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APMO Number Theory

Source: APMO 2023 Problem 2

July 5, 2023
number theoryAPMOAPMO 2023

Problem Statement

Find all integers nn satisfying n≥2n \geq 2 and σ(n)p(n)−1=n\dfrac{\sigma(n)}{p(n)-1} = n, in which σ(n)\sigma(n) denotes the sum of all positive divisors of nn, and p(n)p(n) denotes the largest prime divisor of nn.
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