Friendly Pair
Define
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
, 
, and |  |  | |
 | |  |
Numbers which do not have Friends are called Solitary Numbers. Solitary Numbers satisfy
, where 
is the Greatest Common Divisorof 
and 
.See also Aliquot Sequence, Friend, Solitary Number
References
Anderson, C. W. and Hickerson, D. Problem 6020. ``Friendly Integers.'' Amer. Math. Monthly 84, 65-66, 1977.
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