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 $a\ne b$, 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 $1,2,4,5,10,11,20,22,44,55$ 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 $10000$.