A354349 Dirichlet inverse of A181819, prime shadow of n.

1, -2, -2, 1, -2, 4, -2, -1, 1, 4, -2, -2, -2, 4, 4, 2, -2, -2, -2, -2, 4, 4, -2, 2, 1, 4, -1, -2, -2, -8, -2, -3, 4, 4, 4, 1, -2, 4, 4, 2, -2, -8, -2, -2, -2, 4, -2, -4, 1, -2, 4, -2, -2, 2, 4, 2, 4, 4, -2, 4, -2, 4, -2, 7, 4, -8, -2, -2, 4, -8, -2, -1, -2, 4, -2, -2, 4, -8, -2, -4, 2, 4, -2, 4, 4, 4, 4, 2, -2, 4, 4

Offset

1,2

Comments

Multiplicative because A181819 is.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A181819(n/d) * a(d).

Prog

(PARI)
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
memoA354349 = Map();
A354349(n) = if(1==n, 1, my(v); if(mapisdefined(memoA354349, n, &v), v, v = -sumdiv(n, d, if(d<n, A181819(n/d)*A354349(d), 0)); mapput(memoA354349, n, v); (v)));

Crossrefs

Cf. A181819.

Cf. also A354186, A354351, A354359.

Sequence in context: A228441 A156260 A056671 * A278763 A278762 A374903

Adjacent sequences: A354346 A354347 A354348 * A354350 A354351 A354352

Keyword

sign,mult

Author

Antti Karttunen, Jun 05 2022

Status

approved