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 Divisor of and .

**References**

Anderson, C. W. and Hickerson, D. Problem 6020. ``Friendly Integers.'' *Amer. Math. Monthly* **84**,
65-66, 1977.

© 1996-9

1999-05-26