Let $n\geq 1$ be an integer, $P$ the set of rational prime numbers. I am interested in upper bounds for $\prod_{p\in P; \ p\mid n}(1+1/p)$ in terms of n.

I would like to prove the existence of explicit real numbers $a,b$ such that $\prod_{p\in P; \ p\mid n}(1+1/p)\leq a\log(n)^b$.

Is this possible (reference)?

Can one even take $b=1$?