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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Highly abundant number - Wikipedia, the free encyclopedia
In mathematics, a highly abundant number is a natural number where the sum of its divisors (including itself) is greater than the sum of the divisors of any natural number less than it. Highly abund...
en.wikipedia.org/wiki/Highly_abundant_number
Welcome to the Prime Glossary: a collection of definitions, information and facts all related to prime numbers. This pages contains the entry titled 'abundant number.' Come explore a new prime term today! ... There are infinitely many abundant numbers, both even (e.g., every multiple of 12) and odd (e.g.,
primes.utm.edu/glossary/page.php?sort=AbundantNumber primes.utm.edu/glossary/page.php?sort=AbundantNumber
Write an F program to search for abundant numbers. An abundant number is defined as a positive integer whose proper divisors sum to a value greater than the number itself. For instance, 12 is an abundant number since 1+2+3+4+6=16 > 12. On the other hand, 6 is not abundant since 1+2+3=6.
www.dsm.fordham.edu/~moniot/Classes/CompPhysicsF02/abun... www.dsm.fordham.edu/~moniot/Classes/CompPhysicsF02/abundant-numbers-prog.html
Any multiple of a perfect number or an abundant number is also abundant. Every number greater than 20161 can be expressed as a sum of two abundant numbers. ...
mathworld.wolfram.com/AbundantNumber.html mathworld.wolfram.com/AbundantNumber.html
Classify the numbers 28, 50, 120 and 4173 as being abundant, deficient, or perfect. You might find the Prime Factorization Calculator helpful. ... Are prime numbers abundant, deficient or perfect? ... 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
Attachments: theorem on multiples of abundant numbers (Theorem) by CompositeFan; abundance (Definition) by CompositeFan; quasiperfect number (Definition) by CompositeFan; every even integer greater than 46 is the sum of two abundant numbers (Theorem) by PrimeFan; positive multiple of an abundant number is abundant...
planetmath.org/encyclopedia/AbundantNumber.html planetmath.org/encyclopedia/AbundantNumber.html
Theorem. The product $nm$ of an abundant number $n$ and any integer $m > 0$ is also an abundant number, regardless of the abundance or deficiency of $m$ . ... Choose an abundant number $n$ with $k$ divisors $d_1, \ldots ,d_k$ (where the divisors are sorted in ascending order and $d_1 = 1$ , $d_k = n$ ) that add up to $2n +
planetmath.org/encyclopedia/TheoremOnMultiplesOfAbundan... planetmath.org/encyclopedia/TheoremOnMultiplesOfAbundantNumbers.html
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. The 8000th is 19826562430675.
www.primepuzzles.net/puzzles/puzz_329.htm
Thus, this study demonstrates that senescent CD8 T cells are induced in abundant numbers during viral infections in vivo. ... Viral Infections Induce Abundant Numbers of Senescent CD8 T Cells1...
www.jimmunol.org/cgi/content/full/167/9/4838
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