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# Abundant number

## Definition of the noun Abundant number

What does Abundant number mean as a name of something?

noun

1. [number theory] A number that is less than the sum of all of its divisors except itself.

## Explanation

Abundant number: In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4, for example.

• also known as 过剩数

## Printed dictionaries and other books with definitions for Abundant number

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### The Kingdom of Infinite Number (2001)

A Field Guide by Bryan Bunch

FIELD MARKS An abundant number is a whole number for which the sum of its divisors, not including the number itself, is greater than the number. The lowest abundant number is 12, since its proper divisors (excluding itself) are 1, 2, 3, 4, and ...

### How to Think About Analysis (2014)

by Lara Alcock

Definition: An abundant number is a positive integer n whose divisors add up to more than .

### CRC Concise Encyclopedia of Mathematics, Second Edition (2002)

by Eric W. Weisstein

See also ABUNDANCE, ABUNDANT NUMBER References Guy, R. K. "The Second Strong Law of Small Numbers." Math. Mag. 63, 3Á/0, 1990. Abundant Number An abundant number is an INTEGER n which is not a PERFECT NUMBER and ...

### The Mathematics of Egypt, Mesopotamia, China, India, and Islam (2007)

A Sourcebook by Victor J. Katz, Annette Imhausen

The two kinds related to the perfect number are the abundant number and the deficient number. The abundant number is a number such ...

### Math Dictionary for Kids (2006)

The Essential Guide to Math Terms, Strategies, and Tables by Theresa R. Fitzgerald

Example: |+3| = 3 and |-3| = 3 Abundant Number A ...

### The Penguin Dictionary of Curious and Interesting Numbers (1997)

by David Wells

The numbers of spheres that can touch one sphere in higher dimensions up to dimension 9 are: Abundant numbers 12 is the first abundant number, meaning that it is less than the sum of its factors excluding itself: 1 + 2 + 3 + 4 + 6 = 16.

### Mathematics Illustrated Dictionary (2003)

Facts, Figures, and People by Jeanne Bendick

absolute value 15 abundant number or excessive number Larger measures use the mks (meter, kilogram, and second) system. absolute value. The absolute value of a number, whether it is positive or negative, is always positive. For example ...

### Encyclopaedia Britannica; Or A Dictionary of Arts, Sciences, and Miscellaneous Literature (1823)

IMPERFEct Number, is that whose aliquot parts, taken all together, do not make a sum that is equal to the number itself, but either exceed it, or fall short of it; being an abundant number in the former case, and a defective number in the latter.

### Dictionary of Phrase and Fable (1900)

Giving the Derivation, Source, Or Origin of Common Phrases, Allusions, and Words that Have a Tale to Tell by Ebenezer Cobham Brewer

Abundant Number (An}. A number such that the «um of all its divisors (except itself) is greater than the number itself.

### Encyclopaedia of the History of Science, Technology, and Medicine in Non-Westen Cultures (2013)

by Helaine Selin

every even-times-even number has factors less than itself, • the first abundant number is 12, and the first odd one in this class is 945; and • if 2" S is a perfect number, then 2" S is an abundant number, and 2" S is a deficient number.

### Encyclopaedia Perthensis, Or, Universal Dictionary of the Arts, Sciences, Literature, Etc (1816)

Intended to Supersede the Use of Other Books of Reference

An abundant number is opposed to a deficient number, or that which is greater than all its aliquot parts taken together; as 14, whose aliquot parts are, 1, 2, and 7 , which make no more than 10: and to a perfä number, or one to which its aliquot ...

### The Century Dictionary and Cyclopedia: The Century dictionary ... prepared under the superintendence of William Dwight Whitney ... rev. & enl. under the superintendence of Benjamin E. Smith (1911)

Abundant number, in arith., a number the sum of whose aliquot parts exceeds the number itself. Thus, 12 is an abundant number, for the sum of its aliquot parts (1 + 2 + 3 + 4 +6) is 16. It is thus distinguished ...

### The Encyclopedia of Eastern Orthodox Christianity, 2 Volume Set (2010)

by John Anthony McGuckin

The church is renowned for sending out an abundant number of priests to ...

### Encyclopaedia Metropolitana: Miscellaneous and lexicographical (1845)

by Edward Smedley, Hugh James Rose, Henry John Rose

ABUNDANT NUMBER, a number, the sum of whose aliquot parts exceeds the number itself. Thus 18 is an abundant number because 1, 2, 3, 6, and 9, its aliquot parts, are 21, or greater than that number. When the aliquot parts of any number ...

### Encyclopædia metropolitana; or, Universal dictionary of knowledge, ed. by E. Smedley, Hugh J. Rose and Henry J. Rose. [With] Plates (1845)

by Edward Smedley

ABUNDANT number, a number, the sum of whose aliquot parts exceeds the number itsejf. Thus 18 is an abundant number because 1, 2, 3, 6, and 9, its aliquot parts, are 31, or greater than that number. When the aliquot parts of any number ...

### Encyclopaedia Metropolitana; Or, Universal Dictionary of Knowledge on an Original Plan Comprising the Twofold Advantage of a Philosophical and an Alphabetical Arrangement, with Appropriate Engravings Edited by Edward Smedley, Hugh James Rose, Henry John Rose (1845)

Miscellaneous and lexicographical, vol. 1

Thus l8 is an Abundant Number, because 1, 2, 3, 6. and 9, its aliquot parts, are 21, or greater than that number. When the aliquot parts of any number are ...

### The Mathematics Dictionary (1992)

by R.C. James, Glenn James

abundant number. See NUMBER — perfect number. Acceleration Accumulation AC-CEL'ER-A'TION, n. The time rate of change of.

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