Finding the limit of $\left(\sum\limits_{k=2}^n\frac1{k\log k}\right)-\left(\log \log n\right)$
What is known about the 'Double log Eulers constant', $\lim_{n \to \infty}{\sum_{k=2}^n\frac{1}{k\ln{k}}-\ln\ln{n}}$?