Mark writes the expression $\sqrt{d}$ for each positive divisor $d$ of $8!$ on the board. Rishabh simplifies each expression to the form $a \sqrt{b}$, where $a$ and $b$ are integers such that $b$ is not divisible by the square of a prime number. For example, $\sqrt{20}$, $\sqrt{16}$, and $\sqrt{6}$ simplify to $2\sqrt{5}$, $4\sqrt{1}$, and $1\sqrt{6}$, respectively. Compute the sum of $a+b$ across all expressions that Rishabh writes.

Let's think step by step and output the final answer within \boxed{}.
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