I stumbled upon a problem in my number theory class regarding the divisor function $d(n)$ and the totient function $\phi(n)$, where the problem states:
Does there exist a constant $C$ such that $\frac{\phi(d(n))}{d(\phi(n))}\le C$ ?
I already know how to solve this problem and the answer seems to be "No", however i am more interested in the motive behind this question. if this problem is important, then why is it important to prove such constants exist or does not exist ? What are the implications for when it does exist or doesnt exist?
Could anyone give me an elaborate explanation to this ?