Ascending proper divisors
Source: 239 2008 S1
July 28, 2020
Problem Statement
Composite numbers and have equal number of divisors. All proper divisors of were written in ascending order and all proper divisors of were written under them in ascending order, then the numbers that are below each other were added together. It turned out that the resulting numbers formed a set of all proper divisors of a certain number. What are the smallest values that and take?