PERFECT NUMBER

In mathematics, a perfect number is defined as a positive integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors not including the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors, or σ(n) = 2 n.
Example:
The factors of 6 are 1, 2, 3 and 6.1 + 2 + 3 = 6 = 2^ (2-1)*(2^2 – 1)
The factors of 28 are 1, 2, 4, 7, 14 and 28.1 + 2 + 4 + 7 + 14 = 28.
28 = 2^ (3-1)*(2^3 – 1)
The factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496.1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496.
496= 2^ (5-1)*(2^5 – 1)
The factors of 8128 are 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064 and 8128. I'll let you add them up.
8128= 2^ (7-1)*(2^7 – 1)
Formula to calculate Perfect Number:
Perfect Number = 2^ (n-1) * (2^n - 1)
Where n and 2^n – 1 has to be prime numbers.
Note: It is not necessary that when n is prime 2^n – 1 is always prime.
Put n = 11, 2^11 – 1 = 2047= 23*89 .