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Greatest prime factor of n^n + (n+1)^(n+1).
6

%I #31 Mar 13 2019 03:33:41

%S 2,5,31,283,23,743,331,1600069,410353,60042893,8969,7438489991,116803,

%T 4879633159,61215157711,338142271,34041259347101651,45072130459,

%U 6564253087266573169,22022174223585405703,121937899012999,69454092876521107983605569601,5311242856728321929909

%N Greatest prime factor of n^n + (n+1)^(n+1).

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

%C 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

%C As of today, the first unknown term is a(143). - _Daniel Suteu_, Mar 11 2019

%H Daniel Suteu, <a href="/A056790/b056790.txt">Table of n, a(n) for n = 0..142</a>

%H Walter Nissen, <a href="http://upforthecount.com/math/nnpomega.html">np(n) = n^n + (n+1)^(n+1) -- 2 prominent questions</a>. (Updated Oct 02 2012)

%F a(n) = A006530(A056788(n+1)). - _M. F. Hasler_, Oct 04 2012

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

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

%o (PARI) A056790(n)=vecmax(factor((n+1)^(n+1)+n^n)[,1]) \\ _M. F. Hasler_, Oct 04 2012

%Y Cf. A056187, A192397.

%Y Cf. A217435.

%K nonn,hard

%O 0,1

%A _Walter Nissen_, Aug 20 2000

%E a(0) = 2 added by _Arkadiusz Wesolowski_, Jun 30 2011

%E a(21)-a(22) added by _Daniel Suteu_, Mar 11 2019