Are there any natural numbers $n$ (other than 1) for which $gnu(n)=n$? We define $gnu(n)$ to be the number of isomorphism classes of groups of order $n$. This question popped into my head today, and I couldn't come up with a proof one way or another.

In the paper by Conway, et al. entitled "Counting Groups: Gnus, Moas, and other Exotica, Conjecture 10.1 implies that there should be no such natural number $n$ which satisfies $gnu(n)=n$.

Does anybody have an argument to show that there is no natural number $n$ (other than 1) for which $gnu(n)=n$? If it is really straightforward, just say so and I'll work it out for myself when I find time. Thanks!

Are there any natural numbers $n$ (other than 1) for which $gnu(n)=n$? This question popped into my head today, and I couldn't come up with a proof one way or another.

In the paper by Conway, et al. entitled "Counting Groups: Gnus, Moas, and other Exotica, Conjecture 10.1 implies that there should be no such natural number $n$ which satisfies $gnu(n)=n$.

Does anybody have an argument to show that there is no natural number $n$ (other than 1) for which $gnu(n)=n$? If it is really straightforward, just say so and I'll work it out for myself when I find time. Thanks!