A349354 Sum of A328203 and its Dirichlet inverse.

2, 0, 0, 4, 0, 20, 0, 8, 25, 32, 0, 20, 0, 44, 80, 16, 0, 30, 0, 32, 110, 68, 0, 40, 64, 80, 75, 44, 0, 8, 0, 32, 170, 104, 176, 80, 0, 116, 200, 64, 0, 12, 0, 68, 140, 140, 0, 80, 121, 84, 260, 80, 0, 146, 272, 88, 290, 176, 0, 168, 0, 188, 195, 64, 320, 20, 0, 104, 350, 24, 0, 160, 0, 224, 242, 116, 374, 24, 0

Offset: 1

Author

Antti Karttunen, Nov 15 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A328203, A349353.

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];
A349354(n) = (A328203(n)+A349353(n));

Formula

a(n) = A328203(n) + A349353(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A328203(d) * A349353(n/d).