Sum divides product?

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

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.

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