What is the smallest integer with 100 non trivial factors? Excluding 1 and itself as factors, what is the smallest integer with 100 different factor values? 
Example: 20 has 4 non trivial factors (2*10 and 4*5)

This can be found with OEIS entry A061799, for which $a_n$ is the smallest number with at least $n$ divisors. Your definition excludes 1 and the number itself, so we're looking for $a_{102}$ which is 50400.
Alternatively, use OEIS entry A005179, for which $a_n$ is the smallest number with exactly $n$ divisors. In this case $a_{102}$ is 2949120.
