The sequence $\{a_n\}$ is defined as follows: $a_1$ is a positive rational number, $a_n= \frac{p_n}{q_n}$, ($n= 1,2,…$) is a positive integer, where $p_n$ and $q_n$ are positive integers that are relatively prime, then $a_{n+1} = \frac{p_n^2+2015}{p_nq_n}$ Is there a$_1>2015$, making the sequence $\{a_n\}$ a bounded sequence? Justify your conclusion.