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A182598 Number of prime factors of form cn+1 for numbers 6^n+1 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 6 20:39 EDT 2020. Contains 333286 sequences. (Running on oeis4.)