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A086257 Number of primitive prime factors of 2^n+1. 5
1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 3, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 1, 1, 2, 2, 1, 2, 1, 4, 2, 2, 1, 3, 3, 2, 2, 2, 2, 2, 2, 2, 3, 1, 1, 4, 1, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 4, 1, 3, 3, 4, 1, 2, 3, 4, 5, 2, 1, 4, 1, 3, 3, 3, 3, 1, 2, 3, 2, 1, 4, 3, 2, 4, 1, 4, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,15

COMMENTS

A prime factor of 2^n+1 is called primitive if it does not divide 2^r+1 for any r<n. Zsigmondy's theorem says that there is at least one primitive prime factor except for n=3. See A086258 for those n that have a record number of primitive prime factors.

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..1062 (terms 0..500 from T. D. Noe)

Eric Weisstein's World of Mathematics, Zsigmondy Theorem

EXAMPLE

a(14) = 2 because 2^14+1 = 5*29*113 and 29 and 113 do not divide 2^r+1 for r < 14.

MATHEMATICA

nMax=200; pLst={}; Table[f=Transpose[FactorInteger[2^n+1]][[1]]; f=Complement[f, pLst]; cnt=Length[f]; pLst=Union[pLst, f]; cnt, {n, 0, nMax}]

CROSSREFS

Cf. A046799 (number of distinct prime factors of 2^n+1), A054992 (number of prime factors, with repetition, of 2^n+1), A086258.

Sequence in context: A214054 A330739 A076398 * A161098 A136177 A212178

Adjacent sequences:  A086254 A086255 A086256 * A086258 A086259 A086260

KEYWORD

hard,nonn

AUTHOR

T. D. Noe, Jul 14 2003

STATUS

approved

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Last modified May 18 22:37 EDT 2022. Contains 353826 sequences. (Running on oeis4.)