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Largest prime factor of 9^n - 1.
13

%I #36 Jul 25 2023 19:35:58

%S 2,5,13,41,61,73,1093,193,757,1181,3851,6481,797161,16493,4561,

%T 21523361,34511,530713,363889,42521761,368089,570461,23535794707,6481,

%U 22996651,4795973261,19927,647753,20381027,47763361,22434744889,926510094425921,2413941289

%N Largest prime factor of 9^n - 1.

%H <a href="/A274909/b274909.txt">Table of n, a(n) for n = 1..691</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(A024101(n)).

%F a(n) = A074477(2*n). - _Amiram Eldar_, Feb 02 2020

%F a(n) = max(A074476(n),A074477(n)). - _Max Alekseyev_, Apr 25 2022

%e 9^4 - 1 = 6560 = 2^5*5*41, so a(4) = 41.

%t Table[FactorInteger[9^n-1][[-1,1]],{n,40}]

%o (Magma) [Maximum(PrimeDivisors(9^n-1)): n in [1..40]];

%Y Cf. A006530, A024101, A074477.

%Y Cf. similar sequences listed in A274906.

%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(330) in b-file from _Amiram Eldar_, Feb 02 2020

%E a(331)-a(691) in b-file from _Max Alekseyev_, May 22 2022, Jul 25 2023