Some properties of perfect nos...

1. sum of reciprocals of all d divisors of a perfect no. is always 2.
2. Every even perfect no. can be written as 2^x-1(2^x-1), where 2^x-1 is a prime.
3. First 4 perfect nos. are 6, 28, 496 and 8128.
6=2^2-1(2²-1)
28=2^3-1(2³-1)
496=2^5-1(2⁵-1)
8128=2^7-1(2⁷-1)
4. Till d date, there is no known odd perfect no.It does not mean that thr is not any odd perfect no.