Diophantine Equations Won't Work Here!

Determine the sum of all unique integer solutions of $n$ for the following congruence: $\dbinom{n}{\left\lceil \frac{n}{2} \right\rceil} \equiv 0 \bmod n$ where $2 \leq n \leq 25$ .

Note: Before you answer this problem, take a look at the following problem . This should help us understand the pattern of $n$ 's.