if $G$ is a group whose order is $n$ can we determine the number of isomorphism types for this number or not ?
for instance, if $n=4$ we have 2 types, $Z_4$ and $Z_2 \times Z_2$ " Klein 4-group"
for any number n, is a similar calculation possible ?
in other words, let $P$ is a function from Natural numbers into natural numbers which for any number $n$ gives the number of possible structures for a group of order $n$
can we find a formula for this function in terms of $n$ and using operation like addition, multiplication, etc ?