Christmas Contest - Individual Round - Problem 15

Consider the sequence of numbers $a_1,a_2,a_3, ...$, which has $a_1 = 1$ and $a_m = \dfrac{\sum_{i=1}^{m-1}i\cdot a_i}{a_{m-1}}$ for all positive integers $m \ge 2$. Find the biggest positive integer $n$ such that $a_n \le 2024$.