BALTIC-WAY 2001 Problem 16

Let $f$ be a real-valued function defined on the positive integers satisfying the following condition: For all $n>1$ there exists a prime divisor $p$ of $n$ such that

$$f(n)=f\left(\frac{n}{p}\right)-f(p)$$

Given that $f(2001)=1$, what is the value of $f(2002)$ ?