# Multiplicative functions

• March 9th 2013, 05:26 AM
Lockdown
Multiplicative functions
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 $n=p^a q^b$ where q,p are prime and a,b larger than or equal to 1, then $\sigma(n) <2n$.
2. Prove that
$\sum _{d|n} \frac{\mu^2 (d)}{\phi(d)} = \frac{n}{\phi (n)}$

Here the sigma function is the sum of the divisors, phi is the euler phi function.
• March 9th 2013, 05:54 AM
Lockdown
Re: Multiplicative functions
Ah nevermind, I solved them