digplanet beta 1: Athena
Share digplanet:

Agriculture

Applied sciences

Arts

Belief

Business

Chronology

Culture

Education

Environment

Geography

Health

History

Humanities

Language

Law

Life

Mathematics

Nature

People

Politics

Science

Society

Technology

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 [n, n + (\log n)^2] 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]

  1. ^ Sándor et al (2006) p.108

External links[edit]


Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Deficient_number — Please support Wikipedia.
This page uses Creative Commons Licensed content from Wikipedia. A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
8063 videos foundNext > 

Deficient, Abundant and Perfect Numbers

Produced as an assignment for EDUC 220.

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...

Why all of a sudden is everyone deficient in vitamin D?

http://drberg.com/body-type-quiz?source=youtube For more information about Dr. Berg's 3-day intensive program in Alexandria, Virginia, call 703-354-7336. htt...

abundant, deficient, and perfect numbers

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 ...

Dr. Oz The 1# Deficiency Leading To A Number Of Diseases!

http://www.sgn80.com/shop/blue-ice-fermented-cod-liver-oil-120-caps.html The Best Vitamin D Alternative. Blue Ice Fermented Cod Liver Oil surpasses every oth...

Hidden Signs of Protein Deficiency

http://lifespa.com/protein-deficiency-the-hidden-signs/ http://lifespa.com/Newsletter http://lifespa.com/3seasondiet Every winter I find myself treating an i...

Deficient blood test results after 7.5 years Vegan?

I show you my blood tests after 7.5 years on a Vegan diet. ☆ My ebook http://www.30bananasaday.com/Freeleesebook ☆ Follow me on Facebook: http://www.facebook...

6 Warning Signs of Protein Deficiency

Dr. Ching Chen's Website (http://drchingchen.com/) Blog (http://fitlife.tv/6-warning-signs-of-protein-deficiency/) Juice with Drew (http://bit.ly/1t5CD8i) "I...

"Are you Vitamin D deficient?"

Are you Vitamin D deficient?. Vitamin D deficiency is common and the number one way to boost your levels naturally is explained. Matt Cho is a Personal Train...

8063 videos foundNext > 

2 news items

Bemidji Pioneer

Bemidji Pioneer
Sat, 25 Oct 2014 21:33:41 -0700

Although the community sees homeless people in Bemidji on a daily basis, there is still a deficient number of beds in local shelters to house these men, women and children — and it's going to get cold soon. Last October, a group formed with the intent ...
 
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 ...
Loading

Oops, we seem to be having trouble contacting Twitter

Support Wikipedia

A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia. Please add your support for Wikipedia!

Searchlight Group

Digplanet also receives support from Searchlight Group. Visit Searchlight