Exercise (2.1).12

 The sigma function $𝜎 (n)$ in number theory is defined as the sum of positive factors of $n$.

For example,

$$𝜎 (12) = 1 + 2 + 3 + 4 + 6 + 12 = 28$$

Show that for a prime number, $p$, we have $𝜎 (p) = p + 1$.

A prime number $p$ has only two positive factors, 1 and $p$. Therefore the sum is $p+1$.

$$ \sigma(p) = p + 1 $$