The numbers you mention are called highly composite numbers.
This link might be of interest: Highly composite number - Wikipedia, the free encyclopedia
And this link has an algorithm: http://wwwhomes.uni-bielefeld.de/ach...anuscript3.pdf
The number 12 is the smallest number with 6 distinct factors: 1, 2, 3, 4, 6, and 12. Find the smallest number that has 24 distinct factors.
Now, I can do this given some time and trial and error. What I am interested in knowing is if there is a more "constructive" way to do this? I can't seem to think of one.
Thanks!
-Dan
The numbers you mention are called highly composite numbers.
This link might be of interest: Highly composite number - Wikipedia, the free encyclopedia
And this link has an algorithm: http://wwwhomes.uni-bielefeld.de/ach...anuscript3.pdf