A133801 Number of distinct prime divisors of 3^n - 1.

1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 5, 2, 3, 4, 5, 3, 6, 3, 5, 4, 5, 3, 7, 4, 3, 6, 6, 4, 8, 4, 6, 5, 6, 5, 9, 3, 5, 6, 7, 4, 8, 3, 8, 8, 4, 5, 12, 7, 7, 6, 6, 4, 11, 6, 9, 7, 7, 3, 12, 3, 6, 6, 7, 6, 10, 4, 9, 6, 8, 2, 12, 5, 6, 9, 8, 7, 12, 4, 11, 9, 6, 5, 14, 6, 4, 8, 12, 4, 16, 5, 7, 7, 8, 6, 15, 4, 10, 8

Offset

1,3

Links

Table of n, a(n) for n = 1..690

Eric Weisstein's World of Mathematics, Prime Factor.

Formula

a(n) = omega(3^n - 1) = A001221(3^n - 1).

Example

a(4) = omega(3^4 - 1) = omega(80) = omega(2^4 * 5) = 2.

Mathematica

Table[PrimeNu[3^n - 1], {n, 1, 50}] (* G. C. Greubel, May 21 2017 *)

Prog

(PARI) for(n = 1, 100, print1(omega(3^n - 1), ", "))

Crossrefs

Cf. A001221, A024023, A113913.

Sequence in context: A182576 A368869 A128330 * A181630 A112310 A350240

Adjacent sequences: A133798 A133799 A133800 * A133802 A133803 A133804

Keyword

nonn

Author

Ryan Propper, Jan 06 2008

Extensions

Terms to a(660) in b-file from Amiram Eldar, Feb 03 2020

a(661)-a(690) in b-file from Max Alekseyev, May 22 2022

Status

approved