# For how many integers $a$ between $-200$ and $-1$ inclusive is the product of the divisors of $a$ negative?

Recall that an integer $d$ is said to be a divisor of an integer $a$ if $a/d$ is also an integer. For how many integers $a$ between $-200$ and $-1$ inclusive is the product of the divisors of $a$ negative?

I have no idea how to approach this problem. Any helps is greatly appreciated.

The largest one is then $- (14)^2 = -196$, which has factors $-1, -2, -4, -7, -14, -28, -49,-98, -196$ ($9$ numbers)
Therefore, there are $14$ integers.