abundant number

Pronunciation Noun

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Pronunciation Noun

**abundant number** (*plural* abundant numbers)

- (
*number theory*) A number that is less than the sum of its proper divisors (all divisors except the number itself).*The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30, and 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42, which is greater than 30, so 30 is an***abundant number**.

**1970**,*Geometric Transformations III*, Random House, page 128 ↗,- It has been shown that the largest odd number which cannot be written as the sum of two
**abundant numbers**is 20161.

- It has been shown that the largest odd number which cannot be written as the sum of two
**1992**, Stanley Rabinowitz (editor),*Index to Mathematical Problems, 1980-1984*, MathPro Press, page 185 ↗,- (a) Let
*k*be fixed. Do there exist sequences of*k*consecutive**abundant numbers**?

- (a) Let
**1996**, Richard R. Hall,*Sets of Multiples*, Cambridge University Press}, page xi ↗,- We shall not be concerned with
**abundant numbers**in this book, nevertheless it may be helpful to use this historical example as an illustration. We note the property that any multiple of an**abundant number**is abundant.

- We shall not be concerned with

- (
*number that is less than the sum of its proper divisors*) excessive number

- French: nombre abondant
- Italian: numero abbondante
- Spanish: número abundante

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.004