A378607 Dirichlet convolution of sigma and the Dirichlet inverse of A003961 (A346234).

1, 0, -1, -2, -1, 0, -3, -6, -7, 0, -1, 2, -3, 0, 1, -14, -1, 0, -3, 2, 3, 0, -5, 6, -11, 0, -25, 6, -1, 0, -5, -30, 1, 0, 3, 14, -3, 0, 3, 6, -1, 0, -3, 2, 7, 0, -5, 14, -31, 0, 1, 6, -5, 0, 1, 18, 3, 0, -1, -2, -5, 0, 21, -62, 3, 0, -3, 2, 5, 0, -1, 42, -5, 0, 11, 6, 3, 0, -3, 14, -79, 0, -5, -6, 1, 0, 1, 6, -7, 0, 9, 10

Offset

1,4

Links

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

Index entries for sequences related to prime indices in the factorization of n.

Index entries for sequences related to sigma(n).

Formula

a(n) = Sum_{d|n} A000203(d)*A346234(n/d).

a(n) = Sum_{d|n} A349388(d).

Prog

(PARI)
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A346234(n) = (moebius(n)*A003961(n));
A378607(n) = sumdiv(n, d, sigma(d)*A346234(n/d));

Crossrefs

Cf. A000203, A003961, A016825, A346234, A378606 (Dirichlet inverse).

Inverse Möbius transform of A349388.

Sequence in context: A230360 A244117 A263426 * A378606 A357103 A278882

Adjacent sequences: A378604 A378605 A378606 * A378608 A378610 A378611

Keyword

sign,mult,new

Author

Antti Karttunen, Dec 11 2024

Status

approved