Question 68
For each positive integer $n$, denote by $\omega(n)$ the number of prime divisors of $n$. Find all polynomials $f(x)$ with integer coefficients, such that if $n$ is a positive integer satisfying $\omega(n) \gt 2023^{2023}$, then $f(n)$ is also a positive integer with
$$
\omega(f(n)) \le \omega(n).
$$
$$
\omega(f(n)) \le \omega(n).
$$