A248175 Least positive integer m such that m + n divides q(m*n), where q(.) is the strict partition function given by A000009.

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, 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, 10, 25, 40, 7, 91, 61, 20

Offset: 1

Author

Zhi-Wei Sun, Oct 03 2014

Keywords

• nonn

Comments

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

(ii) For each n > 0, there is a positive integer m such that m + n divides q(m) + q(n).

Examples

			a(3) = 9 since 9 + 3 = 12 divides q(9*3) = 192 = 12*16.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..405

Crossrefs

Cf. A000009, A247824, A248004, A248143, A248144.

Programs

Mathematica

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}]