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A005420
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Largest prime factor of 2^n - 1.
(Formerly M2609)
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34
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3, 7, 5, 31, 7, 127, 17, 73, 31, 89, 13, 8191, 127, 151, 257, 131071, 73, 524287, 41, 337, 683, 178481, 241, 1801, 8191, 262657, 127, 2089, 331, 2147483647, 65537, 599479, 131071, 122921, 109, 616318177, 524287, 121369, 61681, 164511353, 5419
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OFFSET
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2,1
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REFERENCES
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J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Charles R Greathouse IV and Amiram Eldar, Table of n, a(n) for n = 2..1206 (terms up to 500 from T. D. Noe, terms 501..1000 from Charles R Greathouse IV, terms 1001..1206 from Amiram Eldar)
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
factordb.com, Status of 2^1207-1. The factorization of the composite factor C337 of 2^1207-1 with 337 decimal digits is considered by many to be the most desired open factorization problem.
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FORMULA
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EXAMPLE
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2^6 - 1 = 63 = 3*21 = 9*7, so a(6) = 7.
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MATHEMATICA
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a[n_] := a[n] = FactorInteger[2^n-1] // Last // First; Table[Print[{n, a[n]}, If[2^n-1 == a[n], " Mersenne prime", " "]]; a[n], {n, 2, 127}] (* Jean-François Alcover, Dec 11 2012 *)
Table[FactorInteger[2^n - 1][[-1, 1]], {n, 2, 40}] (* Vincenzo Librandi, Jul 13 2016 *)
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PROG
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(PARI) for(n=2, 44, v=factor(2^n-1)[, 1]; print1(v[#v]", "));
(PARI) a(n) = vecmax(factor(2^n-1)[, 1]); \\ Michel Marcus, Dec 15 2022
(Magma) [Maximum(PrimeDivisors(2^n-1)): n in [2..45]]; // Vincenzo Librandi, Jul 13 2016
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CROSSREFS
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Cf. similar sequences listed in A274906.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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