MathNet 2019-part-01 — 184 problems (EN–VI) Question 176

The sequence $a_1, a_2, a_3, \dots$ of positive integers is defined in the following way: $a_1$ is given, and for each $n \ge 2$ the number $a_n$ is the smallest positive integer divisible by $n$, which is not less than $a_{n-1}$. (For example, if $a_5 = 115$, then $a_6 = 120$, $a_7 = 126$, $a_8 = 128$.)
Prove that from a certain moment this sequence coincides with an arithmetic progression.