Is it true that if $A\subseteq \{1,\dots ,n\}$ is a set such that $[a,b]>n$ for all $a\ne b$, where $[a,b]$ is the least common multiple, then$$\sum _{a\in A}\frac{1}{a}\le \frac{31}{30}?$$Is it true that there must be $\gg n$ many $m\le n$ which do not divide any $a\in A$?