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Numbers dividing their pairwise sums

Source: Tuymaada 2021/J3

July 30, 2021
number theory

Problem Statement

For nn distinct positive integers all their n(nāˆ’1)/2n(n-1)/2 pairwise sums are considered. For each of these sums Ivan has written on the board the number of original integers which are less than that sum and divide it. What is the maximum possible sum of the numbers written by Ivan?
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