Interview Questions: Write programs to do the following.

• Check for a Perfect Number 
• A perfect number is a number that is equal to the sum of its proper divisors. Eg 6 is a perfect number because its proper divisors are 1, 2 and 3 where 1+2+3=6. Another perfect number is 28.
• Check for an Armstrong Number
• An Armstrong Number is equal to the sum of the cubes of its digits. Eg  153 has the digits 1, 5 and 3. 1³ + 5³ + 3³ = 1 + 125 + 27= 153
• Check for a Happy Number
• A Happy Number is a number that finally reaches 1 when replaced continuously by the sum of the square of its digits. Eg 19 = 1² + 9² = 82 = 8² + 2² = 68 = 6² + 8² = 100 = 1² + 0² + 0² = 1.
• Check for a Prime Number
• Everybody knows what a prime number is
• Check if a number is a perfect cube