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%I #13 Oct 02 2014 05:02:28
%S 1,3,1,1,7,2,2,2,1,1,7,4,37,145,35,1,25,16,5,16,1,1,18,19,3,11,41,1,7,
%T 2,48,415,1,2,15,7,13,34,97,1,27,18,56,22,1,1,5,26,22,36,18,1,117,52,
%U 376,11,1,1,23,26
%N Least positive integer m such that m + n divides T(m) + T(n), where T(.) is given by A002426.
%C Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n^2 - n + 1 except for n = 274.
%C Note that a(274) = 188847 > 2*274^2.
%H Zhi-Wei Sun, <a href="/A248133/b248133.txt">Table of n, a(n) for n = 1..10000</a>
%e a(5) = 7 since 5 + 7 divides T(5) + T(7) = 51 + 393 = 444 = 12*37.
%e a(2539) = 643425 since 2539 + 643425 = 645964 divides T(2539) + T(643425).
%t T[n_]:=Sum[Binomial[n,2k]Binomial[2k,k],{k,0,n/2}]
%t Do[m=1;Label[aa];If[Mod[T[m]+T[n],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]
%Y Cf. A002426, A247824, A247937, A247940, A248124, A248125, A248136, A248137, A248139, A248142.
%K nonn
%O 1,2
%A _Zhi-Wei Sun_, Oct 02 2014
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