hyperperfect number

noun

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.

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Meanings

nounhyperperfect number (plural hyperperfect numbers)

plural hyperperfect numbers

  1. mathematicsAny 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.

    2 more examples

    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

    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

Origin

From hyper- + perfect number.

Full word history & related roots →
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APA

hyperperfect number. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/hyperperfect%20number

MLA

“hyperperfect number.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/hyperperfect%20number. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “hyperperfect number,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/hyperperfect%20number.

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