If $A\subset \mathbb{N}$ is a finite set then let $G(A)$ denote the greatest integer which is not expressible as a finite sum of elements from $A$ (with repetitions allowed). Let$$g(k,n)=\max G(A)$$where the maximum is taken over all $A\subseteq \{1,\dots ,n\}$ of size $|A|=k$ which has no common divisor. Is it true that$$g(k,n)\sim \frac{n^2}{k-1}?$$