A005420 Largest prime factor of 2^n - 1.
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
Offset: 2
Keywords
Examples
2^6 - 1 = 63 = 3*21 = 9*7, so a(6) = 7.
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, 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.
- 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
Crossrefs
Programs
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Magma
[Maximum(PrimeDivisors(2^n-1)): n in [2..45]]; // Vincenzo Librandi, Jul 13 2016
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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 *) -
PARI
for(n=2,44, v=factor(2^n-1)[,1]; print1(v[#v]", "));
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PARI
a(n) = vecmax(factor(2^n-1)[,1]); \\ Michel Marcus, Dec 15 2022
Formula
Extensions
Description corrected by Michael Somos, Feb 24 2002
More terms from Rick L. Shepherd, Aug 22 2002
Incorrect comments removed by Michel Marcus, Dec 15 2022