harmonic number

number equal to a partial sum of the harmonic series: the sum of the first n whole number reciprocals; 1/1 + 1/2 + 1/3 + ... + 1/n
Thing general Q13407133
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harmonic number

Summary

harmonic number ranks in the top 2% of general entities by monthly Wikipedia readership (229 views/month).[1]

Key Facts

  • harmonic number's image is recorded as HarmonicNumbers.svg[2].
  • harmonic number's subclass of is recorded as rational number[3].
  • harmonic number's subclass of is recorded as partial sum[4].
  • harmonic number's Commons category is recorded as Harmonic number[5].
  • harmonic number's Freebase ID is recorded as /m/01ffqt[6].
  • harmonic number's described by source is recorded as The Art of Computer Programming, Volume 1: Fundamental Algorithms, 3rd edition[7].
  • harmonic number's Encyclopædia Britannica Online ID is recorded as science/harmonic-number[8].
  • harmonic number's defining formula is recorded as \sum_{k=1}^nk^{-1}[9].
  • harmonic number's MathWorld ID is recorded as HarmonicNumber[10].
  • harmonic number's World of Physics ID is recorded as HarmonicNumber[11].
  • harmonic number's maintained by WikiProject is recorded as WikiProject Mathematics[12].
  • harmonic number's Microsoft Academic ID is recorded as 28581250[13].
  • harmonic number's Brilliant Wiki ID is recorded as harmonic-number[14].
  • harmonic number's in defining formula is recorded as k[15].
  • harmonic number's in defining formula is recorded as n[16].
  • harmonic number's Encyclopedia of Mathematics article ID is recorded as Harmonic_number[17].
  • harmonic number's PlanetMath ID is recorded as HarmonicNumber[18].
  • harmonic number's Namuwiki ID is recorded as 조화수(수학)[19].
  • harmonic number's Treccani's Enciclopedia della Matematica ID is recorded as numero-armonico[20].
  • harmonic number's OpenAlex ID is recorded as C28581250[21].

Why It Matters

harmonic number ranks in the top 2% of general entities by monthly Wikipedia readership (229 views/month).[1] It has Wikipedia articles in 17 language editions, a strong signal of global cultural recognition.[22] It is known by 3 alternative names across languages and contexts.[23]

References

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

Direct Wikidata claims

  1. [2] . wikidata.org.
  2. [3] . wikidata.org.
  3. [4] . wikidata.org.
  4. [5] . wikidata.org.
  5. [6] . Freebase Data Dumps. wikidata.org.
  6. [7] . wikidata.org.
  7. [8] . wikidata.org.
  8. [9] . wikidata.org.
  9. [10] . wikidata.org.
  10. [11] . wikidata.org.
  11. [12] . wikidata.org.
  12. [13] . wikidata.org.
  13. [14] . wikidata.org.
  14. [15] . wikidata.org.
  15. [16] . wikidata.org.
  16. [17] . wikidata.org.
  17. [18] . wikidata.org.
  18. [19] . wikidata.org.
  19. [20] . wikidata.org.
  20. [21] . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.

Aggregate / graph-position facts

  1. [1] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [22] . Wikidata sitelinks. wikidata.org.
  3. [23] . 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). harmonic number. Retrieved April 11, 2026, from https://4ort.xyz/entity/harmonic-number
MLA “harmonic number.” 4ort.xyz Knowledge Graph, 4ort.xyz, 11 Apr. 2026, https://4ort.xyz/entity/harmonic-number.
BibTeX @misc{4ortxyz_harmonic-number_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{harmonic number}}, year = {2026}, url = {https://4ort.xyz/entity/harmonic-number}, note = {Accessed: 2026-04-11}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): harmonic number — https://4ort.xyz/entity/harmonic-number (retrieved 2026-04-11)

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