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A182599 Number of prime factors of form cn+1 for numbers 7^n+1 0
2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 4, 2, 1, 1, 2, 1, 2, 2, 3, 3, 3, 1, 1, 1, 2, 1, 4, 1, 4, 3, 3, 2, 3, 5, 4, 2, 1, 3, 3, 4, 2, 7, 3, 4, 4, 1, 3, 7, 4, 4, 3, 4, 3, 6, 5, 5, 4, 4, 3, 1, 3, 8, 3, 2, 5, 3, 3, 4, 4, 2, 5, 3, 1, 5, 5, 5, 4, 4, 3, 4, 3, 2, 5, 3, 3, 4, 2, 5, 4, 5, 4, 5, 3, 6, 6, 3, 5, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

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

EXAMPLE

For n=12, 7^12+1=13841287202=2*73*193*409*1201 has four prime factors of form, namely 73=6n+1, 193=16n+1, 409=34n+1, 1201=100n+1. Thus a(12)=4.

MATHEMATICA

m = 7; 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[7^n+1]]; Sum[If[Mod[p[[i]], n]==1, e[[i]], 0], {i, Length[p]}], {n, 2, 50}]

CROSSREFS

Sequence in context: A046081 A190592 A062501 * A183015 A183018 A067390

Adjacent sequences:  A182596 A182597 A182598 * A182600 A182601 A182602

KEYWORD

nonn

AUTHOR

Seppo Mustonen, Nov 24 2010

STATUS

approved

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Last modified November 24 00:27 EST 2017. Contains 295164 sequences.