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%I #6 Oct 03 2014 10:12:08
%S 11,4,9,2,12,10,9,16,3,6,1,5,2,18,7,8,5,14,11,36,2,34,4,8,31,6,15,36,
%T 23,2,9,14,17,22,11,18,1,22,11,7,1,22,12,7,55,7,19,40,15,6,31,12,43,
%U 10,25,40,7,91,61,20
%N Least positive integer m such that m + n divides q(m*n), where q(.) is the strict partition function given by A000009.
%C Conjecture: (i) a(n) exists for any n > 0.
%C (ii) For each n > 0, there is a positive integer m such that m + n divides q(m) + q(n).
%H Zhi-Wei Sun, <a href="/A248175/b248175.txt">Table of n, a(n) for n = 1..405</a>
%e a(3) = 9 since 9 + 3 = 12 divides q(9*3) = 192 = 12*16.
%t Do[m=1;Label[aa];If[Mod[PartitionsQ[m*n],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]
%Y Cf. A000009, A247824, A248004, A248143, A248144.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Oct 03 2014