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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Oct 03 2014
STATUS
approved