  The number of tuples with positive integers pairwise relatively prime to each
other with product at most $n$ is considered. A generalization of $\mu^{2}$
where $\mu$ is the M\"{o}bius function is used to formulate this divisor sum
and establish some identities. One such identity is a weighted sum of
reciprocal of square-free numbers not exceeding $n$. Some auxiliary number
theoretic functions are introduced to formulate this sum.
