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

%I A102347 #25 Apr 26 2022 18:54:22
%S A102347 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,
%T A102347 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,
%U A102347 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
%N A102347 Number of distinct prime factors of 10^n - 1.
%H A102347 <a href="/A102347/b102347.txt">Table of n, a(n) for n = 1..352</a>
%F A102347 a(n) = A001221(A002283(n)) = A001221(10^n - 1).
%F A102347 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
%p A102347 A102347 := proc(n)
%p A102347     10^n-1 ;
%p A102347     A001221(%) ;
%p A102347 end proc: # _R. J. Mathar_, Dec 02 2016
%t A102347 Table[PrimeNu[10^n-1],{n,100}] (* The program will take a long time to execute *) (* _Harvey P. Dale_, Jan 18 2015 *)
%o A102347 (PARI) a(n) = omega(10^n-1); \\ _Michel Marcus_, Apr 22 2017
%Y A102347 Cf. A001221, A002283, A070528.
%K A102347 nonn
%O A102347 1,2
%A A102347 Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Feb 20 2005
%E A102347 Terms to a(280) and a(323)-a(352) in b-file from _Max Alekseyev_, Dec 28 2011, Apr 26 2022
%E A102347 a(281)-a(322) in b-file from _Ray Chandler_, Apr 22 2017