# Find all $n$ such $\sigma(n) = 546$

Find all $n$ such $\sigma(n) = 546$. I find $n = 180$ is an answer. But I know there is more. I tried to used the formula $$\sigma(n) = \frac{{p_1}^{a_1 + 1} - 1}{p_1 - 1} \ldots \frac{{p_k}^{a_k + 1} - 1}{p_k - 1}.$$ But I got stuck to make a way to find the other $n$'s.

Hint: We find that $n\in \{180, 234, 362, 369\}$. For the proof, see here, and similar questions, e.g., this MSE-question. Also the question about $\sigma(n)=165$ has helpful answers.