# Perfect Number Generator

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A deficient number is a number that is greater than the sum of its proper divisors, a perfect number is equal to the sum of its proper divisors, and an abundant number is less than the sum of its proper divisors. For example, , so the proper divisors of are , , , , ; because , is a perfect number. Letting be the sum of the proper divisors of , the points plotted are , so blue dots fall above deficient numbers, red dots under abundant numbers, and large black dots on perfect numbers.

Contributed by: Osman Tuna Gökgöz (January 2010)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

[1] R. Fitzpatrick, "Proposition 22," *Euclid's Elements in Greek: Vol. II: Books 5–9*, 2005 p. 207.

## Permanent Citation

"Perfect Number Generator"

http://demonstrations.wolfram.com/PerfectNumberGenerator/

Wolfram Demonstrations Project

Published: January 14 2010