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A sociable number is a generalization of the concepts of amicable numbers and perfect numbers. A set of sociable numbers is an aliquot sequence, or a sequence of numbers, with each number being the sum of the factors of the preceding number, excluding the preceding number itself. In the case of sociable numbers, the sequence is cyclic (eventually returning to its starting point).
The period of the sequence, or order of the set of sociable numbers, is the number of numbers in this cycle.
Sociable numbers are similar to amicable numbers. A chain of numbers is sociable if the sum of the proper divisors of each number is the next number in the chain, the last number preceding the first.
Poulet found the first two chains in 1918. The first chain contains five members, 12,496 -> 14,288 -> 15,472 -> 14,536 -> 14,264 -> 12,496, while the second chain contains a remarkable 28 numbers.
These two chains were the only known sociable chains until 1969, when Henri Cohen used a computer to check all numbers below 60,000,000, and he discovered seven new chains of four links. More have been found since then. Curiously, no chains with just three links (which someone named "crowds") have been found. Your Password: