A182593 Number of prime factors of form c*n+1 for numbers 6^n-1.

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, 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, 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

Offset: 2

Author

Seppo Mustonen, Nov 22 2010

Keywords

• nonn

Examples

			For n=6, 6^n-1=46655=5*7*31*43 and has three prime factors of form c*n+1, namely 7=n+1, 31=5*n+1, and 43=7*n+1. Thus a(6)=3. [Corrected by _N. J. A. Sloane_, Nov 16 2024]
		

Links

• Seppo Mustonen, On prime factors of numbers m^n+-1
• Seppo Mustonen, On prime factors of numbers m^n+-1 [Local copy]

Programs

Mathematica

m = 6; n = 2; nmax = 120;
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}]