Lecture Notes on 5 October 2012

def sumDigits (n):
  sum = 0
  while (n > 0):
    sum = sum + (n % 10)
    n = n // 10
  return sum

def revNum (n):
  rev_num = 0
  while (n > 0):
    rev_num = rev_num * 10 + (n % 10)
    n = n // 10
  return rev_num

def sumDivisors (n):
  sum = 0
  for divisor in range (1, n // 2 + 1):
    if (n % divisor == 0):
      sum = sum + divisor
  return sum

def isPalindromic (num):
  return (num == revNum(num))

def isPrime (num):
  limit = int (num ** 0.5)
  divisor = 2
  while (divisor <= limit):
    if (num % divisor == 0):
      return False
    divisor = divisor + 1
  return True


def main ():
  # Test sumDivisors() function
  num = eval (input ("Enter a number: "))
  sum_divisors = sumDivisors (num)
  print ("Sum of divisors is ", sum_divisors)

  # print all perfect numbers less than 10000
  for num in range (2, 10001):
    if (num == sumDivisors (num)):
      print (num)

  # print all prime numbers in a user defined range
  lo, hi = eval (input ("Enter a range: "))
  for n in range (lo, hi + 1):
    if (isPrime (n)):
      print (n)

  # find the non palindromic number whose cube is palindromic
  for n in range (1000, 10000):
    if (not isPalindromic (n) and isPalindromic (n * n * n)):
      print (n)
      break

  # find the prime that remains prime when added to it reversal
  for n in range (100, 1000):
    if (isPrime(n) and isPrime (n + revNum(n))):
      print (n)
      break

main()