In number theory, a perfect number is a positive integer that is equal to
the sum of its positive divisors, excluding the number itself. For instance, 6
has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a
perfect number.
The sum of divisors of a number, excluding the number itself, is called its
aliquot sum, so a perfect number is one that is equal to its aliquot sum.
Equivalently, a perfect number is a number that is half the sum of all of its
positive divisors including itself; in symbols, σ 1 ( n ) = 2 n
{\displaystyle \sigma {1}(n)=2n} where σ 1 {\displaystyle \sigma is
the sum-of-divisors function. For instance, 28 is perfect as 1 + 2 + 4 + 7 +
14 = 28.