A274908 Largest prime factor of 8^n - 1.

7, 7, 73, 13, 151, 73, 337, 241, 262657, 331, 599479, 109, 121369, 5419, 23311, 673, 131071, 262657, 1212847, 1321, 649657, 599479, 10052678938039, 38737, 10567201, 22366891, 97685839, 14449, 9857737155463, 18837001, 658812288653553079, 22253377

Offset: 1

Author

Vincenzo Librandi, Jul 11 2016

Keywords

• nonn

Examples

			8^5 -1 = 32767 = 7*31*151, so a(5) = 151.
		

Links

• Table of n, a(n) for n = 1..500
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

Crossrefs

Cf. A005420, A006530, A024088, A274905.

Cf. similar sequences listed in A274906.

Programs

Magma

[Maximum(PrimeDivisors(8^n-1)): n in [1..40]];

Maple

f:= n -> max(map(t -> max(numtheory:-factorset(subs(x=2,t[1]))), factors(x^(3*n)-1)[2])):
map(f, [$1..120]); # Robert Israel, Jul 12 2016

Mathematica

Table[FactorInteger[8^n - 1][[-1, 1]], {n, 40}]

Formula

a(n) = A006530(A024088(n)). - Michel Marcus, Jul 11 2016

a(n) = A005420(3*n). - Robert Israel, Jul 12 2016

Extensions

Terms to a(100) in b-file from Vincenzo Librandi, Jul 13 2016

a(101)-a(402) in b-file from Amiram Eldar, Feb 02 2020

a(403)-a(500) in b-file from Max Alekseyev, Apr 25 2022, Sep 11 2022, Dec 05 2022, Feb 25 2023