Abundant number - Wikipedia, the free encyclopedia
In mathematics, an abundant number or excessive number is a number n for which σ ( n ) > 2 n . Here σ ( n ) is the sum-of-divisors function: the sum of all positive divisors of n , i...
en.wikipedia.org/wiki/Abundant_number
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There are 26 abundant numbers not divisible by 2 or 3 and less than 10^11, from 5391411025 to 97974952075. There are 394 less than 10^12, 4343 less than 10^11 and 8060 less than 2*10^11. ... Regarding your puzzle 329 "Odd abundant numbers not divided by 2 or 3" , It is to inform that there are many many numbers known.
www.primepuzzles.net/puzzles/puzz_329.htm
Theorem 1 There exist infinitely many odd abundant numbers. Table 1 shows all the odd abundant numbers less than 50000. Outcomes of the form ...
www.rowan.edu/open/depts/math/SCHIFFMAN/Odd%20Abundant%... www.rowan.edu/open/depts/math/SCHIFFMAN/Odd%20Abundant%20Numbers.pdf
is sometimes called the Abundance. The first few abundant numbers are 12, 18, 20, 24, 30, 36, ... (Sloane's A005101). Abundant numbers are sometimes called Excessive Numbers. ... There are only 21 abundant numbers less than 100, and they are all Even. The first Odd abundant number is ;
www.math.sdu.edu.cn/mathency/math/a/a039.htm
Numbers can be classified in many ways. They are either even or odd, prime or composite (or 1), they may have more or less than 12 divisors, etc. ... This week for homework, one question you'll consider is whether there are any odd abundant numbers.
www.math.upenn.edu/~deturck/m170/wk4/lecture/properdiv.... www.math.upenn.edu/~deturck/m170/wk4/lecture/properdiv.html
There are infinitely many abundant numbers, both even (e.g., every multiple of 12) and odd (e.g., every odd multiple of 945). Every proper multiple of a perfect number, and every multiple of an abundant number, is abundant (because when n > 1, sigma(n)/n > 1+1/n;
primes.utm.edu/glossary/page.php?sort=AbundantNumber primes.utm.edu/glossary/page.php?sort=AbundantNumber
Abundant numbers are part of a branch of mathematics, called number theory. It is generally agreed upon that Pythagoras (born around 572 B.C.) and his followers started this branch of mathematics. ... According to Pythagorean number lore, odd numbers were thought to be male and even numbers were considered female.
intermath.coe.uga.edu/tweb/gwin1-01/apley/Dictionary/Nu... intermath.coe.uga.edu/tweb/gwin1-01/apley/Dictionary/Number/number.html
DICKSON, L.E., \Finiteness of the Odd Perfect Primitive Abundant Numbers with n Distinct Prime Factors , American J. Math. 35 (1913) 413-422. 4 A. Urquhart has remarked that in order to be complete on this point, it must be shown that ERA 6` Kripke's lemma ! LR decidable. ... ; This paper is cited in the following contexts:
citeseer.ist.psu.edu/context/1805797/0
What are "abundant" numbers? Why would such numbers be called plentiful? ... Not all abundant numbers, however, are even; the first odd abundant number is 945. ... Every multiple of an abundant number is itself abundant, so there is an infinite number of abundant numbers. In 1998, the mathematician Marc Deleglise showed...
www.bookrags.com/research/numbers-abundant-deficient-pe... www.bookrags.com/research/numbers-abundant-deficient-perfect--mmat-03/
In ancient times, the mathematician Nicomachus of Gerasa (60 to 120 A.D.) summed the proper divisors of many numbers (all the divisors except the original number) and discovered they could be categorized into three different classes: 1. Abundant numbers - those with a divisor sum larger than the original number.
www.associatedcontent.com/article/675399/facts_and_curi... www.associatedcontent.com/article/675399/facts_and_curiosities_about_abundant.html
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