Estimate for a specific series For a positive integer $m$ define
$$
a_m=\prod_{p\mid m}(1-p),
$$
where the product is taken over all prime divisors of $m$, and
$$
S_n=\sum_{m=1}^n a_n.
$$
I am interested in an estimate for $|S_n|$. Any references, hints, ideas, etc., will be appreciated.

As Oussama Boussif notice, using the Euler product for the totient function $$\phi\left(m\right)=m\prod_{p\mid m}\left(1-\frac{1}{p}\right)
 $$ we have $$a_{m}=\prod_{p\mid m}\left(1-p\right)=\left(-1\right)^{\omega\left(m\right)}\frac{\phi\left(m\right)}{m}\prod_{p\mid m}p
 $$ where $\omega\left(m\right)
 $ is the number of distinct prime factors of $m
 $, so we have using the fact that $\prod_{p\mid m}p\leq m
 $ (equality holds if $m
 $ is a squarefree number) $$\left|\sum_{m=1}^{n}a_{m}\right|\leq\sum_{m=1}^{n}\phi\left(m\right)=\frac{3}{\pi^{2}}n^{2}+O\left(n\log\left(n\right)\right).
 $$ 
