A353470 - OEIS

A353470

a(n) = 1 if the number of its divisors, tau(n), is divisible by 3, otherwise 0.

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, 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, 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

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OFFSET

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions.

Index entries for sequences computed from exponents in factorization of n.

FORMULA

a(n) = 1 if A010872(A000005(n)) is zero, otherwise 0.

For all n >= 1, a(n) >= A302048(n).

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

MATHEMATICA

a[n_] := If[Divisible[DivisorSigma[0, n], 3], 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 24 2022 *)