i am so nice and cute!

If $m$ has four divisors, then its divisors would be 1, $a$ , $b$ and $ab$ , where $a$ and $b$ are prime. Therefore, the sum of the divisors of $m$ is $1+a+b+ab=(a+1)(b+1)$

If either $a+1$ or $b+1$ are odd, then $a$ or $b$ are even. Therefore, $a+1$ and $b+1$ are even, so $m$ is a multiple of $4$ . The only two numbers from the range $(2010-2019)$ that are multiples of $4$ are $2012$ and $2016$ .

Factoring 2012, we get $2^2 \times 503$ . To make $a+1$ and $b+1$ even, $WLOG$ , we have $a+1=2$ and $b+1=1006$ . However, if $a$ was $1$ , then $a$ is not prime, so $2012$ is not nice .

Factoring $2016$ , we get $2^5\times 3^2 \times 7$ . $WLOG$ , we have $a<b$ .

Testing for the lowest $a$ , we get $a+1=4$ and $b+1=504$ . Therefore, $a=3$ and $b=503$ , so $n=2016$ is nice , with $m=1509$ . Therefore, the answer is $\boxed{1}$

We find that,

2010 = 2 x 3 x 5 x 67 Therefore, 2010 has 6 positive divisors.

2011 is a prime no. Therefore, 2011 has 2 positive divisors.

2012 = 2 x 2 x 503 or 4 x 503 Therefore, 2012 has 5 positive divisors.

2019 = 3 x 673 Therefore, 2019 has 4 positive divisors.

Therefore, the answer is 2019!!!!!!