Question 94
Denote by $\ell(n)$ the largest prime divisor of $n$. Let $a_{n+1} = a_n + \ell(a_n)$ be a recursively defined sequence of integers with $a_1 = 2$. Determine all natural numbers $m$ such that there exists some $i \in \mathbb{N}$ with $a_i = m^2$.