Find the smallest positive integer n such that n has exactly 144 distinct positive divisors and there are 10 consecutive integers among them (Note: 1 and n are both divisors of n)

(In reply to Slightly improved by Tristan)

We can do better.

I started with another set of 10 consecutive integers with the idea that the integer 12, with its multiple factors would be useful in reducing the final result:

3,4,5,6,7,8,9,10,11,12

The factors required for these divisors:

2³*3²*5*7*11
which has 96 divisors

Adding another factor of 5 gives us 144 divisors.

The resulting number is 2³*3²*5²*7*11 = 138,600.

Perhaps a better solution exists, even yet?

Posted by Mindrod on 2006-02-20 14:24:52