Let $A\subseteq [1,n)$ be a set of integers such that $(a,b)=1$ for all distinct $a,b\in A$. Is it true that $\sum_{a\in A}\frac{1}{n-a}\leq \sum_{p < n}\frac{1}{p}+O(1)$?

In [Er80] he claims he "did not state this quite correctly" in [Er77c]. The problem in [Er77c] which Erdős is presumably referring to states that if $n < q_1 < \cdots < q_k\leq m$ is the set of primes in $(n,m]$ then $\sum \frac{1}{q_i-n} < \sum_{p < m-n}\frac{1}{p}+O(1)$.