In mathematics, a highly abundant number is a natural number with the property that the sum of its divisors (including itself) is greater than the sum of the divisors of any smaller natural number.
Highly abundant numbers and several similar classes of numbers were first introduced by Pillai (1943), and early work on the subject was done by Alaoglu and Erdős (1944). Alaoglu and Erdős tabulated all highly abundant numbers up to 104, and showed that the number of highly abundant numbers less than any N is at least proportional to log2 N. They also proved that 7200 is the largest powerful highly abundant number, and therefore the largest highly abundant number with odd sum of divisors.
Read more about Highly Abundant Number: Formal Definition and Examples, Relations With Other Sets of Numbers
Famous quotes containing the words highly, abundant and/or number:
“As humans have a prior right to existence over dogs by virtue of being more highly evolved and having a superior consciousness, so women have a prior right to existence over men. The elimination of any male is, therefore, a righteous and good act, an act highly beneficial to women as well as an act of mercy.”
—Valerie Solanas (b. 1940)
“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)
“In a number of other cultures, fathers are not relegated to babysitter status, nor is their ability to be primary nurturers so readily dismissed.... We have evidence that in our own society men can rear and nurture their children competently and that men’s methods, although different from those of women, are imaginative and constructive.”
—Kyle D. Pruett (20th century)