login
A355684
Dirichlet inverse of A355448.
2
1, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
1
COMMENTS
Multiplicative because A355448 is.
LINKS
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A355448(n/d) * a(d).
Multiplicative with a(p) = 0, and for e > 1, a(p^e) = -1 if e == 2 or 3 (mod 4) and 1 otherwise. - Amiram Eldar, Feb 09 2023
MATHEMATICA
f[p_, e_] := If[Mod[e, 4] < 2, 1, -1]; f[p_, 1] = 0; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 09 2023 *)
PROG
(PARI)
A355448(n) = (1==gcd(numdiv(n^2), 6));
memoA355684 = Map();
A355684(n) = if(1==n, 1, my(v); if(mapisdefined(memoA355684, n, &v), v, v = -sumdiv(n, d, if(d<n, A355448(n/d)*A355684(d), 0)); mapput(memoA355684, n, v); (v)));
CROSSREFS
Cf. A112526 (apparently gives the absolute values), A355448.
Sequence in context: A075802 A112526 A307423 * A355683 A373374 A120523
KEYWORD
sign,mult
AUTHOR
Antti Karttunen, Jul 14 2022
STATUS
approved