In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. 12 has an abundance of 4, for example.
Read more about Abundant Number: Definition, Examples, Properties, Related Concepts
Famous quotes containing the words abundant and/or number:
“There they lived on, those New England people, farmer lives, father and grandfather and great-grandfather, on and on without noise, keeping up tradition, and expecting, beside fair weather and abundant harvests, we did not learn what. They were contented to live, since it was so contrived for them, and where their lines had fallen.”
—Henry David Thoreau (1817–1862)
“[The] elderly and timid single gentleman in Paris ... never drove down the Champs Elysees without expecting an accident, and commonly witnessing one; or found himself in the neighborhood of an official without calculating the chances of a bomb. So long as the rates of progress held good, these bombs would double in force and number every ten years.”
—Henry Brooks Adams (1838–1918)