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Smith number: Mathematical definition, Properties & Overview

In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free, the factorization is written without exponents, writing the repeated factor as many times as needed.

Language: English [EN]
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Smith number topic overview

The analysis highlights Mathematical definition, Properties and Overview as prominent areas in the source structure around Smith number.

Related topics
62
Source areas
3
Connected nodes
65
Extracted relationships
25
Concept neighborhoods
12
Bridge connections
65

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Mathematical definition · 51 topics
Overview · 9 topics
Properties · 2 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

Author of publication
Albert Wilansky
First terms
4, 22, 27, 58, 85, 94, 121
Named after
Harold Smith (brother-in-law of Albert Wilansky)
OEIS index
A006753
Total no. of terms
infinity

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Mathematical definition

Properties

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Smith number connects Entity context

The extracted context around Smith number shows recurring relationship patterns in the source. For example, Smith number → Archived, Brady Haran, Copeland, December, Ed, Eric, MathWorld, Numberphile, Smith Numbers, Weisstein Another extracted example is Smith number → It, McDaniel, Smith, The, Two. Use these groups to spot repeated connection types before inspecting the individual relationships.

Smith number

Top relations

related to External links · 10
Smith number → Archived, Brady Haran, Copeland, December, Ed, Eric, MathWorld, Numberphile, Smith Numbers, Weisstein
related to Properties · 5
Smith number → It, McDaniel, Smith, The, Two
related to Mathematical definition · 4
Smith number → For, Here, Let, Smith
Author of publication · 1
Smith number → Albert Wilansky
First terms · 1
Smith number → 4, 22, 27, 58, 85, 94, 121
Named after · 1
Smith number → Harold Smith (brother-in-law of Albert Wilansky)
OEIS index · 1
Smith number → A006753
Total no. of terms · 1
Smith number → infinity
is a · 1
Smith number → composite number for which

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

smith number numbers base 10 factorization 22 displaystyle sum prime many brother-in-law named albert wilansky harold known theory given factor

Smith number relationships Subject–Predicate–Object triples

TTTA extracted 25 structured relationships around Smith number. Examples in this analysis include Smith number → Author of publication → Albert Wilansky and Smith number → First terms → 4, 22, 27, 58, 85, 94, 121. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Smith numberAuthor of publicationAlbert Wilansky1.00infobox
Smith numberFirst terms4, 22, 27, 58, 85, 94, 1211.00infobox
Smith numberNamed afterHarold Smith (brother-in-law of Albert Wilansky)1.00infobox
Smith numberOEIS indexA0067531.00infobox
Smith numberTotal no. of termsinfinity1.00infobox
Smith numberis acomposite number for which0.90text
Smith numberrelated to External linksWeisstein0.60section
Smith numberrelated to External linksEric0.60section
Smith numberrelated to External linksMathWorld0.60section
Smith numberrelated to External linksCopeland0.60section
Smith numberrelated to External linksEd0.60section
Smith numberrelated to External linksDecember0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Smith number bring nearby vocabulary together. In this analysis, examples include Smith, Base and Numbers. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Smith number
    • Smith
    • Base
    • Numbers
    • Known
    • Given
    • Factorization
    • Albert
    • Also
    • Brother-in-law
    • Brothers
    • Consecutive
    • Example
  • smith number
    • Smith
    • Base
    • Numbers
    • Known
    • Albert
    • Also
    • Brother-in-law
    • Consecutive
    • Example
    • Given
    • Harold
    • Named
  • number theory
    • Smith
    • Composite
    • Digits
    • Equal
    • Base
    • Given
    • Prime
    • Factorization
    • Sum
    • Albert
    • Also
    • Brother-in-law
  • composite number
    • Digits
    • Equal
    • Smith
    • Given
    • Prime
    • Theory
    • Base
    • Factorization
    • Sum
    • Albert
    • Also
    • Brother-in-law
  • number base
    • Smith
    • Base
    • Number
    • Numbers
    • Consecutive
    • Example
    • Given
    • Sum
    • Albert
    • Also
    • Brother-in-law
    • Harold
  • natural number
    • Smith
    • Mid
    • Stackrel
    • Text
    • Base
    • Prime
    • Wilansky
    • Known
    • Sum
    • Albert
    • Also
    • Brother-in-law
  • base 10
    • Smith
    • Number
    • Numbers
    • Consecutive
    • Example
    • Given
    • Sum
    • Composite
    • Digits
    • Equal
    • Albert
    • Brother-in-law
  • prime factorization
    • Factor
    • Prime
    • Sum
    • Mid
    • Stackrel
    • Text
    • Also
    • Case
    • Natural
    • Square-free
    • Theory
    • Without

Connections between topic areas Semantic bridges

For Smith number, one of the stronger structural bridges in this analysis connects Smith number with Mathematical definition. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Smith numberMathematical definition · splits 14 ⟂ 52
Smith numberOverview · splits 56 ⟂ 10
Smith numberProperties · splits 63 ⟂ 3

Map overview Semantic statistics

Smith number

Nodes66
Edges65
Triples25
Avg. degree1.97
Density0.030303
Components1

Source & methodology

TTTA analyzes the structure around Smith number to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Mathematical definition, Properties & Overview, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Smith number · EN edition · Analysis: TopicsToTalkAbout

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