Verify that \(2620,2924\) and \(17296,18416\) are amicable pairs.

Classify the integers \(2, 3, \ldots, 21\) as abundant, deficient, or perfect.

If \(\sigma(n)=kn\), then \(n\) is called a \(k\)-perfect number. Verify that \(672\) is \(3\)-perfect and \(2178540=2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19\) is \(4\)-perfect.

Show that no number of the form \(2^a3^b\) is \(3\)-perfect.

Show that all even perfect numbers end in \(6\) or \(8\).

If \(n\) is an even perfect number and \(n > 6\), show that the sum of its digits is congruent to \(1 \pmod{9}\).