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9

Part of 2020 Durer Math Competition Finals

Problems(1)

sum of all numbers on the paper having exactly 2 proper divisors

Source: 2020 Dürer Math Competition Finals Day2 E9 https://artofproblemsolving.com/community/c1622639_2020_

1/7/2022
On a piece of paper, we write down all positive integers nn such that all proper divisors of nn are less than 1818. We know that the sum of all numbers on the paper having exactly one proper divisor is 666666. What is the sum of all numbers on the paper having exactly two proper divisors?
We say that kk is a proper divisor of the positive integer nn if k∣nk | n and 1<k<n1 < k < n.
number theorydivisor