digplanet beta 1: Athena
Share digplanet:


Applied sciences






















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.


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.


  • 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]


  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.


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