I am trying to evaluate the following sum: $$b\sum_{i=a}^b\frac{i}{\gcd(i,b)}$$
I have solved the problem if $a=1$ but I am clueless for the case when $a$ is not $1$. For $a=1$, I used the fact that $\gcd(i, b)=\gcd(b-i, b)$ but this doesn't help for the above sum.
Any help is appreciated. Thanks!