hyperperfect number
nounEtymology From hyper- + perfect number.
1
Mathematics, Number theory, Sciences Any natural number n for which, for some positive integer k, n = 1 + k(σ(n) - n - 1), where σ(n) is the sum of the positive divisors of n.
- 1966, American Mathematical Society Translations, page 258, […] the asymptotic density of all hyperperfect numbers, that is, numbers m for which m | σ(m), is equal to zero.
- The rank of a hyperperfect number N is the ratio of divisor sum to N (which equals 2 for perfect numbers).1974, William Judson LeVeque, editor, Reviews in number theory, as printed in Mathematical reviews, 1940 through 1972, volumes 1-44 inclusive, volume 1, page 107:
1 more example
- In 1974, Daniel Minoli and Robert Bear described a number of properties of hyperperfect numbers.1999, James J. Tattersall, Elementary Number Theory in Nine Chapters, page 144:
- Derived terms
- -hyperperfect number
- Related terms
- perfect number, superperfect number