Birthday Special #3 Aditya Raut

For positive integers aa, bb, and cc, define f(a,b,c)=abcgcd(a,b,c)lcm(a,b,c). f(a,b,c)=\frac{abc}{\text{gcd}(a,b,c)\cdot\text{lcm}(a,b,c)}. We say that a positive integer nn is f(λ)f(\lambda) if there exist x,y,z60x,y,z\leq60that satisfy f(x,y,z)=nf(x,y,z)=n. How many f(λ)f(\lambda) integers are there?


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