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%I A005420 M2609 #100 Dec 17 2022 20:01:59
%S A005420 3,7,5,31,7,127,17,73,31,89,13,8191,127,151,257,131071,73,524287,41,
%T A005420 337,683,178481,241,1801,8191,262657,127,2089,331,2147483647,65537,
%U A005420 599479,131071,122921,109,616318177,524287,121369,61681,164511353,5419
%N A005420 Largest prime factor of 2^n - 1.
%D A005420 J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
%D A005420 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005420 T. D. Noe, Charles R Greathouse IV and Amiram Eldar, <a href="/A005420/b005420.txt">Table of n, a(n) for n = 2..1206</a> (terms up to 500 from T. D. Noe, terms 501..1000 from Charles R Greathouse IV, terms 1001..1206 from Amiram Eldar)
%H A005420 J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
%H A005420 factordb.com, <a href="http://factordb.com/index.php?query=2%5E1207-1">Status of 2^1207-1</a>. 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.
%H A005420 R. K. Guy, <a href="/A002968/a002968_1.pdf">Letter to G. B. Huff & N. J. A. Sloane, Aug 1974</a>
%H A005420 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%H A005420 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MersenneNumber.html">Mersenne Number</a>
%F A005420 a(n) = a(2n) iff a(n) > A002587(n). See A337431. - _Thomas Ordowski_, Jan 07 2014
%F A005420 a(n) = A006530(A000225(n)). - _Vincenzo Librandi_, Jul 13 2016
%F A005420 a(n) = 2^n-1 = A000225(n) iff n is a Mersenne exponent (A000043). - _Bernard Schott_, Dec 11 2022
%e A005420 2^6 - 1 = 63 = 3*21 = 9*7, so a(6) = 7.
%t A005420 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 *)
%t A005420 Table[FactorInteger[2^n - 1][[-1, 1]], {n, 2, 40}] (* _Vincenzo Librandi_, Jul 13 2016 *)
%o A005420 (PARI) for(n=2,44, v=factor(2^n-1)[,1]; print1(v[#v]", "));
%o A005420 (PARI) a(n) = vecmax(factor(2^n-1)[,1]); \\ _Michel Marcus_, Dec 15 2022
%o A005420 (Magma) [Maximum(PrimeDivisors(2^n-1)): n in [2..45]]; // _Vincenzo Librandi_, Jul 13 2016
%Y A005420 Cf. A000043, A000225, A006530, A002326, A002587.
%Y A005420 Cf. similar sequences listed in A274906.
%Y A005420 Cf. A337431 (a(n)=a(2n)), A359063 (a(n)=a(2n)=a(4n)), A359088.
%K A005420 nonn
%O A005420 2,1
%A A005420 _N. J. A. Sloane_
%E A005420 Description corrected by _Michael Somos_, Feb 24 2002
%E A005420 More terms from _Rick L. Shepherd_, Aug 22 2002
%E A005420 Incorrect comments removed by _Michel Marcus_, Dec 15 2022

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