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A005420 Largest prime factor of 2^n - 1.
(Formerly M2609)
19
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.

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

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-Fran├žois 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

N. J. A. Sloane.

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 February 19 16:28 EST 2018. Contains 299356 sequences. (Running on oeis4.)