A074477 Largest prime factor of 3^n - 1.

2, 2, 13, 5, 11, 13, 1093, 41, 757, 61, 3851, 73, 797161, 1093, 4561, 193, 34511, 757, 363889, 1181, 368089, 3851, 1001523179, 6481, 391151, 797161, 8209, 16493, 20381027, 4561, 4404047, 21523361, 2413941289, 34511, 2664097031, 530713

Offset: 1

Author

Rick L. Shepherd, Aug 23 2002

Keywords

• nonn

Examples

			3^7 - 1 = 2186 = 2*1093, so a(7) = 1093.
		

Links

• Table of n, a(n) for n = 1..690
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

Cf. A006530 (largest prime factor), A024023 (3^n-1).

Cf. A074476 (largest prime factor of 3^n + 1), A005420 (largest prime factor of 2^n - 1), A074479 (largest prime factor of 5^n - 1).

Programs

Magma

[Maximum(PrimeDivisors(3^n-1)): n in [1..40]]; // Vincenzo Librandi, Aug 23 2013

Maple

A074477 := proc(n)
        A006530( 3^n-1) ;
end proc: # R. J. Mathar, Jul 18 2015
# alternative:
a:= n-> max(seq(i[1], i=ifactors(3^n-1)[2])):
seq(a(n), n=1..40);  # Alois P. Heinz, Jul 18 2015

Mathematica

Table[FactorInteger[3^n - 1] [[-1, 1]], {n, 40}] (* Vincenzo Librandi, Aug 23 2013 *)

PARI

for(n=1,40, v=factor(3^n-1); print1(v[matsize(v)[1],1],","))

Formula

a(n) = A006530(A024023(n)). - Michel Marcus, Jul 18 2015

Extensions

Terms to a(100) in b-file from Vincenzo Librandi, Aug 23 2013

a(101)-a(660) in b-file from Amiram Eldar, Feb 01 2020

a(661)-a(690) in b-file from Max Alekseyev, May 22 2022