A274907 Largest prime factor of 6^n - 1.

5, 7, 43, 37, 311, 43, 55987, 1297, 2467, 311, 3154757, 97, 760891, 55987, 1201, 98801, 30839, 46441, 638073026189, 6781, 1822428931, 51828151, 7505944891, 1678321, 40185601, 760891, 623067280651, 5030761, 7369130657357778596659, 1950271, 49744740983476472807

Offset: 1

Author

Vincenzo Librandi, Jul 11 2016

Keywords

• nonn

Examples

			6^5 - 1 = 7775 = 5*5*311, so a(5) = 311.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..430 (terms 1..100 from Vincenzo Librandi, term 101..420 from Amiram Eldar)
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

Crossrefs

Cf. A006530, A057955, A059888, A085031, A024062, A366620, A366621, A366622, A366623.

Cf. similar sequences listed in A274906.

Programs

Magma

[Maximum(PrimeDivisors(6^n-1)): n in [1..40]];

Mathematica

Table[FactorInteger[6^n - 1][[-1, 1]], {n, 40}]

PARI

a(n) = vecmax(factor(6^n-1)[,1]); \\ Michel Marcus, Jul 13 2016

Formula

a(n) = A006530(A024062(n)). - Michel Marcus, Jul 11 2016