Number Magic 


Question : 
What are Perfect Numbers and Amicable or Sympathetic Numbers ? 
Answer : 
A perfect number can be described as an integer which is equal to the sum of all its factors except itself. 
Euclid discovered that the first four perfect numbers are generated by the formula 2_{n1}(2_{n}  1).

For Example,

The
number 28 is a perfect number since, 
28 = 1 + 2 + 4 + 7 + 14 
Amicable or Sympathetic are two numbers each of which is equal to the sum of all the exact divisors of the other except the
number itself. 
For Example, 
220 and 224 are amicable numbers for 220 has the exact divisors 1, 2, 4, 5, 10, 11, 20, 22, 44,
55 and 110, whose sum is 284 and 284 has the exact divisors 1, 2, 4, 71 and 142 whose sum is 220.

