Problem 1062

Erdős Problem #1062: declared status 'open'. Formalized: yes. Let $f(n)$ be the size of the largest subset $A\subseteq \{1,\ldots,n\}$ such that there are no three distinct elements $a,b,c\in A$ such that $a\mid b$ and $a\mid c$. How large can $f(n)$ be? Is $\lim f(n)/n$ irrational? Prize: no. OEIS: A038372. Tags: number theory.