More problems in 2016 part 3

Nice problem!

The functions $d$ and $\phi(d)$ are multiplicative, and so is their quotient $\frac{d}{\phi(d)}$ and their divisor sum $f(n)=\sum_{d|n}\frac{d}{\phi(d)}$ . Thus $f(67362)=f(31*41*53)=\prod_pf(p)=\prod_p\left(\frac{1}{\phi(1)}+\frac{p}{\phi(p)}\right)=\prod_p\left(1+\frac{p}{p-1}\right)=\frac{34587}{4160}$

where the products are taken over $p=31,41,53$ . The answer is $34587+4160=\boxed{38747}$