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A182591 Number of prime factors of form cn+1 for numbers 3^n-1.

%I A182591 #15 Jun 02 2025 03:14:13
%S A182591 0,1,1,2,2,1,1,1,3,2,2,1,2,1,2,2,3,2,2,2,4,2,2,2,2,4,3,3,4,3,2,1,5,2,
%T A182591 4,2,4,4,2,3,5,2,3,3,3,4,5,5,4,2,4,3,6,3,2,5,6,2,3,2,5,2,2,4,5,3,3,2,
%U A182591 3,1,4,4,5,3,5,4,9,3,3,3,5,4,5,4,3,4
%N A182591 Number of prime factors of form cn+1 for numbers 3^n-1.
%H A182591 Seppo Mustonen, <a href="/A182591/b182591.txt">Table of n, a(n) for n = 2..170</a>
%H A182591 S. Mustonen, <a href="http://www.survo.fi/papers/MustonenPrimes.pdf">On prime factors of numbers m^n+-1</a>
%H A182591 Seppo Mustonen, <a href="/A182590/a182590.pdf">On prime factors of numbers m^n+-1</a> [Local copy]
%e A182591 For n=6, 3^n-1=728 has two prime factors of the form cn+1, namely 7=n+1 and 13=2n+1. Thus a(6)=2.
%t A182591 m = 3; n = 2; nmax = 170;
%t A182591 While[n <= nmax, {l = FactorInteger[m^n - 1]; s = 0;
%t A182591      For[i = 1, i <= Length[l],
%t A182591       i++, {p = l[[i, 1]];
%t A182591        If[IntegerQ[(p - 1)/n] == True, s = s + l[[i, 2]]];}];
%t A182591      a[n] = s;} n++;];
%t A182591 Table[a[n], {n, 2, nmax}]
%K A182591 nonn
%O A182591 2,4
%A A182591 _Seppo Mustonen_, Nov 22 2010