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60 is written on a blackboard, divisors related

Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 2 E16

December 12, 2022
number theoryDivisors

Problem Statement

The number 6060 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 1010 such moves, how many times will 11 appear on the board?