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Practical number

In number theory, a practical number or panarithmic number is a positive integer n {\displaystyle n} such that all smaller positive integers can be represented as sums of distinct divisors of n {\displaystyle n} . For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, 4, and 6: as well…

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Analogies with prime numbers

Prime numbersGoldbach's conjectureTwin prime conjectureMelfiFibonacci numbers
10 related topics

Characterization of practical numbers

Deficient numberComplete sub-sequencePrime factorizationSum of the divisors
4 related topics

Relation to other classes of numbers

Leonhard EulerPrimorialBertrand's postulateRamanujanHighly composite numbers
6 related topics

Practical numbers and Egyptian fractions

Rational numberUnit fractionZhi-Wei SunDavidEppstein
4 related topics

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Overview

Characterization of practical numbers

Properties

Relation to other classes of numbers

Practical numbers and Egyptian fractions

Analogies with prime numbers

The number of prime factors, the number of divisors, and the sum of divisors

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Practical number

Nodes47
Edges46
Triples92
Avg. degree1.96
Density0.042553
Components1

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Practical number

Top relations

related to Analogies with prime numbers · 30
Practical number → A124105, Biggl, Biggr, Cn, Erdős, Euler, Fibonacci, Goldbach's, Hausman, Improving, Indeed, Legendre's, Let, Loxton, Lucas, Margenstern, Margenstern's, Mascheroni, Melfi, Moreover
related to Properties · 16
Practical number → A267124, Equivalently, Every, For, From, Furthermore, In, Its, Mersenne, More, OEIS, Sierpiński, Srinivasan, Stewart, The, This
related to Relation to other classes of numbers · 15
Practical number → Because, By, By Bertrand's, Each, Every, For, From, Generalizing, Leonhard Euler's, Powers, Ramanujan's, Several, The, Therefore, This
related to Characterization of practical numbers · 9
Practical number → For, If, In, Sierpiński, Srinivasan, Srinivasan's, Stewart, The, This
related to External links · 8
Practical number → Archived, Eric, Giuseppe Melfi, MathWorld, PlanetMath, Tables, Wayback Machine, Weisstein
related to Practical numbers and Egyptian fractions · 8
Practical number → Each, Egyptian, Fibonacci, For, If, Liber Abaci, Of, This
related to The number of prime factors, the number of divisors, and the sum of divisors · 6
Practical number → As, In, Kac, That, The, The Erdős

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Important terminology

practical displaystyle number numbers divisors prime every sum log also egyptian leq representation even two positive sequence fraction factorization characterization

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Practical numberrelated to Analogies with prime numbersOne0.60section
Practical numberrelated to Analogies with prime numbersIndeed0.60section
Practical numberrelated to Analogies with prime numbersGoldbach's0.60section
Practical numberrelated to Analogies with prime numbersMelfi0.60section
Practical numberrelated to Analogies with prime numbersFibonacci0.60section
Practical numberrelated to Analogies with prime numbersA1241050.60section
Practical numberrelated to Analogies with prime numbersOEIS0.60section
Practical numberrelated to Analogies with prime numbersSanna0.60section
Practical numberrelated to Analogies with prime numbersCn0.60section
Practical numberrelated to Analogies with prime numbersLucas0.60section
Practical numberrelated to Analogies with prime numbersThe0.60section
Practical numberrelated to Analogies with prime numbersHausman0.60section

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