A182591 Number of prime factors of form cn+1 for numbers 3^n-1.

0, 1, 1, 2, 2, 1, 1, 1, 3, 2, 2, 1, 2, 1, 2, 2, 3, 2, 2, 2, 4, 2, 2, 2, 2, 4, 3, 3, 4, 3, 2, 1, 5, 2, 4, 2, 4, 4, 2, 3, 5, 2, 3, 3, 3, 4, 5, 5, 4, 2, 4, 3, 6, 3, 2, 5, 6, 2, 3, 2, 5, 2, 2, 4, 5, 3, 3, 2, 3, 1, 4, 4, 5, 3, 5, 4, 9, 3, 3, 3, 5, 4, 5, 4, 3, 4

Offset: 2

Author

Seppo Mustonen, Nov 22 2010

Keywords

• nonn

Examples

			For n=6, 3^n-1=728 has two prime factors of the form cn+1, namely 7=n+1 and 13=2n+1. Thus a(6)=2.
		

Links

• Seppo Mustonen, Table of n, a(n) for n = 2..170
• S. Mustonen, On prime factors of numbers m^n+-1
• Seppo Mustonen, On prime factors of numbers m^n+-1 [Local copy]

Programs

Mathematica

m = 3; n = 2; nmax = 170;
While[n <= nmax, {l = FactorInteger[m^n - 1]; s = 0;
     For[i = 1, i <= Length[l],
      i++, {p = l[[i, 1]];
       If[IntegerQ[(p - 1)/n] == True, s = s + l[[i, 2]]];}];
     a[n] = s;} n++;];
Table[a[n], {n, 2, nmax}]