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%I #49 Jul 25 2023 20:01:11
%S 3,5,7,17,31,13,127,257,73,41,683,241,8191,127,331,65537,131071,109,
%T 524287,61681,5419,2113,2796203,673,4051,8191,262657,15790321,3033169,
%U 1321,2147483647,6700417,599479,131071,122921,38737,616318177,525313,22366891
%N Largest prime factor of 4^n - 1.
%H <a href="/A274906/b274906.txt">Table of n, a(n) for n = 1..1122</a>
%H 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.
%F a(n) = A006530(A024036(n)). - _Michel Marcus_, Jul 11 2016
%F a(n) = max(A002587(n),A005420(n)). - _Max Alekseyev_, Apr 25 2022
%e 4^7 - 1 = 16383 = 3*43*127, so a(7) = 127
%t Table[FactorInteger[4^n - 1][[-1, 1]], {n, 40}]
%o (Magma) [Maximum(PrimeDivisors(4^n-1)): n in [1..40]];
%Y Second bisection of A005420. - _Michel Marcus_, Jul 13 2016
%Y Cf. largest prime factor of k^n-1: A005420 (k=2), A074477 (k=3), this sequence (k=4), A074479 (k=5), A274907 (k=6), A074249 (k=7), A274908 (k=8), A274909 (k=9), A005422 (k=10), A274910 (k=11).
%Y Cf. A006530, A024036.
%K nonn
%O 1,1
%A _Vincenzo Librandi_, Jul 11 2016
%E Terms to a(100) in b-file from _Vincenzo Librandi_, Jul 13 2016
%E a(101)-a(603) in b-file from _Amiram Eldar_, Feb 08 2020
%E a(604)-a(1122) in b-file from _Max Alekseyev_, Jul 25 2023
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