Školjka

%V0 A finite set of positive integers $A$ is called [i]meanly[/i] 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.