The number $60$ is written on a blackboard. In every move, Andris wipes the numbers on the board one by one, and writes all its divisors in its place (including itself). After $10$ such moves, how many times will $1$ appear on the board?
Problem
Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 2 E16
Tags: number theory, Divisors