Problem 390

Erdős Problem #390: declared status 'open'. Formalized: yes. Let $f(n)$ be the minimal $m$ such that$$n! = a_1\cdots a_k$$with $n< a_1<\cdots <a_k=m$. Is there (and what is it) a constant $c$ such that$$f(n)-2n \sim c\frac{n}{\log n}?$$ Prize: no. OEIS: A193429. Tags: factorials, number theory.