A349352 Sum of A006368, "the amusical permutation", and its Dirichlet inverse.

2, 0, 0, 9, 0, 12, 0, 9, 4, 24, 0, 24, 0, 30, 16, 27, 0, 42, 0, 30, 20, 48, 0, 21, 16, 60, 20, 51, 0, 54, 0, 45, 32, 78, 40, 30, 0, 84, 40, 51, 0, 90, 0, 78, 52, 102, 0, 96, 25, 90, 52, 84, 0, 90, 64, 57, 56, 132, 0, 27, 0, 138, 74, 99, 80, 138, 0, 111, 68, 114, 0, 114, 0, 168, 68, 132, 80, 150, 0, 138, 61, 186, 0

Offset: 1

Author

Antti Karttunen, Nov 15 2021

Keywords

• sign

Comments

The first negative term is a(2520) = -918.

Links

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

Crossrefs

Cf. A006368, A349351, A349369, A349378.

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(dA006368(n) = ((3*n)+(n%2))\(2+((n%2)*2));
v349351 = DirInverseCorrect(vector(up_to,n,A006368(n)));
A349351(n) = v349351[n];
A349352(n) = (A006368(n)+A349351(n));

Formula

a(n) = A006368(n) + A349351(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A006368(d) * A349351(n/d).