%I #11 Oct 03 2014 16:54:51

%S 1,1,1,61,13,7,1,25,109,41,60,1,5,24,18,6,3,7,38,12,86,31,18,14,8,96,

%T 470,2,37,245,8,6,37,2,20,137,3,19,24,63,10,99,52,32,16,638,15,20,61,

%U 45,288,43,52,12,371,123,94,8,483,11

%N Least integer m > 0 such that m + n divides p(m) + p(n), where p(.) is the partition function given by A000041.

%C Conjecture: a(n) exists for any n > 0.

%H Zhi-Wei Sun, <a href="/A248143/b248143.txt">Table of n, a(n) for n = 1..765</a>

%e a(5) = 13 since 5 + 13 = 18 divides p(5) + p(13) = 7 + 101 = 108.

%t Do[m=1;Label[aa];If[Mod[PartitionsP[m]+PartitionsP[n],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]

%Y Cf. A000041, A247824, A247937, A247940, A248124, A248125, A248133, A248136, A248137, A248139, A248142, A248144.

%K nonn

%O 1,4

%A _Zhi-Wei Sun_, Oct 02 2014