A182592 - OEIS

%I #12 Mar 13 2020 20:36:35

%S 1,1,1,2,2,1,1,2,3,1,2,1,3,3,2,2,3,3,3,3,4,2,3,4,3,4,3,3,5,2,3,3,4,6,

%T 3,3,6,3,5,2,6,2,3,4,4,1,2,1,6,5,3,3,7,5,3,2,5,2,7,3,5,6,4,4,7,5,8,6,

%U 8,2,3,3,6,5,5,3,7,3,4,2,6,3,3,3,6,4,4,6,5,3,2,5,4,7,5,3,4,5,7,3,10,4,5,8,6,5,2,4,7,3,6,8,5,10,2,3,6,5,7

%N Number of prime factors of form cn+1 for numbers 5^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=10, 5^n-1=9765624=2^3*3*11*71*521 has three prime factors of the form cn+1, namely 11=n+1, 71=7n+1, 521=52n+1. Thus a(10)=3.

%t m = 5; 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}]

%t Table[Count[FactorInteger[5^n-1][[All,1]],_?(Mod[#,n]==1&)],{n,2,130}] (* _Harvey P. Dale_, Dec 11 2016 *)

%K nonn

%O 2,4

%A _Seppo Mustonen_, Nov 22 2010