Amicable numbers

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 \( a ≠ b \), 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 \( 10000 \).