[Jefferson]

How about the zenzizenzic ((n^2)^2) club?
1, 16, 81, 256, the now defunct 625 (it's hard to survive in AK), 1296, 2401 (ND might as well be AK), and 4096

Next year we will welcome the newest member, 6561, who will also be a member of the even more exclusive zenzizenzizenzic ((n^2)^2)^2) club including only 1 and 256 so far.