Let $k\le n$. What choice of $A\subseteq \{1,\dots ,n\}$ (with $\gcd (A)=1$) 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 $\{n,n-1,\dots ,n-k+1\}$?

AMS 11 · solved (literature)

theorem erdos_434.parts.i (n k : ℕ) (hn : 1 ≤ n) (hk : 1 ≤ k) (h : k ≤ n) :
    IsGreatest
      { Nat.NcardUnrepresentable S | (S : Finset ℕ) (_ : S ⊆ Finset.Icc 1 n)
        (_ : #S = k) (_ : S.gcd id = 1) }
      (Nat.NcardUnrepresentable <| answer(sorry))