Intuitively, you can think of N as a rough measure of the "ballpark" around where you are in the number line. As you move up to higher numbers, perfect powers g

Intuitively, you can think of N as a rough measure of the "ballpark" around where you are in the number line. As you move up to higher numbers, perfect powers get more and more scarce, so the probability of finding one by picking a number at random becomes lower.