digplanet beta 1: Athena
Share digplanet:

Agriculture

Applied sciences

Arts

Belief

Chronology

Culture

Education

Environment

Geography

Health

History

Humanities

Language

Law

Life

Mathematics

Nature

People

Politics

Science

Society

Technology

In number theory, a deficient number or defective 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

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

• 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

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).

## References

1. ^ Sándor et al (2006) p.108
 15036 videos foundNext >
 Deficient, Abundant and Perfect NumbersProduced as an assignment for EDUC 220. Perfect Number Generatorhttp://demonstrations.wolfram.com/PerfectNumberGenerator The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new e... abundant, deficient, and perfect numbers Ishihara's Test For Colour Deficiency - 24 Plates Edition Building Collapse: 36 Deficient Buildings Reported in Lagos - NEMAThe spokesperson for the National Emergency Management Agency (NEMA), south west zone; Mr. Ibrahim Farinloye has confirmed to Channels Television that about ... Recovering from my Vitamin D DeficiencyHow I recovered from my Vitamin D deficiency, how long it took, supplementing, etc. For more info on how to recover, visit the group I formed to share info: ... abundant, deficient or perfect A number of garages in Devon found to carry out 'seriously deficient' work on cars. How to Prevent Painful Muscle Cramps, Spasms, & Magnesium Deficiency While Intermittent Fasting!How to Prevent Painful Muscle Cramps, Spasms, & Magnesium Deficiency While Intermittent Fasting! In this video, the Low Carb Legend shares with you one of th... Hundreds of bridges classified deficient in central PAOriginal 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...
 15036 videos foundNext >
 2 news items
 GeekDad Puzzle of the Week Solution – Excessive Sums GeekDad (blog) Tue, 15 Apr 2014 02:56:15 -0700 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 Deficient Numbers are 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, and 17. If a number ... GeekDad Puzzle of the Week – Excessive Sums GeekDad (blog) Wed, 09 Apr 2014 03:09:39 -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 ...
 Limit to books that you can completely read online Include partial books (book previews) .gsc-branding { display:block; }

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!