I didn't realize we were going beyond simple brute force.
20 minutes of coding later calculates up to the 4480 factor value in less than 2 seconds (on a slow machine).
This takes less than 45 seconds.
Code:
  Limit    Index          Number Factors
>= 1000    41040       842161320    1024
>= 2000   313599     49172323200    2304
>= 3000   453375    102774672000    3072
>= 4000  1890944   1787835551040    4480
>= 5000  2203200   2427046221600    5760
>= 6000  2756159   3798207594720    6144
>= 7000  7289919  26571463158240    7680
>= 8000 10497024  55093761676800    8640
>= 9000 11851839  70233049766880    9216
>=10000 14753024 108825865948800   13824
But I guess code is secret now.