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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
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Summary

harmonic number ranks in the top 2% of general entities by monthly Wikipedia readership (691 views/month).[1]

Key Facts

  • harmonic number is a type of rational number[2].
  • harmonic number is a type of partial sum[3].
  • harmonic number's Commons category is recorded as Harmonic number[4].
  • harmonic number's described by source is recorded as The Art of Computer Programming, Volume 1: Fundamental Algorithms, 3rd edition[5].
  • harmonic number's described by source is recorded as Mathwords[6].
  • harmonic number's maintained by WikiProject is recorded as WikiProject Mathematics[7].

Body

Definition and Type

Recorded subclass of include rational number[2] and partial sum[3].

Why It Matters

harmonic number ranks in the top 2% of general entities by monthly Wikipedia readership (691 views/month).[1] It has Wikipedia articles in 17 language editions, a strong signal of global cultural recognition.[8] It is known by 19 alternative names across languages and contexts.[9]

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] ↑ . wikidata.org.
  6. [7] ↑ . wikidata.org.

Aggregate / graph-position facts

  1. [1] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [8] ↑ . Wikidata sitelinks. wikidata.org.
  3. [9] ↑ . 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 October 13, 2026, from https://4ort.xyz/entity/harmonic-number
MLA “harmonic number.” 4ort.xyz Knowledge Graph, 4ort.xyz, 13 Oct. 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: 2026-10-13}}
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 2026-10-13)

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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. 6d ago · AddyLockPool · 2026-10-07 view diff on Wikidata ↗
    Encyclopedia of mathematics article id → Harmonic_number, Harmonic_number
    Claims rich → —
    "/* wbsetclaim-update:2||1 */ Encyclopedia of mathematics article id: Harmonic_number"
  2. 7d ago · AddyLockPool · 2026-10-07 view diff on Wikidata ↗
    Encyclopedia of mathematics article id → Harmonic_number, Harmonic_number
    Described by source → The Art of Computer Programming, Volume 1: Fundamental Algorithms, 3rd edition, Mathwords
    Subclass of → —
    Subclass of → rational number, partial sum
    + 3 other properties edited (see Wikidata diff for full list)
    "/* wbeditentity-statements-multiple-properties-add:0||2 */ Add 2 sources/identifiers (via Wikidata Source Saver, user-initiated)"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.