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Search: id:A086257
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| A086257 |
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Number of primitive prime factors of 2^n+1. |
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+0
4
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| 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; listen)
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OFFSET
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0,15
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COMMENT
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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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..500 (using data from A001269)
Eric Weisstein's World of Mathematics, Zsigmondy Theorem
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EXAMPLE
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a(14) = 2 because 2^14+1 = 5*29*113, and 29 and 113 do not divide 2^r+1 for r < 14.
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MATHEMATICA
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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}]
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CROSSREFS
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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: A102097 A050330 A076398 this_sequence A136177 A066922 A033183
Adjacent sequences: A086254 A086255 A086256 this_sequence A086258 A086259 A086260
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KEYWORD
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hard,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jul 14 2003
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