Question 90
By $\text{rad}(x)$ we denote the product of all distinct prime factors of a positive integer $n$. Given $a \in \mathbb{N}$, a sequence $(a_n)$ is defined by $a_0 = a$ and $a_{n+1} = a_n + \text{rad}(a_n)$ for all $n \ge 0$. Prove that there exists an index $n$ for which $\frac{a_n}{\text{rad}(a_n)} = 2022$.