9772

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.

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DETAILS

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