Sum divides product?

Number Theory Level 5

$\large \prod_{j=1}^n j \not \equiv 0 \quad \left ( \text{mod} \ \sum_{j=1}^n j \right)$

For how many integers $n$ satisfying $1 \le n \le 180$ is the non-congruence above fulfilled?

You may use this List of Primes as a reference.