$n$th prime number Is there an explicit formula that tells us what the $n$th prime number is if we know what the $nth$ squareful number is? If there is, what are its applications, and if there isn't, what use would such a formula be, if any?
If there is no explicit formula, but a statement that describes the asymptotic relationship between primes and squarefuls, I would be grateful to hear.

There are plenty of formulas for the $n$th prime, most of which are useless curiosities. I don't know of any that uses a formula for squareful numbers. We can't really say what applications such a formula would have before actually seeing it. 
