Question 149
For a finite set $A$ of positive integers, we call a partition of $A$ into two disjoint nonempty subsets $A_1$ and $A_2$ good if the least common multiple of the elements in $A_1$ is equal to the greatest common divisor of the elements in $A_2$.
Determine the minimum value of $n$ such that there exists a set of $n$ positive integers with exactly $2015$ good partitions.
(IMO-2015 Shortlist, Problem C3)
Determine the minimum value of $n$ such that there exists a set of $n$ positive integers with exactly $2015$ good partitions.
(IMO-2015 Shortlist, Problem C3)