Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Smooth number

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…

Applications, Powersmooth numbers & Definition

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Smooth number. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. 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.

Map overview Semantic statistics

Smooth number

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

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

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 Word statistics

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

Entity relationships Subject–Predicate–Object triples

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

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.