Phrase guide

hyperperfect number

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, number-theory, sciences

Examples

  • 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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

From hyper- + perfect number.