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Divisors of number

Source: All Russian Olympiad 2017,Day2,grade 11,P7

May 1, 2017
number theoryalgebra

Problem Statement

There is number NN on the board. Every minute Ivan makes next operation: takes any number aa written on the board, erases it, then writes all divisors of aa except aa( Can be same numbers on the board). After some time on the board there are N2N^2 numbers. For which NN is it possible?
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