We have $\prod \tfrac{p_i-1}{p_i} \geq \tfrac{\varphi(n)}{n}=1-\tfrac{402}{\prod p_i^{e_i}}\implies 402\geq \left(1-\prod \tfrac{p_i-1}{p_i}\right)\prod p_i^{e_i}\geq \prod p_i-\prod \left(p_i-1\right)$. The problem is now computable (since $n$ can't be prime).

This problem is IzHO 2006/1