Birthday Special #3 Aditya Raut

For positive integers \(a\), \(b\), and \(c\), define \[ f(a,b,c)=\frac{abc}{\text{gcd}(a,b,c)\cdot\text{lcm}(a,b,c)}. \] We say that a positive integer \(n\) is \(f(\lambda)\) if there exist \(x,y,z\leq60\)that satisfy \(f(x,y,z)=n\). How many \(f(\lambda)\) integers are there?


(x,y,z) are pairwise distinct positive integers
Happy Birthday Aditya Raut! (9th June)
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