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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, ....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 pratica.html.
- Practical_number wikiPageExternalLink 179.pdf.
- Practical_number wikiPageID "1205310".
- Practical_number wikiPageRevisionID "603114079".
- Practical_number hasPhotoCollection Practical_number.
- Practical_number title "Practical Number".
- Practical_number urlname "PracticalNumber".
- Practical_number subject Category:Egyptian_fractions.
- Practical_number subject Category:Integer_sequences.
- Practical_number type Abstraction100002137.
- Practical_number type Arrangement107938773.
- Practical_number type Chemical114806838.
- Practical_number type EgyptianFractions.
- Practical_number type Fraction114922107.
- Practical_number type Group100031264.
- Practical_number type IntegerSequences.
- Practical_number type Material114580897.
- Practical_number type Matter100020827.
- Practical_number type Ordering108456993.
- Practical_number type Part113809207.
- Practical_number type PhysicalEntity100001930.
- Practical_number type Relation100031921.
- Practical_number type Sequence108459252.
- Practical_number type Series108457976.
- Practical_number type Substance100019613.
- 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 "Nombre pratique".
- Practical_number label "Numero pratico".
- Practical_number label "Practical number".
- Practical_number label "實際數".
- Practical_number sameAs Nombre_pratique.
- Practical_number sameAs Numero_pratico.
- Practical_number sameAs m.04h553.
- Practical_number sameAs Q577211.
- Practical_number sameAs Q577211.
- Practical_number sameAs Practical_number.
- Practical_number wasDerivedFrom Practical_number?oldid=603114079.
- Practical_number isPrimaryTopicOf Practical_number.