Perfect Number

A number is said to be Perfect if the sum of factors of its proper divisor is equal to the number itself.
Example:- 6, 28, 496, 8128 ...

6 is the smallest Perfect number.
St. Augustine wrote in The City of God (413–426):

Six is a number perfect in itself, and not because God created all things in six days; rather, the converse is true. God created all things in six days because the number is perfect.

The first reference of Perfect number is found in Euclid's Element (Volume 9) where Euclid proved that 2^p−1(2^p − 1) is an even perfect number whenever 2^p − 1 is prime

The first four numbers according to this definition are

for p = 2: 2^1(2^2 − 1) = 6
for p = 3: 2^2(2^3 − 1) = 28
for p = 5: 2^4(2^5 − 1) = 496
for p = 7: 2^6(2^7 − 1) = 8128.
Perfect Number can also be expressed in form of Triangular Number

(Source of Image :- Wikipedia)

Dr Rajesh Kumar Thakur