## 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 Divisor of and .

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