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Square-free integer

In mathematics, a square-free integer (or squarefree integer) is an integer that is divisible by no square number other than 1. That is, its prime factorization has exactly one factor for each prime that appears in it. For example, 10 = 2 ⋅ 5 is square-free, but 18 = 2 ⋅ 3 ⋅ 3 is not, because 18 is divisible by 9 = 32. The smallest positive square-free…

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Overview

Square-free factorization

Square-free factors of integers

Equivalent characterizations

Dirichlet series

Distribution

Encoding as binary numbers

Erdős squarefree conjecture

Squarefree core

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Square-free integer

Nodes61
Edges60
Triples25
Avg. degree1.97
Density0.032787
Components1

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Square-free integer

Top relations

related to Distribution · 7
Square-free integer → A013928, Because, Chinese, For, Let, OEIS, This
related to Dirichlet series · 6
Square-free integer → Euler, Möbius, Riemann, The, The Dirichlet, This
related to Square-free factorization · 4
Square-free integer → Every, Then, This, To
related to Square-free factors of integers · 4
Square-free integer → Each, Every, The, This
related to Squarefree core · 4
Square-free integer → In, Let, That, The

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Important terminology

square-free displaystyle integer positive integers factorization prime factor numbers every product number one square largest squarefree divisible also part function

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Square-free integerrelated to Dirichlet seriesThe0.60section
Square-free integerrelated to Dirichlet seriesMöbius0.60section
Square-free integerrelated to Dirichlet seriesThe Dirichlet0.60section
Square-free integerrelated to Dirichlet seriesRiemann0.60section
Square-free integerrelated to Dirichlet seriesThis0.60section
Square-free integerrelated to Dirichlet seriesEuler0.60section
Square-free integerrelated to DistributionLet0.60section
Square-free integerrelated to DistributionOEIS0.60section
Square-free integerrelated to DistributionA0139280.60section
Square-free integerrelated to DistributionFor0.60section
Square-free integerrelated to DistributionBecause0.60section
Square-free integerrelated to DistributionChinese0.60section

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