Meaning of superabundant number | Babel Free

Definitions

1. A positive integer whose abundancy index is greater than that of any lesser positive integer.
2. Used other than figuratively or idiomatically: see superabundant, number.

Equivalents

Examples

“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.”

CEFR level