Let d(<var>n</var>) be defined as the sum of proper divisors of <var>n</var> (numbers less than <var>n</var> which divide evenly into <var>n</var>).
If d(<var>a</var>) = <var>b</var> and d(<var>b</var>) = <var>a</var>, where <var>a</var> ≠ <var>b</var>, then <var>a</var> and <var>b</var> are an amicable pair and each of <var>a</var> and <var>b</var> are called amicable numbers.
For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
Evaluate the sum of all the amicable numbers under <var>n</var>.