superabundant number
Word Rarity
Very rare
Frequency: Zipf frequency 1.45 in modern English
28
Scrabble Score
19
Letters
6
Syllables
11
Unique Chars
Meaning
noun
A positive integer whose abundancy index is greater than that of any lesser positive integer.
noun
Used other than figuratively or idiomatically: see superabundant, number.
Example Sentences
- "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, 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."
- "1995, József Sándor, Dragoslav S. Mitrinović, Borislav Crstici, Handbook of Number Theory I, Springer, page 111, 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."
- "It follows that there is a superabundant number in each real interval #91;x,2x#93; and that the number of superabundant numbers is thus infinite."
Inflected Forms
Phrases
abundant number
highly abundant number