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%I M4401 N1856 #55 Sep 08 2022 08:44:31
%S 1,7,31,127,73,89,8191,151,131071,524287,337,178481,1801,262657,2089,
%T 2147483647,599479,122921,616318177,121369,164511353,2099863,23311,
%U 13264529,4432676798593,131071,20394401,201961,1212847,3203431780337
%N a(n) = largest noncomposite factor of 2^(2n+1) - 1.
%C a(n) is also the largest noncomposite factor of A147590(n). - _César Aguilera_, Jul 31 2019
%D 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 M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 2, p. 84.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Max Alekseyev, <a href="/A002588/b002588.txt">Table of n, a(n) for n = 0..602</a> (terms 1..494 from Sean A. Irvine)
%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.
%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%t Table[FactorInteger[2^(2 n + 1) - 1] [[-1, 1]], {n, 0, 30}] (* _Vincenzo Librandi_, Aug 02 2019 *)
%o (PARI) a(n) = if (n==0, 1, vecmax(factor(2^(2*n+1) - 1)[, 1])); \\ _Michel Marcus_, Aug 03 2019
%o (Magma) [1] cat [Maximum(PrimeDivisors(2^(2*n+1) - 1)): n in [1..60]]; // _Vincenzo Librandi_, Aug 02 2019
%Y Cf. A002184, A005420, A147590.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Don Reble_, Nov 14 2006
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