A359422 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

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