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In number theory, a deficient or deficient number is a number n for which the sum of divisors σ(n)<2n, or, equivalently, the sum of proper divisors (or aliquot sum) s(n)<n. The value 2n − σ(n) (or n − s(n)) is called the number's deficiency.
Examples[edit]
The first few deficient numbers are:
 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, … (sequence A005100 in OEIS)
As an example, consider the number 21. Its divisors are 1, 3, 7 and 21, and their sum is 32. Because 32 is less than 2 × 21, the number 21 is deficient. Its deficiency is 2 × 21 − 32 = 10.
Properties[edit]
 An infinite number of both even and odd deficient numbers exist
 All odd numbers with one or two distinct prime factors are deficient
 All proper divisors of deficient or perfect numbers are deficient.
 There exists at least one deficient number in the interval for all sufficiently large n.^{[1]}
Related concepts[edit]
Closely related to deficient numbers are perfect numbers with σ(n) = 2n, and abundant numbers with σ(n) > 2n. The natural numbers were first classified as either deficient, perfect or abundant by Nicomachus in his Introductio Arithmetica (circa 100).
See also[edit]
References[edit]
 ^ Sándor et al (2006) p.108
External links[edit]
Divisibilitybased sets of integers


Overview 



Factorization forms 


Constrained divisor sums 


With many divisors 


Aliquot sequencerelated 


Other sets 


Deficient, Abundant and Perfect Numbers Produced as an assignment for EDUC 220.  Deficient number Meaning and Pronunciation Deficient number Meaning and Pronunciation. A number that greater than the sum of all of its divisors except itself.. deficient number synonyms: defective nu...  Number Names: Abundant, Deficient, Perfect! In this video we define "Abundant", "Deficient", and "Perfect" numbers: the Goldilocks of Mathematics!  Deficient Numbers & Factoring  Number Type Vocabulary.mp4 Attached: Number Type Vocabulary.mp4 Sent using Google Docs http://docs.google.com/ Goes over the following Vocabularies: Prime Number Composite number Squar...  Structurally Deficient Bridges North Carolina continues to struggle with a growing number of aging and deteriorating bridges, while funding to fix and repair them hasn't kept pace. That's ...  Magnesium  Are you deficient? Magnesium is the number 1 deficiency in North America. Are you deficient too? Learn the symptoms and how to overcome this deficiency. Find Magnesium at Goodn...  Why all of a sudden is everyone deficient in vitamin D? http://drberg.com/bodytypequiz?source=youtube For more information about Dr. Berg's 3day intensive program in Alexandria, Virginia, call 7033547336. htt...  abundant, deficient, and perfect numbers  Vitamin B12 Deficiency Symptoms  10 Signs you could be Deficient and the Consequences! http://utahtexans.com/ Click on the link above for a free report to choosing supplements for better health. Almost 40% of the population just in the U.S. is ... 

The PatriotNews  PennLive.com
Mon, 22 Sep 2014 13:53:48 0700
"It's going to knock down this structurally deficient number that we've had hanging over our heads for a long time." Work on the bridge replacements is expected to begin next year and 99 percent of the 558 bridges are to be finished by August 31, 2018.
 
Main Line
Mon, 21 Jul 2014 04:09:52 0700
“We've made great strides in reducing that structurally deficient number in the last few years,” she said. “That doesn't mean that each one is going to fall into the water tomorrow,” said Rapoport. “It could be that a couple of them do, similar to that ...
 Hurriyet Daily News 
Hurriyet Daily News
Thu, 11 Sep 2014 02:22:50 0700
This, sadly, is a deficient number,” Aslan said. “According to the data from the ministry, 22,000 people chose Kurdish as an elective course this year across Turkey. There will be one Kurdish teacher for every 1,100 students if only 20 teachers are ...
 
GeekDad (blog)
Tue, 15 Apr 2014 03:06:01 0700
In the field of Number Theory, you can classify a given counting number based on how it compares to the sum of its proper divisors. If a number is exactly equal to the sum of its proper divisors, it is a Perfect Number. These are the least common, and ...
 
Arkansas News
Mon, 21 Jul 2014 17:00:00 0700
Give Arkansas a Raise, a group seeking to place on the ballot a proposed initiated act to raise the state minimum wage, also submitted signatures to Martin's office on July 7 and also has been given 30 days to make up for a deficient number of valid ...
 
Times of India
Fri, 17 Oct 2014 13:29:15 0700
The fee is stringent when it comes to parking. An amount of Rs 5 lakh is levied as regularization fee for every deficient number. "This is one factor which every builder has to keep in mind while applying for levying parking fee. If the building has ...
 
Edison Sentinel
Tue, 18 Mar 2014 07:55:07 0700
Grygiel said the variances needed for the project — for the deficient number and size of parking spaces, the size of the front yard setback, the building height and several waivers — will not outweigh its positives. “This is a textbook example of ...
 New York Daily News 
New York Daily News
Fri, 02 Aug 2013 17:28:37 0700
One in nine U.S. bridges are structurally deficient, but few Washington politicians seem willing to confront the problem. BY David Knowles. NEW YORK DAILY NEWS. Published: Friday, August 2, 2013, 8:26 PM. Updated: Friday, August 2, 2013, 8:26 PM.

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