Let $\left\langle a_n\right\rangle$ 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
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