The Zen Way

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

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

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