Aliquot chains, which are sometimes referred to as sociable chains, are iterative processes or loops. The process is:
The behaviour of these loops varies. Most chains end at zero (if you have a prime number, its only proper divisor is 1, and 1 has no proper divisors). A perfect number will sum to itself again and again and again. Amicable or sociable numbers will iterate over the same set of two, or four, or even more, numbers. There are a few numbers that seem to increase indefinitely.