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%I #10 Dec 25 2018 16:56:07
%S 1,2,1,4,1,3,1,2,1,5,1,4,1,14,1,16,1,3,1,5,1,10,1,3,1,6,1,4,1,4,1,18,
%T 1,17,1,9,1,26,1,10,1,6,1,20,1,7,1,6,1,8,1,12,1,10,1,8,1,3,1,3,1,6,1,
%U 29,1,6,1,6,1,5,1,6,1,17,1,19,1,12,1,20,1,5,1,12,1,42,1
%N Least number k such that (k^k+n^n)/(k+n) is an integer.
%C If n is odd, a(n) = 1.
%C a(n) <= n for all n.
%C a(A242901(n)) = n and a(m) <> n for m < A242901(n). - _Reinhard Zumkeller_, May 25 2014
%H Reinhard Zumkeller, <a href="/A242885/b242885.txt">Table of n, a(n) for n = 1..10000</a>
%e (1^1+6^6)/(1+6) = 46657/7 is not an integer. (2^2+6^6)/(2+6) = 46660/8 = 11665/2 is not an integer. (3^3+6^6)/(3+6) = 46683/9 = 5187 is an integer. Thus a(6) = 3.
%t lnk[n_]:=Module[{k=1,n2=n^n},While[!IntegerQ[(k^k+n2)/(k+n)],k++];k]; Array[lnk, 90] (* or, using the lnk function defined above *) Riffle[ Table[lnk[n],{n,2,100,2}],1,{1,-1,2}] (* _Harvey P. Dale_, Dec 25 2018 *)
%o (PARI) a(n)=for(k=1,2500,s=(k^k+n^n)/(k+n);if(floor(s)==s,return(k)))
%o n=1;while(n<100,print(a(n));n+=1)
%o (Haskell)
%o a242885 n = head [k | let nn = n ^ n,
%o k <- [1..], mod (k ^ k + nn) (k + n) == 0]
%o -- _Reinhard Zumkeller_, May 25 2014
%K nonn,look
%O 1,2
%A _Derek Orr_, May 25 2014
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