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A class is a user-defined type provided to represent a concept in the code of a program. Essentially, all language facilities beyond the fundamental types, operators, and statements exist to help define better class or to use them more conveniently.

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 \(d(284) = 220\).