I am trying to solve the following question:
Consider the set $S_N=\{\log_a b | 2\leq a,b \leq N\}$. How many distinct values are there inside $S_N$?
For example, $S_5={log_22,log_23,log_24,log_25,log_32,log_33,log_34,log_35,...,log_55}$ In which $log_22=log_33=log_44=log_55$, so the answer for $N=5$ would be 13
I currently have no idea on how to do it so any ideas would be helpful, thanks