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Number of prime factors of form cn+1 for numbers 6^n-1
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%I #10 Mar 13 2020 20:36:49

%S 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 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 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 Number of prime factors of form cn+1 for numbers 6^n-1

%H S. Mustonen, <a href="http://www.survo.fi/papers/MustonenPrimes.pdf">On prime factors of numbers m^n+-1</a>

%H Seppo Mustonen, <a href="/A182590/a182590.pdf">On prime factors of numbers m^n+-1</a> [Local copy]

%e For n=6, 6^n-1=46655=5*7*31*43 and has three prime factors of form cn+1, namely 7=n+1, 31=3n+1, 43=7n+1. Thus a(6)=3.

%t m = 6; n = 2; nmax = 120;

%t While[n <= nmax, {l = FactorInteger[m^n - 1]; s = 0;

%t For[i = 1, i <= Length[l],

%t i++, {p = l[[i, 1]];

%t If[IntegerQ[(p - 1)/n] == True, s = s + l[[i, 2]]];}];

%t a[n] = s;} n++;];

%t Table[a[n], {n, 2, nmax}]

%K nonn

%O 2,1

%A _Seppo Mustonen_, Nov 22 2010