where is the Divisor Function. Then a Pair of distinct numbers is a friendly pair
(and is said to be a Friend of ) if
For example, 4320 and 4680 are a friendly pair, since
Numbers which do not have Friends are called Solitary Numbers.
Solitary Numbers satisfy
, where is the Greatest Common Divisor
of and .
See also Aliquot Sequence, Friend, Solitary Number
Anderson, C. W. and Hickerson, D. Problem 6020. ``Friendly Integers.'' Amer. Math. Monthly 84,
© 1996-9 Eric W. Weisstein