|
%I #15 Jul 24 2022 04:25:28
%S 0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,1,0,0,
%T 0,1,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,
%U 0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,1
%N a(n) = 1 if the number of its divisors, tau(n), is divisible by 3, otherwise 0.
%H Antti Karttunen, <a href="/A353470/b353470.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F a(n) = 1 if A010872(A000005(n)) is zero, otherwise 0.
%F For all n >= 1, a(n) >= A302048(n).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 - zeta(3)/zeta(2) = 0.2692370305... . - _Amiram Eldar_, Jul 24 2022
%t a[n_] := If[Divisible[DivisorSigma[0, n], 3], 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jul 24 2022 *)
%o (PARI) A353470(n) = !(numdiv(n)%3);
%Y Characteristic function of A059269.
%Y Cf. A000005, A010872, A302048.
%K nonn
%O 1
%A _Antti Karttunen_, Apr 21 2022
|
