Perfect Number/Examples/28

Example of Perfect Number

$28$ is a perfect number:

$1 + 2 + 4 + 7 + 14 = 28$

Proof

\(\ds 28\)

\(=\)

\(\ds 4 \times 7\)

\(\ds \)

\(=\)

\(\ds 2^{3 - 1} \paren {2^3 - 1}\)

Thus $28$ is in the form $2^{p - 1} \paren {2^p - 1}$.

$2^3 - 1 = 7$ is prime.

So $28$ is perfect by the Theorem of Even Perfect Numbers.

The aliquot parts of $28$ are enumerated at $\sigma_0$ of $28$.

$1, 2, 4, 7, 14$

$\blacksquare$

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): perfect number
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): perfect number