A056790 Greatest prime factor of n^n + (n+1)^(n+1).

2, 5, 31, 283, 23, 743, 331, 1600069, 410353, 60042893, 8969, 7438489991, 116803, 4879633159, 61215157711, 338142271, 34041259347101651, 45072130459, 6564253087266573169, 22022174223585405703, 121937899012999, 69454092876521107983605569601, 5311242856728321929909

Offset: 0

Author

Walter Nissen, Aug 20 2000

Keywords

• nonn
• hard

Comments

Note that n^n + (n+1)^(n+1) = A056788(n+1).

Becomes "hard" (unknown) around n ~ 112, cf. link: As of today, even A217435(113) (number of prime factors) is unknown. - M. F. Hasler, Oct 04 2012

As of today, the first unknown term is a(143). - Daniel Suteu, Mar 11 2019

Examples

			a(4) = 23 because 4^4 + 5^5 = 3381 = 3 * 7^2 * 23.
		

Links

• Daniel Suteu, Table of n, a(n) for n = 0..142
• Walter Nissen, np(n) = n^n + (n+1)^(n+1) -- 2 prominent questions. (Updated Oct 02 2012)

Crossrefs

Cf. A056187, A192397.

Cf. A217435.

Programs

Mathematica

Join[{2},FactorInteger[Total[#]][[-1,1]]&/@Partition[Table[n^n,{n,30}],2,1]] (* Harvey P. Dale, Apr 21 2018 *)

PARI

A056790(n)=vecmax(factor((n+1)^(n+1)+n^n)[,1])  \\ M. F. Hasler, Oct 04 2012

Formula

a(n) = A006530(A056788(n+1)). - M. F. Hasler, Oct 04 2012

Extensions

a(0) = 2 added by Arkadiusz Wesolowski, Jun 30 2011

a(21)-a(22) added by Daniel Suteu, Mar 11 2019