### 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