A355685 Dirichlet inverse of A353380.

1, 0, 0, -1, 0, -1, 0, -1, -1, 0, 0, -1, 0, -1, -1, 1, 0, -1, 0, -1, 0, 0, 0, 2, -1, -1, -1, -1, 0, 0, 0, 1, -1, 0, -1, 2, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 3, -1, -1, -1, -1, 0, 2, 0, 2, 0, -1, 0, 1, 0, 0, -1, -1, -1, 0, 0, -1, -1, 0, 0, 5, 0, -1, -1, -1, -1, 0, 0, 2, 1, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, -1, -1, 0, -1, -2, 0, -1, -1, 1, 0, 0, 0, 2, 0

Offset

1,24

Links

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

Index entries for sequences computed from indices in prime factorization

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A353380(n/d) * a(d).

a(p) = 0 for all primes p.

a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.

Prog

(PARI)
A332823(n) = { my(f = factor(n), u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u, -1, u); };
A353354(n) = sumdiv(n, d, A332823(d));
A353380(n) = (0==A353354(n));
memoA355685 = Map();
A355685(n) = if(1==n, 1, my(v); if(mapisdefined(memoA355685, n, &v), v, v = -sumdiv(n, d, if(d<n, A353380(n/d)*A355685(d), 0)); mapput(memoA355685, n, v); (v)));

Crossrefs

Cf. A003961, A048675, A332823, A348717, A353354, A353355, A353380.

Cf. also A353348, A353418.

Sequence in context: A056977 A309144 A085425 * A244250 A167230 A093658

Adjacent sequences: A355682 A355683 A355684 * A355686 A355687 A355688

Keyword

sign

Author

Antti Karttunen, Jul 14 2022

Status

approved