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A349354
Sum of A328203 and its Dirichlet inverse.
3
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
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
Sequence in context: A354867 A346247 A323412 * A354352 A273346 A369731
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 15 2021
STATUS
approved