MEMO 2014 ekipno problem 7

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24. rujna 2014.
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.
Izvor: Srednjoeuropska matematička olimpijada 2014, ekipno natjecanje, problem 7