# Hard Number Theory Problem

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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