what is the distribution of prime numbers and their powers?

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I know that Prime number theorem says that the that $P_n$ ~ $\log(n)n$ or $\frac{P_n}{\log(n)n}=1$ as n goes to infinty

My question is what is a ~ formula for not just prime numbers but all numbers that factorization looks like $P_m^n$

$n$ and $m$ are natural numbers.

what is the distribution of primes and their powers?