OPEN
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
\[g(n,t)=\max G(A)\]
where the maximum is taken over all $A\subseteq \{1,\ldots,t\}$ of size $\lvert A\rvert=n$ which has no common divisor. Is it true that
\[g(n,t)\sim \frac{t^2}{n-1}?\]
This type of problem is associated with Frobenius. Erdős and Graham
[ErGr72] proved $g(n,t)<2t^2/n$, and there are examples which show that
\[g(n,t) \geq \frac{t^2}{n-1}-5t\]
for $n\geq 2$.
The problem is written as Erdős and Graham describe it, but presumably they had in mind the regime where $n$ is fixed and $t\to \infty$.
