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

1,1

Comments

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

Links

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

Formula

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

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

Prog

(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(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A006368(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));

Crossrefs

Cf. A006368, A349351, A349369, A349378.

Sequence in context: A000425 A230878 A349369 * A323896 A345065 A323364

Adjacent sequences: A349349 A349350 A349351 * A349353 A349354 A349355

Keyword

sign

Author

Antti Karttunen, Nov 15 2021

Status

approved