Caldwell, Chris K.

Problem Statement

Let \(d(n)\) be defined as the sum of proper divisors of \(n\) (numbers less than \(n\) which divide evenly into \(n\)).

If \(d(a) = b\) and \(d(b) = a\), where \(a \neq b\), then \(a\) and \(b\) are an amicable pair and each of \(a\) and \(b\) are called amicable numbers.

For example, the proper divisors of \(220\) are \(1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110\); therefore \(d(220) = 284\). The proper divisors of \(284\) are \(1, 2, 4, 71, 142\); so \(d(284) = 220\).