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A182593 Number of prime factors of form c*n+1 for numbers 6^n-1.

%I A182593 #18 Jun 02 2025 03:14:24
%S A182593 2,1,2,1,3,1,1,2,3,2,3,2,3,2,3,4,3,2,3,3,3,4,3,2,5,2,4,1,4,2,3,2,6,3,
%T A182593 5,5,4,4,3,2,4,4,4,4,6,3,5,3,4,5,6,3,5,2,5,3,4,3,7,3,3,4,4,5,6,2,4,4,
%U A182593 8,1,7,4,8,5,4,2,9,3,5,4,5,7,4,3,5,5,4,3,6,2,6,5,4,7,8,5,6,6,7,2,11,4,7,6,7,3,6,2,6,5,6,4,6,7,4,4,4,6,6
%N A182593 Number of prime factors of form c*n+1 for numbers 6^n-1.
%H A182593 Seppo Mustonen, <a href="http://www.survo.fi/papers/MustonenPrimes.pdf">On prime factors of numbers m^n+-1</a>
%H A182593 Seppo Mustonen, <a href="/A182590/a182590.pdf">On prime factors of numbers m^n+-1</a> [Local copy]
%e A182593 For n=6, 6^n-1=46655=5*7*31*43 and has three prime factors of form c*n+1, namely 7=n+1, 31=5*n+1, and 43=7*n+1. Thus a(6)=3. [Corrected by _N. J. A. Sloane_, Nov 16 2024]
%t A182593 m = 6; n = 2; nmax = 120;
%t A182593 While[n <= nmax, {l = FactorInteger[m^n - 1]; s = 0;
%t A182593      For[i = 1, i <= Length[l],
%t A182593       i++, {p = l[[i, 1]];
%t A182593        If[IntegerQ[(p - 1)/n] == True, s = s + l[[i, 2]]];}];
%t A182593      a[n] = s;} n++;];
%t A182593 Table[a[n], {n, 2, nmax}]
%K A182593 nonn
%O A182593 2,1
%A A182593 _Seppo Mustonen_, Nov 22 2010