A347085 Sum of A129283 and its Dirichlet inverse.

2, 0, 0, 9, 0, 24, 0, 21, 16, 36, 0, 22, 0, 48, 48, 49, 0, 34, 0, 36, 64, 72, 0, 63, 36, 84, 56, 50, 0, -26, 0, 113, 96, 108, 96, 102, 0, 120, 112, 101, 0, -30, 0, 78, 76, 144, 0, 156, 64, 90, 144, 92, 0, 126, 144, 139, 160, 180, 0, 203, 0, 192, 104, 257, 168, -38, 0, 120, 192, -34, 0, 230, 0, 228, 124, 134, 192

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, A347083, A347084, A347086.

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]));
A129283(n) = (n + A003415(n));
v347084 = DirInverseCorrect(vector(up_to,n,A129283(n)));
A347084(n) = v347084[n];
A347085(n) = (A129283(n)+A347084(n));

Formula

a(n) = A129283(n) + A347084(n).

For n > 1, a(n) = -Sum_{d|n, 1A129283(d) * A347084(n/d).