Update: I do not why the usual latex brace brackets do not work on this laptop. I'm going to use the round bracket instead of the brace ones.

Consider the set $S=(2,3,...)$ equipped with the operation $n\cdot m=n^m$.

Question: Do there exist a mean on $S$ which is left and right invariant with respect to $\cdot$?

Thanks in advance,

Valerio