Problem 469

Erdős Problem #469: declared status 'open'. Formalized: yes. Let $A$ be the set of all $n$ such that $n=d_1+\cdots+d_k$ with $d_i$ distinct proper divisors of $n$, but this is not true for any $m\mid n$ with $m<n$. Does$$\sum_{n\in A}\frac{1}{n}$$converge? Prize: no. OEIS: A006036, A119425. Tags: divisors, number theory.