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.
- Cardano's Formula
- Cardinality
- Cardinal Number
- Cardioid
- Cardioid Caustic
- Cardioid Evolute
- Cardioid Inverse Curve
- Cardioid Involute
- Cardioid Pedal Curve
- Cards
- Carleman's Inequality
- Carlson-Levin Constant
- Carlson's Theorem
- Carlyle Circle
- Carmichael Condition
- Carmichael Function
- Carmichael Number
- Carmichael's Conjecture
- Carmichael Sequence
- Carmichael's Theorem
- Carmichael's Totient Function Conjecture
- Carnot's Polygon Theorem
- Carnot's Theorem
- Carotid-Kundalini Fractal
- Carotid-Kundalini Function