Return the Carmichael function of a number that is
  represented as a list of (prime,exponent) pairs.

def carmichael_of_factorized( f_list ):
  """Return the Carmichael function of a number that is
  represented as a list of (prime,exponent) pairs.
  """

  if len( f_list ) < 1: return 1

  result = carmichael_of_ppower( f_list[0] )
  for i in range( 1, len( f_list ) ):
    result = lcm( result, carmichael_of_ppower( f_list[i] ) )

  return result