The numbers and are Amicable Numbers if the three Integers
are all Prime numbers for some Positive Integer satisfying
(Dickson 1952, p. 42).
However, there are exotic Amicable Numbers which do not satisfy Euler's rule,
so it is a Sufficient but not
Necessary condition for amicability.
See also Amicable Numbers
Dickson, L. E. History of the Theory of Numbers, Vol. 1: Divisibility and Primality. New York: Chelsea, 1952.
© 1996-9 Eric W. Weisstein