UA-UMO 2023 Problem 92

Positive integers $a_1, a_2, \ldots, a_{101}$ are such that $a_i+1$ is divisible by $a_{i+1}$ for all $1 \le i \le 101$ , where $a_{102} = a_1$ . What is the largest possible value of $\max(a_1, a_2, \ldots, a_{101})$ ?

Proposed by Oleksiy Masalitin