The Zen Way

Number Theory Level 4

\[ \large \frac{1}{x}+\frac{1}{y}=\frac{1}{n}\]

Let \( S(n)\) denote the number of ordered pairs \( (x,y)\) satisfying the equation above for natural numbers \(x,y,n\) with \(n>1\). Find the value of \(S(6) \).