In mathematics, a colossally abundant number (sometimes abbreviated as CA) is a natural number that, in a particular rigorous sense, has many divisors. Formally, a number n is colossally abundant if and only if there is an ε > 0 such that for all k > 1,
where σ denotes the sum-of-divisors function. The first few colossally abundant numbers are 2, 6, 12, 60, 120, 360, 2520, 5040, ... (sequence A004490 in OEIS); all colossally abundant numbers are also superabundant numbers, but the converse is not true.
Read more about Colossally Abundant Number: History, Properties, Relation To The Riemann Hypothesis
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 (18171862)
“While I do not suggest that humanity will ever be able to dispense with its martyrs, I cannot avoid the suspicion that with a little more thought and a little less belief their number may be substantially reduced.”
—J.B.S. (John Burdon Sanderson)