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{
\bf  Quiz \# 8 for Dr. Z.'s Number Theory
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{\bf NAME:} (print!) $\underline
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{\bf E-MAIL ADDRESS:} (print!) 
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{\bf 1.} (i) (2 pts.) Define $\sigma_2(n)$ (ii) (2 pts.) State the formula for $\sigma_2(n)$
in terms of the expression of $n$ as a product of prime powers
(iii) (2 pts.) Verify it for $n=15$ by using the definition and the formula

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{\bf 2.} (4 pts.) Prove that if $p$ is a prime, and $2^p-1$ is also a prime, then
$$
2^{p-1} \cdot (2^p -1) \quad 
$$
is a perfect number.

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