AmicableNumbers.cs

var sumsOfDivisors = from i in Enumerable.Range(1, 10000)
                     select new { Number = (long)i, SumOfDivisors = Toolbox.GetProperDivisors(i).Sum() };

var amicableNumbers = from a in sumsOfDivisors
                      join b in sumsOfDivisors on new { x = a.Number, y = a.SumOfDivisors } equals 
                                                  new { x = b.SumOfDivisors, y = b.Number }
                      where a.Number != b.Number
                      select a.Number;