perfectpower

import math

def introot(value,root):
   a = root
   b = 0
   while math.fabs(a-b) > 0:
      b = a
      a = int(1.0/root *((root-1.0)*a +value/a**(root-1.0)))
   return a

def isperfectpower(value):
   minE,maxE,minB,maxB = 2,int(math.log(value,2)),2,introot(value,2)
   while minB**maxE != value and maxB**minE != value and minE < maxE:
         minE += 1
         maxB = introot(value,minE)
         minB += 1
         maxE = int(math.log(value,minB))
         if minB**maxE == value or maxB**minE == value:
            return True
   return False