2025 IMO 第 4 题

An infinite sequence $a_{1}, a_{2}, \ldots$ consists of positive integers has each of which has at least three proper divisors. Suppose that for each $n \geq 1$ , $a_{n+1}$ is the sum of the three largest proper divisors of $a_{n}$ . Determine all possible values of $a_{1}$ .

无限序列 $a_{1}, a_{2}, \ldots$ 由正整数组成，每个正整数至少有三个真因数。假设对于每个 $n \geq 1$ ， $a_{n+1}$ 是 $a_{n}$ 的三个最大真因数之和。确定 $a_{1}$ 的所有可能值。