Say two positive integers are "*peers*" if they are divisible by precisely the same set of primes, such as 12 and 18 (both divisible by 2 and 3), or 70 and 350 (both divisible by 2, 5 and 7).


What are the best estimates known for the number of pairwise *non-peers* not greater than an arbitrary positive integer *N*?



Numbers divisible by precisely the same set of primes
Your count equals the number of square-free numbers up to $N$. This is because a set of positive integers are pairwise "non-peers" if any only if their [radicals](https://en.wikipedia.org/wiki/Radical_of_an_integer) are distinct. This is a well-studied problem in analytic number theory, see in particular Walfisz's estimate [here](https://en.wikipedia.org/wiki/Square-free_integer#Distribution).


