A353815 - OEIS

%I #29 Jul 03 2024 20:06:46

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A353815/b353815.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

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

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

%F a(n) <= A353816(n).

%F 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

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

%o (PARI) A353815(n) = (0!=(sigma(n)%3));

%o (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

%Y Characteristic function of A329963.

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

%K nonn,mult

%O 1

%A _Antti Karttunen_, May 15 2022

%E Keyword:mult added and incorrect comment removed by _Antti Karttunen_, Jul 03 2024