Let $\phi(\cdot)$ be the Euler totient function, and let $n=p\_1^{k\_1}\cdots p\_s^{k\_s}$ be the prime factorization of $n\in \mathbb{N}$. The well-known Euler's product formula states that $\phi(n)=n(1-\frac{1}{p\_1})\cdots(1-\frac{1}{p\_s})$. For some fixed positive integer $a\leq n$, let $\phi(n,a)$ denote the number of positive integers which are less than $a$ but coprime to $n$. My question is that whether there is some formula for computing $\phi(n,a)$.



Euler's Totient Function
The formula is given in [this question](https://mathoverflow.net/questions/88777/bound-the-error-in-estimating-a-relative-totient-function), while the answers thereto discuss the accuracy of the obvious approximation (that this is like $a \phi(n)/n.$)


