A347083 Sum of -A168036 and its Dirichlet inverse.

2, 0, 0, 1, 0, 4, 0, -1, 4, 8, 0, -4, 0, 12, 16, -7, 0, -2, 0, -6, 24, 20, 0, -19, 16, 24, 4, -8, 0, -14, 0, -21, 40, 32, 48, -18, 0, 36, 48, -33, 0, -18, 0, -12, 4, 44, 0, -58, 36, 6, 64, -14, 0, -22, 80, -47, 72, 56, 0, -29, 0, 60, 8, -47, 96, -26, 0, -18, 88, -22, 0, -62, 0, 72, 20, -20, 120, -30, 0, -108, -11, 80

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, A168036, A347082, A347085.

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]));
A168036(n) = (A003415(n)-n);
v347082 = DirInverseCorrect(vector(up_to,n,-A168036(n)));
A347082(n) = v347082[n];
A347083(n) = (A347082(n)-A168036(n));

Formula

a(n) = A347082(n) - A168036(n).

For n > 1, a(n) = Sum_{d|n, 1A168036(d) * A347082(n/d).