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Smooth number: Applications, Powersmooth numbers & Definition

In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is a number in which every prime factor is at most 7. Therefore, 49 = 72 and 15750 = 2 × 32 × 53 × 7 are both 7-smooth, while 11 and 702 = 2 × 33 × 13 are not 7-smooth. The term seems to have been coined by…

Language: English [EN]
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Smooth number topic overview

The analysis highlights Applications, Powersmooth numbers and Definition as prominent areas in the source structure around Smooth number.

Related topics
45
Source areas
6
Connected nodes
54
Extracted relationships
38
Concept neighborhoods
29
Bridge connections
54

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.

Applications · 14 topics
Powersmooth numbers · 8 topics
Definition · 7 topics
Overview · 7 topics
Smooth over a set A · 6 topics
Distribution · 3 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.

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

Definition

Applications

Distribution

Powersmooth numbers

Smooth over a set A

Bibliography

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 Smooth number connects Entity context

The extracted context around Smooth number shows recurring relationship patterns in the source. For example, Smooth number → An, B-smooth, Babylonian, Bluestein's FFT, By, Cooley, FFT, Fourier, Large, Limit, Numbers, They, Tukey FFT Another extracted example is Smooth number → AMS, Computational, Granville, Introduction, ISBN, MSRI, Proc, Smooth, Tenenbaum. Use these groups to spot repeated connection types before inspecting the individual relationships.

Smooth number

Top relations

has application · 13
Smooth number → An, B-smooth, Babylonian, Bluestein's FFT, By, Cooley, FFT, Fourier, Large, Limit, Numbers, They, Tukey FFT
related to Bibliography · 9
Smooth number → AMS, Computational, Granville, Introduction, ISBN, MSRI, Proc, Smooth, Tenenbaum
related to External links · 8
Smooth number → B-smooth, Bs, Eric, Integer Sequences, MathWorld, OEIS, The On-Line Encyclopedia, Weisstein
related to Definition · 6
Smooth number → All, B-smooth, For, Hamming, The, This
is a · 1
Smooth number → number in which every prime factor is at most 7

Important terminology

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

Important terminology

numbers number prime smooth displaystyle factors 5-smooth integer also example equal set b-smooth theory less factor factorization 7-smooth applications positive

Smooth number relationships Subject–Predicate–Object triples

TTTA extracted 38 structured relationships around Smooth number. Examples in this analysis include Smooth number → is a → number in which every prime factor is at most 7 and Bluestein's FFT algorithm → instance of → Large prime sizes require less-efficient algorithms. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Smooth numberis anumber in which every prime factor is at most 70.90text
Bluestein's FFT algorithminstance ofLarge prime sizes require less-efficient algorithms0.80text
Smooth numberhas applicationAn0.60section
Smooth numberhas applicationFourier0.60section
Smooth numberhas applicationFFT0.60section
Smooth numberhas applicationCooley0.60section
Smooth numberhas applicationTukey FFT0.60section
Smooth numberhas applicationBy0.60section
Smooth numberhas applicationB-smooth0.60section
Smooth numberhas applicationLarge0.60section
Smooth numberhas applicationBluestein's FFT0.60section
Smooth numberhas applicationNumbers0.60section

Related concept clusters Concept neighborhoods

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

  • Smooth number
    • Applications
    • Less
    • Equal
    • Smoothness
    • Prime
    • B-smooth
    • Smooth
    • Displaystyle
    • Numbers
    • Function
    • Sieve
    • N-powersmooth
  • smooth number
    • Applications
    • Less
    • Theory
    • Equal
    • Smoothness
    • Prime
    • B-smooth
    • Smooth
    • Displaystyle
    • Numbers
    • Function
    • Sieve
  • number theory
    • N-smooth
    • Applications
    • Less
    • Number
    • Theory
    • Equal
    • Also
    • Smoothness
    • Prime
    • B-smooth
    • Important
    • Numbers
  • integer
    • Known
    • Positive
    • N-smooth
    • Applications
    • Less
    • B-smooth
    • Equal
    • Factors
    • Numbers
    • Algorithms
    • Function
    • Greater
  • prime factors
    • Prime
    • Factor
    • Factorization
    • Set
    • B-smooth
    • Example
    • 5-smooth
    • Greater
    • Smooth
    • Integer
    • Primes
    • Numbers
  • regular numbers
    • Also
    • 5-smooth
    • Smooth
    • Applications
    • Small
    • Important
    • Positive
    • Regular
    • N-powersmooth
    • Prime
    • Algorithm
    • Called
  • the sum of the reciprocals of the natural numbers
    • Also
    • 5-smooth
    • Smooth
    • Applications
    • Important
    • Positive
    • Regular
    • N-powersmooth
    • Small
    • Prime
    • Algorithm
    • Called
  • highly composite numbers
    • Also
    • 5-smooth
    • Smooth
    • Applications
    • Regular
    • Important
    • Positive
    • N-powersmooth
    • Small
    • Prime
    • Algorithm
    • Called

Connections between topic areas Semantic bridges

For Smooth number, one of the stronger structural bridges in this analysis connects Smooth number with Applications. 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
Smooth numberApplications · splits 40 ⟂ 15
Smooth numberPowersmooth numbers · splits 46 ⟂ 9
Smooth numberOverview · splits 47 ⟂ 8
Smooth numberDefinition · splits 47 ⟂ 8
Smooth numberSmooth over a set A · splits 48 ⟂ 7
Smooth numberDistribution · splits 51 ⟂ 4
Smooth numberBibliography · splits 52 ⟂ 3

Map overview Semantic statistics

Smooth number

Nodes55
Edges54
Triples38
Avg. degree1.96
Density0.036364
Components1

Source & methodology

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

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

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