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.
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.
Performance improvements:
1) Eliminate doubleness by limit the search to a > b.2) Search dividers until sqrt(n). Boost 489 ms -> 3,6 ms.
Problem21 = 31626 elapsed time: 3 ms. Test Passed.
