Diophantine equation with factorial

[Hans Havermann]

> %S A000001 1 2 6 3 5
> %N A000001 Least number of positive cubes needed to represent n!.

Hope I did this right...

1, 2, 6, 3, 5, 8, 4, 4, 6, 6, 5, 7, 5, 8, 9, 7, 12, 10, 9, 9, 10, 9, 8, 
10, 12, 8, 10, 8, 10, 10, 12, 10, 14, 11, 10, 13, 10, 11, 13, 13, 10, 
12, 14, 12, 13, 19, 16, 19, 15, 16, 18, 16, 17, 14, 11, 15, 10, 13, 16, 
13, 14, 16, 14, 14, 20, 10, 18, 19, 13, 17, 20, 19, 19, 20, 16, 14, 17, 
15, 16, 16, 19, 20, 15, 15, 14, 19, 17, 20, 12, 17, 20, 18, 18, 15, 17, 
14, 16, 15, 14, 14, 16, 14, 16, 22, 18, 13, 16, 17, 17, 12, 18, 19, 14, 
21, 17, 15, 13, 18, 17, 15, 19, 19, 17, 17, 22, 16, 16, 12, 15, 17, 16, 
18, 14, 22, 18, 17, 13, 23, 22, 17, 17, 16, 15, 15, 19, 15, 19, 15, 16, 
22, 16, 15, 20, 19, 15, 18, 16, 18, 19, 21, 16, 16, 21, 21, 22, 23, 13, 
20, 15, 16, 15, 20, 22, 15, 15, 17, 19, 16, 14, 18, 15, 20, 15, 20, 19, 
15, 15, 15, 15, 23, 19, 22, 21, 21, 16, 22, 17, 17, 15, 18, ...