Problem 684

Erdős Problem #684: declared status 'open'. Formalized: no. For $0\leq k\leq n$ write$$\binom{n}{k} = uv$$where the only primes dividing $u$ are in $[2,k]$ and the only primes dividing $v$ are in $(k,n]$. Let $f(n)$ be the smallest $k$ such that $u>n^2$. Give bounds for $f(n)$. Prize: no. OEIS: A392019. Tags: binomial coefficients, number theory, primes.