Counting divisors of a number

Question

Let m be any positive integer and consider $\Sigma_{d|m} \frac{1}{d} $.

I wish to ask whether there is a closed form expression for the above sum.

Answer 1

It depends on what one considers closed form. Note that our sum is equal to $$\frac{1}{m}\sum_{d\mid m} \frac{m}{d}.$$ But $\sum_{d\mid m} \frac{m}{d}$ is the sum of the divisors of $m$, often called $\sigma(m)$ or $d(m)$.

Thus our sum is $\dfrac{\sigma(m)}{m}$.