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Perfect numbers.

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View Resource Perfect, Amicable and Sociable Numbers

These friendly sounding numbers are defined by their divisibility and sums. A perfect number is a number whose positive divisors (except for itself) sum to itself; an amicable number is a pair of numbers each of which equals the sum of the other's aliquot parts; and the members of aliquot cycles of length greater than two are often called sociable numbers. This page, housed at (but not officially...

http://djm.cc/amicable.html