Mathematics Question from JEE Main 2023 · 12 April, Shift 1

Let $\langle a_n \rangle$ be a sequence such that $a_1 + a_2 + \dots + a_n = \frac{n^2 + 3n}{(n+1)(n+2)}$. If

$$28\sum_{k=1}^{10} \frac{1}{a_k} = p_1p_2p_3 \dots p_m$$

where $p_1, p_2, \dots, p_m$ are the first $m$ prime numbers, then $m$ is equal to: