A347084 Dirichlet inverse of A129283, n + A003415(n).

1, -3, -4, 1, -6, 13, -8, 1, 1, 19, -12, -6, -14, 25, 25, 1, -18, -5, -20, -8, 33, 37, -24, -5, 1, 43, 2, -10, -30, -87, -32, 1, 49, 55, 49, 6, -38, 61, 57, -7, -42, -113, -44, -14, -8, 73, -48, -4, 1, -5, 73, -16, -54, -9, 73, -9, 81, 91, -60, 51, -62, 97, -10, 1, 85, -165, -68, -20, 97, -163, -72, 2, -74, 115

Offset: 1

Author

Antti Karttunen, Aug 17 2021

Keywords

• sign

Links

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

Crossrefs

Cf. A003415, A129283, A347082, A347085, A347086, A348995 (positions of 1's).

Cf. also A346241, A348976.

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(dA003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
v347084 = DirInverseCorrect(vector(up_to,n,n+A003415(n)));
A347084(n) = v347084[n];

Formula

a(1) = 1; and for n > 2, a(n) = -Sum_{d|n, dA129283(n/d).

a(n) = A347085(n) - A129283(n).

a(n) = A347082(n) - A347086(n).