cp's OEIS Frontend

A182599 Number of prime factors of form cn+1 for numbers 7^n+1.

%I A182599 #12 Jun 02 2025 03:14:51
%S A182599 2,1,1,2,2,2,2,1,2,2,4,2,1,1,2,1,2,2,3,3,3,1,1,1,2,1,4,1,4,3,3,2,3,5,
%T A182599 4,2,1,3,3,4,2,7,3,4,4,1,3,7,4,4,3,4,3,6,5,5,4,4,3,1,3,8,3,2,5,3,3,4,
%U A182599 4,2,5,3,1,5,5,5,4,4,3,4,3,2,5,3,3,4,2,5,4,5,4,5,3,6,6,3,5,3,3
%N A182599 Number of prime factors of form cn+1 for numbers 7^n+1.
%C A182599 Repeated prime factors are counted.
%H A182599 S. Mustonen, <a href="http://www.survo.fi/papers/MustonenPrimes.pdf">On prime factors of numbers m^n+-1</a>
%H A182599 Seppo Mustonen, <a href="/A182590/a182590.pdf">On prime factors of numbers m^n+-1</a> [Local copy]
%e A182599 For n=12, 7^12+1=13841287202=2*73*193*409*1201 has four prime factors of form, namely 73=6n+1, 193=16n+1, 409=34n+1, 1201=100n+1. Thus a(12)=4.
%t A182599 m = 7; n = 2; nmax = 100;
%t A182599 While[n <= nmax, {l = FactorInteger[m^n + 1]; s = 0;
%t A182599      For[i = 1, i <= Length[l],
%t A182599       i++, {p = l[[i, 1]];
%t A182599        If[IntegerQ[(p - 1)/n] == True, s = s + l[[i, 2]]];}];
%t A182599      a[n] = s;} n++;];
%t A182599 Table[a[n], {n, 2, nmax}]
%t A182599 Table[{p,e}=Transpose[FactorInteger[7^n+1]]; Sum[If[Mod[p[[i]], n]==1, e[[i]], 0], {i, Length[p]}], {n, 2, 50}]
%K A182599 nonn
%O A182599 2,1
%A A182599 _Seppo Mustonen_, Nov 24 2010