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- Practical_number abstract "In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of 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 as these divisors themselves, we have 5 = 3 + 2, 7 = 6 + 1, 8 = 6 + 2, 9 = 6 + 3, 10 = 6 + 3 + 1, and 11 = 6 + 3 + 2.The sequence of practical numbers (sequence A005153 in OEIS) begins1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66, 72, 78, 80, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 128, 132, 140, 144, 150....Practical numbers were used by Fibonacci in his Liber Abaci (1202) in connection with the problem of representing rational numbers as Egyptian fractions. Fibonacci does not formally define practical numbers, but he gives a table of Egyptian fraction expansions for fractions with practical denominators.The name "practical number" is due to Srinivasan (1948), who first attempted a classification of these numbers that was completed by Stewart (1954) and Sierpiński (1955). This characterization makes it possible to determine whether a number is practical by examining its prime factorization. Every even perfect number and every power of two is also a practical number.Practical numbers have also been shown to be analogous with prime numbers in many of their properties.".
- Practical_number wikiPageExternalLink 179.pdf.
- Practical_number wikiPageExternalLink pratica.html.
- Practical_number wikiPageID "1205310".
- Practical_number wikiPageLength "15212".
- Practical_number wikiPageOutDegree "37".
- Practical_number wikiPageRevisionID "681121562".
- Practical_number wikiPageWikiLink American_Journal_of_Mathematics.
- Practical_number wikiPageWikiLink Bertrands_postulate.
- Practical_number wikiPageWikiLink Category:Egyptian_fractions.
- Practical_number wikiPageWikiLink Category:Integer_sequences.
- Practical_number wikiPageWikiLink Communications_on_Pure_and_Applied_Mathematics.
- Practical_number wikiPageWikiLink Current_Science.
- Practical_number wikiPageWikiLink Divisor.
- Practical_number wikiPageWikiLink Divisor_function.
- Practical_number wikiPageWikiLink Egyptian_fraction.
- Practical_number wikiPageWikiLink Factorial.
- Practical_number wikiPageWikiLink Fibonacci.
- Practical_number wikiPageWikiLink Fibonacci_number.
- Practical_number wikiPageWikiLink Fibonacci_prime.
- Practical_number wikiPageWikiLink Giuseppe_Melfi.
- Practical_number wikiPageWikiLink Goldbachs_conjecture.
- Practical_number wikiPageWikiLink Highly_composite_number.
- Practical_number wikiPageWikiLink Integer_factorization.
- Practical_number wikiPageWikiLink Journal_of_Number_Theory.
- Practical_number wikiPageWikiLink Legendres_conjecture.
- Practical_number wikiPageWikiLink Leonhard_Euler.
- Practical_number wikiPageWikiLink Liber_Abaci.
- Practical_number wikiPageWikiLink London_Mathematical_Society.
- Practical_number wikiPageWikiLink Number_theory.
- Practical_number wikiPageWikiLink Perfect_number.
- Practical_number wikiPageWikiLink Power_of_two.
- Practical_number wikiPageWikiLink Prime_factorization.
- Practical_number wikiPageWikiLink Prime_number.
- Practical_number wikiPageWikiLink Prime_number_theorem.
- Practical_number wikiPageWikiLink Prime_numbers.
- Practical_number wikiPageWikiLink Primorial.
- Practical_number wikiPageWikiLink Ramanujan.
- Practical_number wikiPageWikiLink Rational_number.
- Practical_number wikiPageWikiLink Srinivasa_Ramanujan.
- Practical_number wikiPageWikiLink Twin_prime.
- Practical_number wikiPageWikiLink Twin_prime_conjecture.
- Practical_number wikiPageWikiLink Unit_fraction.
- Practical_number wikiPageWikiLinkText "Practical number".
- Practical_number wikiPageWikiLinkText "practical number".
- Practical_number hasPhotoCollection Practical_number.
- Practical_number title "Practical Number".
- Practical_number urlname "PracticalNumber".
- Practical_number wikiPageUsesTemplate Template:Citation.
- Practical_number wikiPageUsesTemplate Template:Classes_of_natural_numbers.
- Practical_number wikiPageUsesTemplate Template:Divisor_classes.
- Practical_number wikiPageUsesTemplate Template:Harvtxt.
- Practical_number wikiPageUsesTemplate Template:Mathworld.
- Practical_number wikiPageUsesTemplate Template:OEIS.
- Practical_number wikiPageUsesTemplate Template:PlanetMath.
- Practical_number wikiPageUsesTemplate Template:Reflist.
- Practical_number subject Category:Egyptian_fractions.
- Practical_number subject Category:Integer_sequences.
- Practical_number hypernym N.
- Practical_number type Band.
- Practical_number type Combinatoric.
- Practical_number type Integer.
- Practical_number comment "In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n.".
- Practical_number label "Practical number".
- Practical_number sameAs Praktika_nombro.
- Practical_number sameAs Nombre_pratique.
- Practical_number sameAs Numero_pratico.
- Practical_number sameAs Praktisch_getal.
- Practical_number sameAs m.04h553.
- Practical_number sameAs Nùmmuru_pràticu.
- Practical_number sameAs Praktiskt_tal.
- Practical_number sameAs நடைமுறை_எண்.
- Practical_number sameAs Q577211.
- Practical_number sameAs Q577211.
- Practical_number sameAs 實際數.
- Practical_number wasDerivedFrom Practical_number?oldid=681121562.
- Practical_number isPrimaryTopicOf Practical_number.