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

Offset

1

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 *)

Prog

(PARI) A353470(n) = !(numdiv(n)%3);

Crossrefs

Characteristic function of A059269.

Cf. A000005, A010872, A302048.

Sequence in context: A221151 A359474 A359429 * A342753 A358752 A368913

Adjacent sequences: A353467 A353468 A353469 * A353471 A353472 A353473

Keyword

nonn

Author

Antti Karttunen, Apr 21 2022

Status

approved