A248143 Least integer m > 0 such that m + n divides p(m) + p(n), where p(.) is the partition function given by A000041.

1, 1, 1, 61, 13, 7, 1, 25, 109, 41, 60, 1, 5, 24, 18, 6, 3, 7, 38, 12, 86, 31, 18, 14, 8, 96, 470, 2, 37, 245, 8, 6, 37, 2, 20, 137, 3, 19, 24, 63, 10, 99, 52, 32, 16, 638, 15, 20, 61, 45, 288, 43, 52, 12, 371, 123, 94, 8, 483, 11

Offset

1,4

Comments

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

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..765

Example

a(5) = 13 since 5 + 13 = 18 divides p(5) + p(13) = 7 + 101 = 108.

Mathematica

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

Crossrefs

Cf. A000041, A247824, A247937, A247940, A248124, A248125, A248133, A248136, A248137, A248139, A248142, A248144.

Sequence in context: A106426 A106416 A224730 * A012860 A002108 A087409

Adjacent sequences: A248140 A248141 A248142 * A248144 A248145 A248146

Keyword

nonn

Author

Zhi-Wei Sun, Oct 02 2014

Status

approved