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sum and product equal to $n$

Source: 2022 Centroamerican and Caribbean Mathematical Olympiad, P6

December 1, 2022
number theory

Problem Statement

A positive integer nn is inverosimilinverosimil if there exists nn integers not necessarily distinct such that the sum and the product of this integers are equal to nn. How many positive integers less than or equal to 20222022 are inverosimilsinverosimils?
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