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

Demonstration, with Cuisenaire rods, of the deficiency of the number 8

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, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, ... (sequence A005100 in the 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]

  • Since the aliquot sums of prime numbers equal 1, all prime numbers are deficient.
  • 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]

  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.
20418 videos foundNext > 

Deficient, Abundant and Perfect Numbers

Produced as an assignment for EDUC 220.

Deficient number Meaning

Video shows what deficient number means. A number that greater than the sum of all of its divisors except itself.. deficient number synonyms: defective number.

Deficient Numbers & Factoring

Number Names: Abundant, Deficient, Perfect!

In this video we define "Abundant", "Deficient", and "Perfect" numbers: the Goldilocks of Mathematics!

Perfect, Abundant, Deficient

Created using PowToon -- Free sign up at http://www.powtoon.com/youtube/ -- Create animated videos and animated presentations for free. PowToon is a free ...

abundant, deficient, and perfect numbers

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 ...

Hidden Signs of Protein Deficiency

Read the associated article: http://lifespa.com/protein-deficiency... Sign up for our free weekly video-newlsetter: http://lifespa.com/newlsetter-signup/ Like us on ...

abundant, deficient or perfect

Are YOU Vitamin D Deficient??

O P E N **************** Good Morning Spoonie family! For tons of more info keep reading, you'll find more here below these links. Vitamin D Deficiency ...

20418 videos foundNext > 

We're sorry, but there's no news about "Deficient number" right now.

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