A182592 Number of prime factors of form cn+1 for numbers 5^n-1

1, 1, 1, 2, 2, 1, 1, 2, 3, 1, 2, 1, 3, 3, 2, 2, 3, 3, 3, 3, 4, 2, 3, 4, 3, 4, 3, 3, 5, 2, 3, 3, 4, 6, 3, 3, 6, 3, 5, 2, 6, 2, 3, 4, 4, 1, 2, 1, 6, 5, 3, 3, 7, 5, 3, 2, 5, 2, 7, 3, 5, 6, 4, 4, 7, 5, 8, 6, 8, 2, 3, 3, 6, 5, 5, 3, 7, 3, 4, 2, 6, 3, 3, 3, 6, 4, 4, 6, 5, 3, 2, 5, 4, 7, 5, 3, 4, 5, 7, 3, 10, 4, 5, 8, 6, 5, 2, 4, 7, 3, 6, 8, 5, 10, 2, 3, 6, 5, 7

Offset

2,4

Links

Table of n, a(n) for n=2..120.

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=10, 5^n-1=9765624=2^3*3*11*71*521 has three prime factors of the form cn+1, namely 11=n+1, 71=7n+1, 521=52n+1. Thus a(10)=3.

Mathematica

m = 5; 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}]
Table[Count[FactorInteger[5^n-1][[All, 1]], _?(Mod[#, n]==1&)], {n, 2, 130}] (* Harvey P. Dale, Dec 11 2016 *)

Crossrefs

Sequence in context: A122915 A327193 A279522 * A030298 A370221 A098281

Adjacent sequences: A182589 A182590 A182591 * A182593 A182594 A182595

Keyword

nonn

Author

Seppo Mustonen, Nov 22 2010

Status

approved