A242899 Least number k > 1 such that (n^k+k^n)/(k+n) is an integer.

2, 2, 3, 4, 3, 3, 3, 2, 3, 6, 8, 4, 11, 5, 3, 16, 7, 6, 5, 5, 3, 10, 5, 3, 4, 5, 3, 4, 11, 4, 7, 11, 3, 30, 5, 3, 7, 19, 3, 10, 7, 6, 7, 11, 5, 12, 14, 6, 7, 5, 3, 12, 13, 9, 5, 8, 6, 6, 11, 4, 4, 6, 3, 64, 5, 6, 10, 6, 3, 10, 6, 6, 5, 37, 3, 30, 7, 12, 7, 20, 3, 40, 19, 9

Offset: 1

Author

Derek Orr, May 25 2014

Keywords

• nonn
• look

Comments

a(n) <= n for all n > 1.

Examples

			(1^2+2^1)/(2+1) = 3/3 = 1 is an integer. Thus a(1) = 2.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A114977, A114978, A242872.

Programs

Mathematica

lnk[n_]:=Module[{k=2},While[!IntegerQ[(n^k+k^n)/(k+n)],k++];k]; Array[lnk,90] (* Harvey P. Dale, Sep 02 2015 *)

PARI

a(n)=if(n==1, 2, for(k=2, n, s=(n^k+k^n)/(k+n); if(floor(s)==s, return(k))))
n=1; while(n<100, print(a(n)); n+=1)

PARI

a(n) = my(k=2); while (denominator((n^k+k^n)/(k+n))!=1, k++); k; \\ Michel Marcus, Jun 03 2021