Hard Number Theory Problem

Number Theory Level pending

Let \(n \in \mathbb{N}\). Define an arithmetical function \(f\) in the following way. \( f(1) = 1\) and for \( n \geq 2 \) define \(\displaystyle f(n) = \prod_{p \mid n} p \). Then the only value of \(n \) for which the equation \[ \sum_{d\mid n} \sum_{p \mid d} f(d) =n\] holds true is \(\text{__________} \).

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