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A182591 Number of prime factors of form cn+1 for numbers 3^n-1 1
0, 1, 1, 2, 2, 1, 1, 1, 3, 2, 2, 1, 2, 1, 2, 2, 3, 2, 2, 2, 4, 2, 2, 2, 2, 4, 3, 3, 4, 3, 2, 1, 5, 2, 4, 2, 4, 4, 2, 3, 5, 2, 3, 3, 3, 4, 5, 5, 4, 2, 4, 3, 6, 3, 2, 5, 6, 2, 3, 2, 5, 2, 2, 4, 5, 3, 3, 2, 3, 1, 4, 4, 5, 3, 5, 4, 9, 3, 3, 3, 5, 4, 5, 4, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,4

LINKS

Seppo Mustonen, Table of n, a(n) for n = 2..170

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, 3^n-1=728 has two prime factors of the form cn+1, namely 7=n+1 and 13=2n+1. Thus a(6)=2.

MATHEMATICA

m = 3; n = 2; nmax = 170;

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}]

CROSSREFS

Sequence in context: A066855 A175685 A331182 * A321393 A058914 A238585

Adjacent sequences: A182588 A182589 A182590 * A182592 A182593 A182594

KEYWORD

nonn

AUTHOR

Seppo Mustonen, Nov 22 2010

STATUS

approved

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Last modified December 1 21:09 EST 2022. Contains 358484 sequences. (Running on oeis4.)