Let \(a_n\) be a sequence such that \(a_1+a_2+\ldots+a_n\) \(=\frac{n^2+3 n}{(n+1)(n+2)}\). If \(28 \sum_{k=1}^{10} \fra…

Let \(a_n\) be a sequence such that \(a_1+a_2+\ldots+a_n\) \(=\frac{n^2+3 n}{(n+1)(n+2)}\).
If \(28 \sum_{k=1}^{10} \frac{1}{a_k}=p_1 p_2 p_3 \ldots p_m\), where \(p_1, p_2, \ldots, p_m\) are the first \(m\) prime numbers, then \(m\) is equal to

[JEE Main 2023, 12 Apr (Shift 1)]