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 between 1 and the input parameter 'max'. The parameter 'max' will be an integer between 1 and 20000. Note that in some cases one or more of the pairs of amicable numbers will be below 'max', while the other one(s) are above 'max'. These still count towards the sum, but only the ones that are below 'max'.