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 A005420 Largest prime factor of 2^n - 1. (Formerly M2609) 20
 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; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 REFERENCES 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). LINKS 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. S. S. Wagstaff, Jr., The Cunningham Project Eric Weisstein's World of Mathematics, Mersenne Number FORMULA 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 EXAMPLE 2^6-1 = 63 = 3*21 = 9*7, so a(6) = 7. MATHEMATICA 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 *) PROG (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 CROSSREFS 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 KEYWORD nonn AUTHOR EXTENSIONS Description corrected by Michael Somos, Feb 24 2002 More terms from Rick L. Shepherd, Aug 22 2002 STATUS approved

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Last modified May 22 19:19 EDT 2019. Contains 323481 sequences. (Running on oeis4.)