想了半天无果qwq

$\sum_{d=1}^{min(n,m)}\text f(d) \sum_{i=1}^{\lfloor \frac{n}{d} \rfloor} \sum_{j=1}^{\lfloor \frac{m}{d} \rfloor} [gcd(i,j)=1] f(id)F(jd) = \sum_{d=1}^{min(n,m)} (\text f*\mu)(d) \sum_{i=1}^{\lfloor \frac{n}{d} \rfloor} \sum_{j=1}^{\lfloor \frac{m}{d} \rfloor} f(id)F(jd)$