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 $\text{\_\_\_\_\_\_\_\_\_\_}$ .