Perfect numbers

Perfect numbers are positive integers where the sum of all their proper divisors (divisors excluding the number itself) equals the number. For example, 6 is perfect because its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. These numbers are rare and have special mathematical properties connecting them to perfect squares and prime numbers. Historically, perfect numbers have intrigued mathematicians and are linked to ancient mathematical theories. They are part of number theory's rich landscape, illustrating the beauty of the relationships among numbers.