Is 26 a perfect number

Answer 1

No. The proper divisors of 26 are 1,2, and 13 but 1+2+13 =16 which does not equal 26.

6 is perfect because is proper divisors are 1,2 ,3 and 1+2+3=6.

28 is perfect because its proper divisors are 1,2,4,7,14 and 1+2+4+7+14 = 28.

All known perfect numbers are of the form (2n-1)2n-1 where

2n-1 is a prime and such numbers are always even.

If n = 2, 22 - 1 = 3 which is prime so 3(2) is perfect

If n = 3, 23 -1 - 7 which is prime so 7(23-1) = 7(22) = 28 which is perfect .

If n = 4, 24 - 1 = 15 which is not prime so the formula does not give a perfect number.

Primes of the form 2n-1 are called Mersennes primes in honor of the mathematician who wrote about them first. See the related link if you want to see a list of known Mersennes primes.