superabundant number
superabundant number noun: a positive integer whose abundancy index is greater than that of any lesser positive integer.
Noun
superabundant number (plural superabundant numbers)
- A positive integer whose abundancy index is greater than that of any lesser positive integer.
- The authors prove a theorem: If Q(X) is the number of superabundant numbers ≦X, then for c<5/48,Q(X)≧( log X)¹⁺ᶜ for sufficiently large X.1984, Richard K. Guy (editor), Reviews in Number Theory 1973-83, Volume 4, Part 1, As printed in Mathematical Reviews, American Mathematical Society, page 173
- 1) A number n is called superabundant if (σ(n))/n>(σ(m))/m for all m with 1Corollary. Q(x)>c log x log log x/( log log log x)².1995, József Sándor, Dragoslav S. Mitrinović, Borislav Crstici, Handbook of Number Theory I, Springer, page 111
- Synonyms:
- SA, superior highly composite number
- Used other than figuratively or idiomatically: see superabundant, number.
Synonyms of superabundant number
Forms of superabundant number
| plural | superabundant numbers |
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Questions about superabundant number
- What does superabundant number mean?
- Superabundant number means a positive integer whose abundancy index is greater than that of any lesser positive integer.
- What part of speech is superabundant number?
- Superabundant number is a noun.
- What is the plural of superabundant number?
- The plural of superabundant number is superabundant numbers.
Words near superabundant number in the dictionary
Source and license
Adapted from Wiktionary: superabundant number (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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