digplanet beta 1: Athena
Share digplanet:


Applied sciences






















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, … (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.


  • 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]


  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.
10267 videos foundNext > 

Deficient, Abundant and Perfect Numbers

Produced as an assignment for EDUC 220.

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 led to a large number of bridges...

A number of garages in Devon found to carry out 'seriously deficient' work on cars.

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...

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

Hidden Signs of Protein Deficiency

http://lifespa.com/ProteinDeficiency http://lifespa.com/Newsletter http://lifespa.com/3seasondiet Every winter I find myself treating an inordinate number of...

"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...

Hundreds of bridges classified deficient in central PA

Original Air Date: 2/7/14 By Melanie Gillespie It's more than likely you drive over at least one bridge, if not more, a day. Pennsylvania has many of them wh...

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...

10267 videos foundNext > 

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


Oops, we seem to be having trouble contacting Twitter

Talk About Deficient number

You can talk about Deficient number with people all over the world in our discussions.

Support Wikipedia

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