Problem 393

Erdős Problem #393: declared status 'open'. Formalized: no. Let $f(n)$ denote the minimal $m\geq 1$ such that$$n! = a_1\cdots a_t$$with $a_1<\cdots <a_t=a_1+m$. What is the behaviour of $f(n)$? Current best: Let $F_m(N)$ count the number of $n\leq N$ such that $f(n)=m$. Prize: no. OEIS: A388302. Tags: factorials, number theory.