cp's OEIS Frontend

A182594 Number of prime factors of form c*n+1 for numbers 7^n-1, counted with multiplicity.

%I A182594 #19 Apr 29 2025 14:30:55
%S A182594 1,1,2,1,2,2,1,3,3,2,2,1,4,2,3,2,4,2,3,1,4,3,4,3,3,4,4,3,3,3,2,4,3,3,
%T A182594 3,3,4,4,5,3,4,2,4,2,4,2,3,4,4,5,5,3,5,1,6,3,4,4,5,4,6,2,3,6,6,4,6,3,
%U A182594 8,2,5,5,5,3,2,3,7,2,5,6,7,7,3,3,9,5,4,3,6,5,5,4,3,3,5,3,11,4,6
%N A182594 Number of prime factors of form c*n+1 for numbers 7^n-1, counted with multiplicity.
%H A182594 Seppo Mustonen, <a href="http://www.survo.fi/papers/MustonenPrimes.pdf">On prime factors of numbers m^n+-1</a>
%H A182594 Seppo Mustonen, <a href="/A182590/a182590.pdf">On prime factors of numbers m^n+-1</a> [Local copy]
%e A182594 For n=9, 7^n-1 = 40353606 = 2*3^3*19*37*1063 has three prime factors of form, namely 19 = 2n+1, 37 = 4n+1, 1063 = 118n+1. Thus a(9) = 3.
%p A182594 f:= proc(n) local F;
%p A182594   F:= select(t -> t[1] mod n = 1, ifactors(7^n-1)[2]);
%p A182594   convert(F[..,2],`+`)
%p A182594 end proc:
%p A182594 map(f, [$2..100]); # _Robert Israel_, Apr 29 2025
%t A182594 m = 7; n = 2; nmax = 80;
%t A182594 While[n <= nmax, {l = FactorInteger[m^n - 1]; s = 0;
%t A182594      For[i = 1, i <= Length[l],
%t A182594       i++, {p = l[[i, 1]];
%t A182594        If[IntegerQ[(p - 1)/n] == True, s = s + l[[i, 2]]];}];
%t A182594      a[n] = s;} n++;];
%t A182594 Table[a[n], {n, 2, nmax}]
%K A182594 nonn
%O A182594 2,3
%A A182594 _Seppo Mustonen_, Nov 22 2010
%E A182594 Definition clarified and more terms from _Robert Israel_, Apr 29 2025