A349351 Dirichlet inverse of A006368, "the amusical permutation", a(2n)=3n, a(4n+1)=3n+1, a(4n-1)=3n-1.

1, -3, -2, 3, -4, 3, -5, -3, -3, 9, -8, 6, -10, 9, 5, 3, -13, 15, -14, 0, 4, 15, -17, -15, -3, 21, 0, 9, -22, 9, -23, -3, 7, 27, 14, -24, -28, 27, 11, -9, -31, 27, -32, 12, 18, 33, -35, 24, -12, 15, 14, 6, -40, 9, 23, -27, 13, 45, -44, -63, -46, 45, 27, 3, 31, 39, -50, 9, 16, 9, -53, 6, -55, 57, 12, 18, 22, 33, -59

Offset: 1

Author

Antti Karttunen, Nov 15 2021

Keywords

• sign

Links

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

Crossrefs

Cf. A006368, A349352, A349368, A349377.

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];

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A006368(n/d) * a(d).

a(n) = A349352(n) - A006368(n).