Problem 864

Erdős Problem #864: declared status 'open'. Formalized: no. Let $A\subseteq \{1,\ldots N\}$ be a set such that there exists at most one $n$ with more than one solution to $n=a+b$ (with $a\leq b\in A$). Estimate the maximal possible size of $\lvert A\rvert$ - in particular, is it true that$$\lvert A\rvert \leq (1+o(1))\frac{2}{\sqrt{3}}N^{1/2}?$$ Prize: no. OEIS: A389182. Tags: additive combinatorics, number theory, sidon sets.