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How many n are divisible by \lfloor \sqrt{n}\rfloor-1?

Source: Czech-Polish-Slovak Junior Match 2024, T-4

May 29, 2024
number theorynumber theory proposedDivisibilityfloor function

Problem Statement

How many positive integers n<2024n<2024 are divisible by n1\lfloor \sqrt{n}\rfloor-1?