Assuming n is an integer (why else would you ask for it?) we can narrow it down rather quickly.
Clearly n>133
A simple upper bound is 133*4^(1/5) < 133*1.5 < 200
(I could probably do better but this is fine.)
So 133<n<200
Now to check factors.
I'll spare the details but using modular arithmetic one can easily show 2, 4, 8, 16 are factors but not 32.
3 and 9 are both factors but not 27.
There's only one number in the interval that is a factor of both 16 and 9: 16*9 = 144.
I'll admit I then used a calculator to prove this works (though it's not hard to do by hand, just tedious). Both sides equal
61917364224. So the assumption n is an integer was correct.
Edited on January 7, 2013, 12:53 pm

Posted by Jer
on 20130106 19:04:30 