Arithmetical Functions Sum, $\sum\limits_{d|n}\sigma(d)\phi(\frac{n}{d})$ and $\sum\limits_{d|n}\tau(d)\phi(\frac{n}{d})$ $$\sum_{d|n}\sigma(d)\phi\left(\frac{n}{d}\right)=n\tau(n)
,\\ \sum_{d|n}\tau(d)\phi\left(\frac{n}{d}\right)=\sigma(n)$$
The problem (7.4.15) of Burton's Elementary Number Theory has been request to prove the above equalities. In this book Dirichlet multiplication or Riemann's zeta function isn't expressed before this problem. In addition, I know that the first time, Pillai has been proved this equalities but I couldn't find the Pillai's paper on the web. Can you please refer me to a link of Pillai's paper? or give me a proof without the use of Dirichlet multiplication or Riemann's zeta function?

Prove that both sides are multiplicative functions and that they coincide when $n$ is a prime power.
