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A248144 Least positive integer m such that m + n divides p(m*n), where p(.) is the partition function given by A000041. 3

%I #9 Oct 03 2014 16:54:40

%S 4,5,3,1,2,14,2,10,1,4,17,5,9,1,1,6,4,10,16,357,1,197,14,1,3,9,6,1123,

%T 15,93,4,1,8,46,77,99,18,53,10,76,4,2,15,152,4,3,10,29,6,12,4,1,25,1,

%U 252,64,106,11,11,136

%N Least positive integer m such that m + n divides p(m*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="/A248144/b248144.txt">Table of n, a(n) for n = 1..496</a>

%e a(6) = 14 since 6 + 14 = 20 divides p(6*14) = 26543660.

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

%Y Cf. A000041, A248004, A248008, A248143, A248175.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Oct 02 2014

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