digitos :: Integer -> [Integer]
digitos n
 | n == 0 = []
 | otherwise =  mod n 10 : digitos (div n 10)

digxdig :: [Integer] -> Integer
digxdig [] = 1
digxdig (x:xs) = x*(digxdig xs)

pers :: Integer -> Integer
pers n
 | n < 10 = 0
 | otherwise = 1 + pers m
      where m =  digxdig (digitos n)