A274906 Largest prime factor of 4^n - 1.

3, 5, 7, 17, 31, 13, 127, 257, 73, 41, 683, 241, 8191, 127, 331, 65537, 131071, 109, 524287, 61681, 5419, 2113, 2796203, 673, 4051, 8191, 262657, 15790321, 3033169, 1321, 2147483647, 6700417, 599479, 131071, 122921, 38737, 616318177, 525313, 22366891

Offset: 1

Author

Vincenzo Librandi, Jul 11 2016

Keywords

• nonn

Examples

			4^7 - 1 = 16383 = 3*43*127, so a(7) = 127
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..1128
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

Crossrefs

Second bisection of A005420. - Michel Marcus, Jul 13 2016

Cf. largest prime factor of k^n-1: A005420 (k=2), A074477 (k=3), this sequence (k=4), A074479 (k=5), A274907 (k=6), A074249 (k=7), A274908 (k=8), A274909 (k=9), A005422 (k=10), A274910 (k=11).

Cf. A006530, A024036.

Programs

Magma

[Maximum(PrimeDivisors(4^n-1)): n in [1..40]];

Mathematica

Table[FactorInteger[4^n - 1][[-1, 1]], {n, 40}]

Formula

a(n) = A006530(A024036(n)). - Michel Marcus, Jul 11 2016

a(n) = max(A002587(n),A005420(n)). - Max Alekseyev, Apr 25 2022

Extensions

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

a(101)-a(603) in b-file from Amiram Eldar, Feb 08 2020

a(604)-a(1128) in b-file from Max Alekseyev, Jul 25 2023, Mar 15 2025