Hi everyone,

I'm stuck on these two problems on multiplicative functions. I've tried numerous things but I haven't found anything that works so far. Can anyone help?

1. Prove that if $\displaystyle n=p^a q^b$ where q,p are prime and a,b larger than or equal to 1, then $\displaystyle \sigma(n) <2n$.

2. Prove that

$\displaystyle \sum _{d|n} \frac{\mu^2 (d)}{\phi(d)} = \frac{n}{\phi (n)}$

Here the sigma function is the sum of the divisors, phi is the euler phi function.