IMO Shortlist 2015 problem C3

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For a finite set A of positive integers, a partition of A into two disjoint nonempty subsets A_1 and A_2 is \textit{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.