perfect number

positive integer which equals the sum of all its divisors
Thing type_of_integer Q170043
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perfect number

Summary

perfect number is a type of integer[1]. It ranks in the top 3% of type_of_integer entities by monthly Wikipedia readership (1,189 views/month).[2]

Key Facts

  • perfect number's image is recorded as Perfect number Cuisenaire rods 6.png[3].
  • perfect number's instance of is recorded as type of integer[4].
  • perfect number's GND ID is recorded as 7683309-4[5].
  • perfect number's subclass of is recorded as pseudoperfect number[6].
  • perfect number's subclass of is recorded as harmonic divisor number[7].
  • perfect number's subclass of is recorded as even number[8].
  • perfect number's Commons category is recorded as Perfect number[9].
  • perfect number's has part is recorded as odd perfect number[10].
  • perfect number's Freebase ID is recorded as /m/05x6v[11].
  • perfect number's OEIS ID is recorded as A000396[12].
  • perfect number's topic's main category is recorded as Category:Perfect numbers[13].
  • perfect number's Gran Enciclopèdia Catalana ID is recorded as 0153761[14].
  • perfect number's described by source is recorded as Otto's encyclopedia[15].
  • perfect number's described by source is recorded as Armenian Soviet Encyclopedia, vol. 5[16].
  • perfect number's Encyclopædia Britannica Online ID is recorded as topic/perfect-number[17].
  • perfect number's Stack Exchange tag is recorded as https://mathoverflow.net/tags/perfect-numbers[18].
  • perfect number's Stack Exchange tag is recorded as https://math.stackexchange.com/tags/perfect-numbers[19].
  • perfect number's defining formula is recorded as \sigma(n)-2n=s(n)-n=0[20].
  • perfect number's MathWorld ID is recorded as PerfectNumber[21].
  • perfect number's Great Russian Encyclopedia Online ID is recorded as 3588903[22].
  • perfect number's does not have part is recorded as odd perfect number[23].
  • perfect number's Great Norwegian Encyclopedia ID is recorded as perfekt_tall[24].
  • perfect number's Rosetta Code page ID is recorded as Abundant,_deficient_and_perfect_number_classifications[25].
  • perfect number's maintained by WikiProject is recorded as WikiProject Mathematics[26].
  • perfect number's Microsoft Academic ID is recorded as 103996166[27].

Why It Matters

perfect number ranks in the top 3% of type_of_integer entities by monthly Wikipedia readership (1,189 views/month).[2] It has Wikipedia articles in 28 language editions, a strong signal of global cultural recognition.[28] It is known by 29 alternative names across languages and contexts.[29]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . Freebase Data Dumps. wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . wikidata.org.
  16. [18] . wikidata.org.
  17. [19] . wikidata.org.
  18. [20] . wikidata.org.
  19. [21] . wikidata.org.
  20. [22] . wikidata.org.
  21. [23] . wikidata.org.
  22. [24] . wikidata.org.
  23. [25] . wikidata.org.
  24. [26] . wikidata.org.
  25. [27] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [28] . Wikidata sitelinks. wikidata.org.
  3. [29] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). perfect number. Retrieved May 3, 2026, from https://4ort.xyz/entity/perfect-number
MLA “perfect number.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/perfect-number.
BibTeX @misc{4ortxyz_perfect-number_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{perfect number}}, year = {2026}, url = {https://4ort.xyz/entity/perfect-number}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): perfect number — https://4ort.xyz/entity/perfect-number (retrieved 2026-05-03)

Canonical URL: https://4ort.xyz/entity/perfect-number · Last refreshed:

Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 15d ago · KrBot bot · 2026-05-06 view diff on Wikidata ↗
    Subclass of
    Subclass of pseudoperfect number, harmonic divisor number, even number
    Maintained by wikiproject WikiProject Mathematics
    Topic's main category Category:Perfect numbers
    + 7 other properties edited (see Wikidata diff for full list)
    "/* wbsetqualifier-update:1| */ [[Property:P9758]]: [[Q16317911]], разрешение перенаправления / resolving redirect [[Q28920044]] → [[Q16317911]] ([[:toollabs:editgroups/b/KrBotResolvingRedirect/Q289200"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.