# Math Help - Multiplicative Question

1. ## Multiplicative Question

Assume $\sigma$ is multiplicative

a) Let p be a prime and a $\in Z^+$. Prove that for an odd prime p, $\sigma(p^a)$ is odd if, and only f, a is even. Also prove that for p = 2, $\sigma(2^a)$ is odd for all a $\in Z^+.$

b) Let n $\in Z^+$. Prove that $\sigma(n)$ is odd if, and only if, either n is a perfect square or twice a perfect square (i.e. $n \in {(m^2 \mid m \in Z^+)} \cup {(2m^2 \mid m \in Z})$

2. $\sigma(5^2)=6\cdot6=36$ (even)

3. Originally Posted by Also sprach Zarathustra
$\sigma(5^2)=6\cdot6=36$ (even)
Wait, I have to prove that if p is an odd prime, then $\sigma(p^a)$ is odd when a is even. But $\sigma(5^2)$ is even which does not follow....