Sociable numbers are a special type of number that form a sequence through a process of summing the proper divisors of each number. A proper divisor is any divisor of a number except the number itself. If you start with a sociable number and repeatedly sum its proper divisors, you eventually return to the original number, creating a cycle. For example, the smallest sociable number is 1, which leads to itself. Other sociable numbers can have longer cycles, such as 28, 28 or 220, 284. These numbers are related to the broader study of amicable numbers and perfect numbers, which also involve the properties of divisors.