A182598 Number of prime factors of form cn+1 for numbers 6^n+1

1, 2, 1, 2, 3, 2, 2, 1, 2, 1, 2, 3, 2, 2, 3, 2, 4, 2, 2, 1, 3, 2, 2, 2, 3, 3, 4, 3, 6, 1, 3, 4, 2, 5, 5, 3, 2, 5, 4, 3, 4, 1, 2, 2, 4, 1, 5, 3, 3, 6, 3, 4, 5, 4, 4, 3, 2, 1, 3, 2, 1, 3, 3, 3, 8, 4, 4, 2, 4, 3, 1, 5, 3, 5, 4, 1, 7, 5, 3, 3, 3, 4, 5, 3, 4, 7, 2, 2, 7, 5, 3, 2, 4, 5, 2, 3, 2, 4, 6

Offset

2,2

Comments

Repeated prime factors are counted.

Links

Table of n, a(n) for n=2..100.

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=6, 6^n-1=46655=5*7*31*43 has three prime factors of form, namely 7=n+1, 31=5n+1, 43=7n+1. Thus a(6)=3.

Mathematica

m = 6; n = 2; nmax = 100;
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}]
Table[{p, e}=Transpose[FactorInteger[6^n+1]]; Sum[If[Mod[p[[i]], n] == 1, e[[i]], 0], {i, Length[p]}], {n, 2, 50}]

Crossrefs

Sequence in context: A248886 A123884 A178412 * A331084 A067694 A131810

Adjacent sequences: A182595 A182596 A182597 * A182599 A182600 A182601

Keyword

nonn

Author

Seppo Mustonen, Nov 24 2010

Status

approved