%hw17.tex: Homework assignment 17
%%a Plain TeX file by Doron Zeilberger

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\centerline
{
\bf Dr. Z.'s Number Theory Homework assignment 17
}

{\bf 1.} Spell-out the explanation for the important formula for $\sigma(n)$ for $n=50$.

{\bf 2.} Spell-out the explanation for the important formula for $\sigma_3(n)$ for $n=24$.

{\bf 3.} Verify the formulas for $d(n)$, $\sigma_1(n)$, $\sigma_2(n)$ and $\sigma_3(n)$ for
for {\bf a.} $n=10$  {\bf b.} $n=26$  {\bf c.} $n=16$ 

{\bf 4.} Verify the Dirichlet series for $\sigma(n)$ for up to $n=10$

{\bf 5.} Verify the Dirichlet series for $\sigma_3(n)$ for up to $n=5$

{\bf 6.}: State the Lambert series for $\sigma_3(n)$ and verify it through $n=8$

{\bf 7.} (challenge) Using a computer (Maple or otherwise), go towards proving the Riemann Hypothesis
by checking the assertion in Robin's Theorem as far as you can.

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