A359422 Dirichlet inverse of A187074, characteristic function of numbers that are neither multiples of 3 nor of the form 4u+2.

1, 0, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, -1, 1, 0, 0, 1, 0, -1, 0, 0, 1, -1, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 1, 1, 0, 0, -1, 0, -1, 0, 0, 1, 1, 0, -1, 1, 0, 0, -1, 0, -1, 0, 0, 1, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 1, -1, 0, 1, 1, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 1, 0

Offset

1

Comments

Multiplicative because A187074 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} A187074(n/d) * a(d).

Multiplicative with a(2^e) = A010892(e), a(3^e) = 0, and for p >= 5, a(p) = -1 and a(p^e) = 0 for e > 1. - Amiram Eldar, Jan 03 2023

Mathematica

s[n_] := If[Mod[n, 3] == 0 || Mod[n, 4] == 2, 0, 1]; a[1] = 1; a[n_] := a[n] = -DivisorSum[n, a[#]*s[n/#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Dec 31 2022 *)
f[p_, e_] := If[e == 1, -1, 0]; f[3, e_] := 0; f[2, e_] := {1, 1, 0, -1, -1, 0}[[Mod[e, 6] + 1]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 03 2023 *)

Crossrefs

Cf. A010892, A187074.

Cf. also A156277, A355688, A355689, A355690.

Sequence in context: A028863 A089012 A083035 * A356161 A187074 A188398

Adjacent sequences: A359419 A359420 A359421 * A359423 A359424 A359425

Keyword

sign,mult

Author

Antti Karttunen, Dec 31 2022

Status

approved