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Largest prime factor of n! + 2n - 1.
4

%I #20 Feb 05 2020 04:02:30

%S 2,5,11,31,43,43,163,2689,362897,3628819,179,1908373,800903,101341,

%T 13999747,104099179,10778406912001,1300448327,356961701,

%U 62382102773760001,10367823077693,11437176299,102338720137,1971511284252461621,4324853339,25264139643338071514377,4403101273925738843820461

%N Largest prime factor of n! + 2n - 1.

%H Robert Israel and Amiram Eldar, <a href="/A139467/b139467.txt">Table of n, a(n) for n = 1..60</a> (terms 1..57 from Robert Israel)

%H Florian Luca and Igor E. Shparlinski, <a href="http://www.emis.de/journals/JTNB/2005-3/article10.pdf">On the largest prime factor of n! + 2^n - 1</a>, Journal de Theorie des Nombres de Bordeaux 17 (2005), 859-870.

%F a(n) = A006530(A139464(n)). - _Amiram Eldar_, Feb 05 2020

%p seq(max(numtheory:-factorset(n!+2*n-1)),n=1..30); # _Robert Israel_, Jun 28 2018

%t a = {}; Do[k = n! + 2 n - 1; c = First[Last[FactorInteger[k]]]; AppendTo[a, c], {n, 1, 40}]; a (*Artur Jasinski*)

%t Table[FactorInteger[n!+2n-1][[-1,1]],{n,30}] (* _Harvey P. Dale_, Aug 31 2011 *)

%o (PARI) a(n)=my(f=factor(n!+2*n-1)[,1]);f[#f] \\ _Charles R Greathouse IV_, Feb 01 2013

%Y Cf. A006530, A127986, A127987, A139023, A139024, A139464, A139465, A139466.

%K nonn

%O 1,1

%A _Artur Jasinski_, Apr 22 2008

%E More terms from _Robert Israel_, Jun 28 2018