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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 Numbers & Factoring  Number Names: Abundant, Deficient, Perfect! In this video we define "Abundant", "Deficient", and "Perfect" numbers: the Goldilocks of Mathematics!  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 ...  UK's number 1 deficient vitamin.  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...  Dr. Oz The 1# Deficiency Leading To A Number Of Diseases! http://www.sgn80.com/shop/blueicefermentedcodliveroil120caps.html The Best Vitamin D Alternative. Blue Ice Fermented Cod Liver Oil surpasses every oth...  abundant, deficient, and perfect numbers  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 Goodnessme.ca: ... 

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.
 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 ...
 
Main Line
Fri, 18 Jul 2014 04:24:42 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 ...
 
Times of India
Thu, 18 Dec 2014 23:30:00 0800
THIRUVANANTHAPURAM: The special squad formed by the district collector to take action against the commercial establishments, which made alterations in their building plan so as to convert their parking space into commercial areas, will begin inspection ...
 
GeekDad (blog)
Tue, 15 Apr 2014 03:06:01 0700
The 10th lowest perfect number has over 50 digits, and the 16th lowest over 1000 digits. If a number is greater than the sum of its proper divisors, it is a Deficient Number. Most odd numbers are Deficient, as are all the prime numbers. The first few ...
 
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 ...
 New York Daily News 
New York Daily News
Fri, 02 Aug 2013 17:28:37 0700
When it comes to improving its infrastructure, America seems to be on a bridge to nowhere. One out of every nine bridges in the United States—a grand total of 66,503 bridges altogether—has been found to have one or more significant defects, according ...

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