Actually, I posted this long ago in MO but did not get a reply as it was unfit.
Now this is an exercise in some textbook (I think Apostol), and I would be happy to receive some answers.
Let $P(n)$ be the product of positive integers which are $\leq n$ and relatively prime to $n$. Prove that $$ \displaystyle P(n) = n^{\phi(n)} \prod\limits_{d \mid n} \left(\frac{d!}{d^d} \right)^{\mu(n/d)}.$$