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Find all such numbers

Source: 2009 József Wildt International Mathematical Competition

April 15, 2020
number theory

Problem Statement

Let Φ\Phi and Ψ\Psi denote the Euler totient and Dedekind‘s totient respectively. Determine all nn such that Φ(n)\Phi(n) divides n+Ψ(n)n +\Psi (n).
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