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Numbers with sum of proper divisors bigger then them

Source: Kvant Magazine No. 2 2019 M2548*

March 14, 2023

number theoryKvant

Problem Statement

A non-negative integer

n

is called [I]redundant[/I] if the sum of all his proper divisors is bigger than

n

. Prove that for each non-negative integer

N

there are

N

consecutive redundant non-negative integers.
[I]Proposed by V. Bragin[/I]