Evaluating a Sum of Floor Logarithms

Denote $ \lfloor n \rfloor $ to be the greatest integer less than or equal to $ n $. For example, $ \lfloor 11.2 \rfloor = 11 $, $ \lfloor 90 \rfloor = 90 $, and $ \lfloor -9.8 \rfloor = -10 $. Evaluate: $ \displaystyle \sum_{k=2}^{\infty} \left\lfloor \log_k 202.5 \right\rfloor $