A349353 Dirichlet inverse of A328203.

1, -2, -5, 0, -8, 10, -11, 0, 5, 16, -17, 0, -20, 22, 38, 0, -26, -10, -29, 0, 52, 34, -35, 0, 11, 40, 1, 0, -44, -76, -47, 0, 80, 52, 82, 0, -56, 58, 94, 0, -62, -104, -65, 0, -34, 70, -71, 0, 19, -22, 122, 0, -80, -2, 126, 0, 136, 88, -89, 0, -92, 94, -46, 0, 148, -160, -101, 0, 164, -164, -107, 0, -110, 112, -45

Offset: 1

Author

Antti Karttunen, Nov 15 2021

Keywords

• sign

Links

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

Crossrefs

Dirichlet convolution of A349134 with A349341, or equally of A349343 with A349344.

Cf. A328203, A349354.

Programs

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(dA328203(n) = if(n%2,(1/2)*(sigma(n)+(n*numdiv(n))),2*A328203(n/2));
v349353 = DirInverseCorrect(vector(up_to,n,A328203(n)));
A349353(n) = v349353[n];

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A328203(n/d) * a(d).

a(n) = A349354(n) - A328203(n).

a(n) = Sum_{d|n} A349134(d) * A349341(n/d).

a(n) = Sum_{d|n} A349343(d) * A349344(n/d).