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

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, 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, 252, 64, 106, 11, 11, 136

Offset: 1

Author

Zhi-Wei Sun, Oct 02 2014

Keywords

• nonn

Comments

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

Examples

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

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..496

Crossrefs

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

Programs

Mathematica

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}]