I am trying to find asymptotics/running time of recurrence $T(n) = 5T(\frac{n}{5}) + \frac{n}{\lg n}$.
Since Master Theorem for solving the reassurances can't be used, I was able to unroll it and came up with $n(\frac{1}{\ lgn} + \frac{1}{\lg (n/5^2)}+...+\frac{1}{ \ lg5} + 5T(1)) = nT(1) + \frac{n}{\lg5}\sum_{i=1}^{\log_5 n}\frac{1}{i}$
I am not sure how to express the the asymptotics/running time of the last expression.
Thanks!