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
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:
The factors required for these divisors:
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