347091(n) - A332844(n).