Perfect Number Generator
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.
 R. Fitzpatrick, "Proposition 22," Euclid's Elements in Greek: Vol. II: Books 5–9, 2005 p. 207.
"Perfect Number Generator"
Wolfram Demonstrations Project
Published: January 14 2010