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_
January 7, 2022
number theorydivisor
Problem Statement
On a piece of paper, we write down all positive integers such that all proper divisors of are less than . We know that the sum of all numbers on the paper having exactly one proper divisor is . What is the sum of all numbers on the paper having exactly two proper divisors?We say that is a proper divisor of the positive integer if and .