I saw this question, and pop up this idea.
I find myself slightly thinking that if by 'integer' you mean 'signed 32-bit integer', then (pseudocode)
return (n == 1)
or (n == 3)
or (n == 9)
...
or (n == 1162261467)
has a certain beautiful simplicity to it (the last number is 3^19, so there aren't an absurd number of cases). Even for an unsigned 64-bit integer there still be only 41 cases (thanks @Alexandru for pointing out my brain-slip). And of course would be impossible for arbitrary-precision arithmetic...