A355693 Dirichlet inverse of A330749, gcd(n, A064989(n)), where A064989 shifts the prime factorization one step towards lower primes.

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

Offset

1,35

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} A330749(n/d) * a(d).

Prog

(PARI)
A330749(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); gcd(n, factorback(f)); };
memoA355693 = Map();
A355693(n) = if(1==n, 1, my(v); if(mapisdefined(memoA355693, n, &v), v, v = -sumdiv(n, d, if(d<n, A330749(n/d)*A355693(d), 0)); mapput(memoA355693, n, v); (v)));

Crossrefs

Cf. A064989, A330749.

Cf. also A354365, A354366.

Sequence in context: A107889 A138384 A129172 * A318291 A251482 A381954

Adjacent sequences: A355690 A355691 A355692 * A355694 A355695 A355696

Keyword

sign

Author

Antti Karttunen, Jul 18 2022

Status

approved