A074943 a(n) = tau(n) mod 3.

1, 2, 2, 0, 2, 1, 2, 1, 0, 1, 2, 0, 2, 1, 1, 2, 2, 0, 2, 0, 1, 1, 2, 2, 0, 1, 1, 0, 2, 2, 2, 0, 1, 1, 1, 0, 2, 1, 1, 2, 2, 2, 2, 0, 0, 1, 2, 1, 0, 0, 1, 0, 2, 2, 1, 2, 1, 1, 2, 0, 2, 1, 0, 1, 1, 2, 2, 0, 1, 2, 2, 0, 2, 1, 0, 0, 1, 2, 2, 1, 2, 1, 2, 0, 1, 1, 1, 2, 2, 0, 1, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2

Offset: 1

Author

Benoit Cloitre, Oct 04 2002

Keywords

• easy
• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Cf. A000005 (tau), A002117, A010872, A059269, A211337, A211338.

Programs

Mathematica

Mod[DivisorSigma[0,Range[110]],3] (* Harvey P. Dale, Dec 22 2013 *)

PARI

a(n)=numdiv(n)%3

Scheme

(define (A074943 n) (modulo (A000005 n) 3)) ;; Antti Karttunen, Jul 26 2017

Formula

From Amiram Eldar, Apr 16 2024: (Start)

a(n) = A010872(A000005(n)).

a(A059269(n)) = 0; a(A211337(n)) = 1; a(A211338(n)) = 2.

Conjecture: Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 9*zeta(3)/Pi^2 = 1.0961... . The conjecture is true if A211337 and A211338 have the same asymptotic density (see also A059269). (End)