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A005420
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Largest prime factor of 2^n - 1.
(Formerly M2609)
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20
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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
(list;
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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 and Charles R Greathouse IV, Table of n, a(n) for n = 2..1000 (up to 500 from Noe)
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
R. K. Guy, Letter to G. B. Huff & N. J. A. Sloane, Aug 1974
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Mersenne Number
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FORMULA
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a(n) = a(2n) iff a(n) > A002587(n). a(n) = a(2n) = a(4n) iff n is prime p == +-1 (mod 8) and 2^p-1 is prime. - Thomas Ordowski, Jan 07 2014
A002326((a(n)-1)/2) = n iff n is odd or n is even such that a(n/2) != a(n). - Thomas Ordowski, Jan 11 2014
a(n) = A006530(A000225(n)). - Vincenzo Librandi, Jul 13 2016
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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]", "));
(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. A000225, A006530.
Cf. similar sequences listed in A274906.
Sequence in context: A292015 A186522 A048857 * A212953 A161818 A161509
Adjacent sequences: A005417 A005418 A005419 * A005421 A005422 A005423
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Description corrected by Michael Somos, Feb 24 2002
More terms from Rick L. Shepherd, Aug 22 2002
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STATUS
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approved
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