A102347 Number of distinct prime factors of 10^n - 1.

1, 2, 2, 3, 3, 5, 3, 5, 3, 5, 3, 7, 4, 5, 6, 7, 3, 8, 2, 8, 7, 7, 2, 10, 6, 7, 5, 9, 6, 13, 4, 12, 6, 7, 8, 11, 4, 4, 6, 12, 5, 14, 5, 11, 9, 7, 3, 13, 5, 11, 8, 10, 5, 12, 9, 13, 6, 9, 3, 20, 8, 6, 13, 16, 8, 14, 4, 11, 6, 13, 3, 17, 4, 8, 12, 7, 9, 15, 7, 16, 10, 8, 4, 21, 8, 9, 10, 15, 6, 21, 13

Offset: 1

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Feb 20 2005

Keywords

• nonn

Links

• Table of n, a(n) for n = 1..352

Crossrefs

Cf. A001221, A002283, A070528.

Programs

Maple

A102347 := proc(n)
    10^n-1 ;
    A001221(%) ;
end proc: # R. J. Mathar, Dec 02 2016

Mathematica

Table[PrimeNu[10^n-1],{n,100}] (* The program will take a long time to execute *) (* Harvey P. Dale, Jan 18 2015 *)

PARI

a(n) = omega(10^n-1); \\ Michel Marcus, Apr 22 2017

Formula

a(n) = A001221(A002283(n)) = A001221(10^n - 1).

a(n) = A001221(R_n) + (n^2 mod 3) = A095370(n) + (n^2 mod 3), where R_n = (10^n-1)/9 = A002275(n). That is, a(n) = A095370(n) for n=3k; otherwise a(n) = A095370(n) + 1. - Lekraj Beedassy, Jun 09 2006

Extensions

Terms to a(280) and a(323)-a(352) in b-file from Max Alekseyev, Dec 28 2011, Apr 26 2022

a(281)-a(322) in b-file from Ray Chandler, Apr 22 2017