A127987 Largest prime factor of n! + 2^n - 1.

2, 5, 13, 13, 151, 29, 5167, 541, 51913, 691, 39918847, 1520653, 9631, 2748457, 171793, 37698720637, 429056005099, 10201231, 4759011791767, 26573, 560275276313059, 30130171848761, 522781919969, 8912567718641664241, 480631246386037, 3215985920374841, 4561301027

Offset

1,1

Comments

A186450 is a subsequence. - Altug Alkan, Oct 28 2015

Links

Kevin P. Thompson, Table of n, a(n) for n = 1..103 (terms 1..75 from Klaus Brockhaus, terms 76..81 from Amiram Eldar)

Florian Luca, Igor E. Shparlinsky, On the largest prime factor of n! + 2^n - 1, J. Th. des Nombres de Bordeaux 2005, Vol.17, Fasc. 3.

Formula

a(n) = A006530(A127986(n)). - Amiram Eldar, Feb 05 2020

Example

a(6) = 29 since 29 is the largest prime factor of n! + 2^n - 1 = 6! + 2^6 - 1 = 783 = 3^3 * 29.

Mathematica

Table[FactorInteger[n! + 2^n - 1][[-1, 1]], {n, 20}] (* Alonso del Arte, Oct 28 2015 *)

Prog

(Magma) largestpf := func<n | f[#f, 1] where f is Factorization(n)>; [largestpf(Factorial(n)+2^n-1): n in [1..24]]; // Klaus Brockhaus, Nov 20 2009
(PARI) a(n)=my(f=factor(n!+2^n-1)[, 1]); f[#f] \\ Charles R Greathouse IV, Feb 01 2013

Crossrefs

Cf. A006530, A127986.

Sequence in context: A112838 A111296 A089728 * A247543 A220268 A049476

Adjacent sequences: A127984 A127985 A127986 * A127988 A127989 A127990

Keyword

nonn

Author

Artur Jasinski, Feb 09 2007

Extensions

Definition corrected by Artur Jasinski, Apr 22 2008

Status

approved