Dictionary

superabundant number en · NOUN

Meanings

1. A positive integer whose abundancy index is greater than that of any lesser positive integer.
   • 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. 2017, Kevin Broughan, Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents, Cambridge University Press, page 151:
   • 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.
2. Used other than figuratively or idiomatically: see superabundant, number.

Forms

Relateds

highly abundant number · abundant number · superabundant

Synonyms

SA (positive integer whose abundancy index is greater than that of any lesser positive integer) · superior highly composite number (positive integer whose abundancy index is greater than that of any lesser positive integer)

Translations (4)

fr nombre superabondant (positive integer whose abundancy index is greater than that of any lesser positive integer) · fi ylirunsas luku (positive integer whose abundancy index is greater than that of any lesser positive integer) · pl liczba supernadmierna (positive integer whose abundancy index is greater than that of any lesser positive integer) · pl liczba supernadmiarowa (positive integer whose abundancy index is greater than that of any lesser positive integer)