A182594 Number of prime factors of form cn+1 for numbers 7^n-1

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, 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, 8, 2, 5, 5, 5, 3, 2, 3, 7, 2, 5

Offset

2,3

Links

Table of n, a(n) for n=2..80.

S. Mustonen, On prime factors of numbers m^n+-1

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

Example

For n=9, 7^n-1=40353606=2*3^3*19*37*1063 has three prime factors of form, namely 19=2n+1, 37=6n+1, 1063=118n+1. Thus a(9)=3.

Mathematica

m = 7; n = 2; nmax = 80;
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}]

Crossrefs

Sequence in context: A276430 A362325 A325002 * A201593 A029287 A055184

Adjacent sequences: A182591 A182592 A182593 * A182595 A182596 A182597

Keyword

nonn

Author

Seppo Mustonen, Nov 22 2010

Status

approved