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A finite set of positive integers A is called meanly if for each of its nonempty subsets the arithmetic mean of its elements is also a positive integer. In other words, A is meanly if \frac{1}{k}(a_1 + \ldots + a_k) is an integer whenever k \geq 1 and a_1, \ldots, a_k \in A are distinct.

Given a positive integer n, determine the least possible sum of the elements of a meanly n-element set.

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