Let $k \le n$. What choice of $A\subseteq\{1, \dots, n\}$ (with $\text{gcd}(A) = 1$) of size $|A| = k$ maximises the number of integers not representable as the sum of finitely many elements from $A$ (with repetitions allowed)? Is it $\{n, n - 1, \dots, n - k + 1\}$?