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:
2^{3}*3^{2}*5*7*11
which has 96 divisors
Adding another factor of 5 gives us 144 divisors.
The resulting number is 2^{3}*3^{2}*5^{2}*7*11 = 138,600.
Perhaps a better solution exists, even yet?

Posted by Mindrod
on 20060220 14:24:52 