How to sort array by divisor sum faster?
Many elements of this code can be much faster.

Calculating the sum of divisors will be faster if you:


Iterate until sqrt(number) instead of number / 2, and include divisor pairs (i and number / i)
Change the type of number from double to int


(See also my review of your related question.)

Use a faster sorting algorithm, for example quicksort or merge sort.
And when you, avoid mistakes like if(( divisorSum( array[ i ]) &gt; divisorSum( array[ j ])) || (( divisorSum( array[ i ] ) == divisorSum( array[ j ])) &amp;&amp; ( array[ i ] &gt; array[ j ]))), which recomputes the sum of divisors twice for array[i] and array[j].
You could store the results of expensive operations in a variable,
and then you can use that variable multiple times in conditions.