A140538 Greatest prime factor of 2*n^4 + 1.

3, 11, 163, 19, 139, 2593, 1601, 2731, 1193, 113, 227, 619, 577, 8537, 73, 43691, 55681, 209953, 307, 9697, 388963, 52057, 1091, 337, 260417, 304651, 3011, 4937, 471521, 1620001, 691, 5419, 32491, 46889, 90947, 25643, 11057, 15619, 7499, 7793

Offset: 1

Author

Donald S. McDonald, Jul 06 2008

Keywords

• easy
• nonn

Examples

			a(2)= 11 because 2*2^4+1 = 33 = 3*11, greatest prime factor is 11.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Programs

Magma

[#f eq 0 select 1 else f[ #f][1] where f is Factorization(2*n^4 + 1): n in [1..50]]; // Vincenzo Librandi, Feb 17 2015

Mathematica

Table[Max[Transpose[FactorInteger[2 n^4 + 1]][[1]]], {n, 50}] (* Vincenzo Librandi, Feb 17 2015 *)

PARI

a(n) = f = factor(2*n^4+1); f[#f~,1]; \\ Michel Marcus, Aug 28 2013

Formula

a(n) = A006530(2n^4+1) = A076565(n^4). - R. J. Mathar, Aug 04 2008

Extensions

Extended from a(16) on by R. J. Mathar, Aug 04 2008