A355684 - OEIS

A355684

Dirichlet inverse of A355448.

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

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OFFSET

COMMENTS

Multiplicative because A355448 is.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

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

Adjacent sequences: A355681 A355682 A355683 * A355685 A355686 A355687

KEYWORD

sign,mult

AUTHOR

Antti Karttunen, Jul 14 2022

STATUS

approved