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

1,1

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).

Links

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

Example

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

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}]

Crossrefs

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

Sequence in context: A352162 A010187 A372761 * A114267 A166205 A141240

Adjacent sequences: A248172 A248173 A248174 * A248176 A248177 A248178

Keyword

nonn

Author

Zhi-Wei Sun, Oct 03 2014

Status

approved