Question 120
For any positive integer $n$, let $f(n)$ be the number of ordered triples $(a, b, c)$ of positive integers such that
- $\max (a, b, c)$ divides $n$ and
- $\operatorname{gcd}(a, b, c)=1$.
Compute $f(1)+f(2)+\cdots+f(100)$.
- $\max (a, b, c)$ divides $n$ and
- $\operatorname{gcd}(a, b, c)=1$.
Compute $f(1)+f(2)+\cdots+f(100)$.