A349354 Sum of A328203 and its Dirichlet inverse.

2, 0, 0, 4, 0, 20, 0, 8, 25, 32, 0, 20, 0, 44, 80, 16, 0, 30, 0, 32, 110, 68, 0, 40, 64, 80, 75, 44, 0, 8, 0, 32, 170, 104, 176, 80, 0, 116, 200, 64, 0, 12, 0, 68, 140, 140, 0, 80, 121, 84, 260, 80, 0, 146, 272, 88, 290, 176, 0, 168, 0, 188, 195, 64, 320, 20, 0, 104, 350, 24, 0, 160, 0, 224, 242, 116, 374, 24, 0

Offset

1,1

Links

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

Formula

a(n) = A328203(n) + A349353(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A328203(d) * A349353(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.
A328203(n) = if(n%2, (1/2)*(sigma(n)+(n*numdiv(n))), 2*A328203(n/2));
v349353 = DirInverseCorrect(vector(up_to, n, A328203(n)));
A349353(n) = v349353[n];
A349354(n) = (A328203(n)+A349353(n));

Crossrefs

Cf. A328203, A349353.

Sequence in context: A354867 A346247 A323412 * A354352 A273346 A369731

Adjacent sequences: A349351 A349352 A349353 * A349355 A349356 A349357

Keyword

nonn

Author

Antti Karttunen, Nov 15 2021

Status

approved