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A182597 Number of prime factors of form cn+1 for numbers 5^n+1 0
1, 1, 1, 1, 2, 2, 2, 1, 2, 3, 2, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 1, 2, 2, 3, 1, 2, 3, 3, 3, 4, 4, 2, 3, 3, 2, 4, 2, 4, 3, 4, 1, 1, 1, 3, 4, 3, 3, 5, 4, 3, 1, 2, 4, 3, 1, 4, 4, 4, 2, 6, 3, 4, 2, 1, 5, 4, 3, 3, 2, 3, 3, 5, 3, 2, 4, 4, 4, 5, 4, 3, 4, 6, 3, 4, 4, 3, 3, 2, 2, 4, 4, 4, 4, 5, 4, 1, 4, 1, 7, 1, 5, 5, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,5

COMMENTS

Repeated prime factors are counted.

LINKS

Table of n, a(n) for n=2..107.

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=11, 5^n+1=48828126=2*3*23*67*5281 has three prime factors of form, namely 23=2n+1, 67=6n+1, 5281=480n+1. Thus a(11)=3.

MATHEMATICA

m = 5; n = 2; nmax = 107;

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[5^n+1]]; Sum[If[Mod[p[[i]], n] == 1, e[[i]], 0], {i, Length[p]}], {n, 2, 50}]

CROSSREFS

Sequence in context: A151931 A185636 A333212 * A290491 A194314 A006371

Adjacent sequences:  A182594 A182595 A182596 * A182598 A182599 A182600

KEYWORD

nonn

AUTHOR

Seppo Mustonen, Nov 24 2010

STATUS

approved

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Last modified April 6 12:08 EDT 2020. Contains 333273 sequences. (Running on oeis4.)