Problem

Source: 2016 China Northern MO Grade 11, Problem 3

Tags: number theory, function, Euler



$m(m>1)$ is an intenger, define $(a_n)$: $a_0=m,a_{n}=\varphi(a_{n-1})$ for all positive intenger $n$. If for all nonnegative intenger $k$, $a_{k+1}\mid a_k$, find all $m$ that is not larger than $2016$. Note: $\varphi(n)$ means Euler Function.