If N= 144 How many sets of two values (a,b) are there for which the LCM (a,b) is 144 ??
What the general formula for this (with proof) ??
Note that . Therefore one of a or b must be divisible by , and one of a or b must be divisible by . How many ordered pairs (a,b) satisfy these conditions?
This method definitely generalizes, but I doubt there is a general formula since it becomes one giant counting problem when N has more prime divisors.