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A015906 First k>n such that k | n^k + n.

%I A015906 #13 Jan 28 2019 19:24:32
%S A015906 1,2,6,4,10,6,14,8,12,10,22,12,15,14,30,16,34,18,38,20,28,22,46,24,28,
%T A015906 26,54,28,35,30,51,32,44,34,70,36,52,38,78,40,70,42,86,44,60,46,94,48,
%U A015906 56,50,66,52,106,54,66,56,76,58,118,60,85,62,66,64,80,66,134,68
%N A015906 First k>n such that k | n^k + n.
%H A015906 Robert Israel, <a href="/A015906/b015906.txt">Table of n, a(n) for n = 0..10000</a>
%F A015906 a(n)=n+1 if n is odd. a(n) <= 2n+2. - _Robert Israel_, Sep 13 2018
%p A015906 f:= proc(n) local k;
%p A015906   for k from n+1 do
%p A015906     if n &^k + n mod k = 0 then return k fi
%p A015906   od
%p A015906 end proc:
%p A015906 map(f, [$0..100]); # _Robert Israel_, Sep 13 2018
%t A015906 fk[n_]:=Module[{k=n+1},While[!Divisible[n^k+n,k],k++];k]; Array[fk,70,0] (* _Harvey P. Dale_, Jan 28 2019 *)
%K A015906 nonn,look
%O A015906 0,2
%A A015906 _Robert G. Wilson v_
%E A015906 a(0)=1 and a(1)=2 inserted by _Robert Israel_, Sep 13 2018