Sum of Dirichlet's Character Over Divisors of Natural Number

Question

It is said in Explanation for a theorem pertaining on Dirichlet character sums it is well-known that $A\left(n\right)=\sum_{d\mid n}\chi\left(d\right)$ is non-negative for $\chi$ is character modulo $k$, and $\geq 1$ when $n$ is square-free. Where can I find the proof for this fact?

Answer 1

The proof of this result is available in chapter 6 of Apostol's Introduction to Analytic Number Theory. In the book, the result is labeled as Theorem 6.19.