abundant number en · NOUN
Pronunciation
- /əˈbn̩.dn̩t ˈnʌm.bɚ/ (US)
- (US) audio
- /əˈbʌn.dn̩t ˈnʌm.bɚ/ (US)
- /əˈbʌn.dn̩t ˈnʌm.bə/ (Received-Pronunciation)
Meanings
-
A number that is less than the sum of its proper divisors (all divisors except the number itself).
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.
1996, Richard R. Hall, Sets of Multiples, Cambridge University Press, page xi: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.
It has been shown that the largest odd number which cannot be written as the sum of two abundant numbers is 20161.
1970, Geometric Transformations III, Random House, page 128:1992, 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?
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| abundant numbers | Number=Plur | lexicographic |
Deriveds
extremely abundant number · superabundant number · highly abundant number
Hyponyms
Relateds
abundancy index · abundance · sociable number · amicable number · deficient number · perfect number · semiperfect number
Synonyms
Translations (15)
it numero abbondante (number that is less than the sum of its proper divisors) · ja 過剰数 (number that is less than the sum of its proper divisors) · ko 과잉수 (number that is less than the sum of its proper divisors) · es número abundante (number that is less than the sum of its proper divisors) · cmn 豐數 /丰数 (number that is less than the sum of its proper divisors) · pl liczba nadmiarowa (number that is less than the sum of its proper divisors) · cmn 過剩數 /过剩数 (number that is less than the sum of its proper divisors) · cmn 盈數 /盈数 (number that is less than the sum of its proper divisors) · sv rikt tal (number that is less than the sum of its proper divisors) · pl liczba nadmierna (number that is less than the sum of its proper divisors) · fr nombre abondant (number that is less than the sum of its proper divisors) · sv ymnigt tal (number that is less than the sum of its proper divisors) · sk abundantné čislo (number that is less than the sum of its proper divisors) · fi runsas luku (number that is less than the sum of its proper divisors) · la numerus superfluus (number that is less than the sum of its proper divisors)