A353815 a(n) = 1 if sigma(n) is not a multiple of 3, otherwise 0.

1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0

Offset

1

Links

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

Index entries for characteristic functions

Index entries for sequences related to sigma(n)

Formula

a(n) = A011655(A000203(n)).

a(n) = [A074941(n) > 0], where [ ] is the Iverson bracket.

a(n) <= A353816(n).

Multiplicative with a(3^e) = 1, and if p == 1 (mod 3), a(p^e) = 0 if e == 2 (mod 3), otherwise 1, and if p == 2 (mod 3), then a(p^e) = 1 if e is even, otherwise 0. - Antti Karttunen, Jul 03 2024

Mathematica

a[n_] := If[!Divisible[DivisorSigma[1, n], 3], 1, 0]; Array[a, 100] (* Amiram Eldar, May 15 2022 *)

Prog

(PARI) A353815(n) = (0!=(sigma(n)%3));
(PARI) A353815(n) = { my(f=factor(n)); prod(i=1, #f~, if(3==f[i, 1], 1, 1==(f[i, 1]%3), 2!=(f[i, 2]%3), (1+f[i, 2])%2)); }; \\ Antti Karttunen, Jul 03 2024

Crossrefs

Characteristic function of A329963.

Cf. A000203, A011655, A070563, A074941, A353816, A373593.

Sequence in context: A266502 A075438 A118174 * A156258 A132138 A141212

Adjacent sequences: A353812 A353813 A353814 * A353816 A353817 A353818

Keyword

nonn,mult

Author

Antti Karttunen, May 15 2022

Extensions

Keyword:mult added and incorrect comment removed by Antti Karttunen, Jul 03 2024

Status

approved