NB. Perfect powers

NB. Integer logs and roots; work for extended precision.
ilog=: <.@^.
iroot=: <.@%:

NB. 'x isEvenRoot y' is true if the xth root of y is an integer.
isEvenRoot=: ] = iroot ^ [

NB. 'primesTo y' returns the primes up to the first prime >= y.
primesTo=: 3 : 'p: i.>: _1 p: y'

NB. Return a list of the prime powers that "factor" y.
perfectPowersOf=: 3 : '(primesTo 2 ilog y) (isEvenRoot # [) y'

NB. Just check if that list is longer than 0.
isPerfectPower=: 3 : '0<#perfectPowersOf y'