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Perfect Number
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28. The first four perfect numbers are 6 (number), 6, 28 (number), 28, 496 (number), 496 and 8128 (number), 8128. The sum of proper divisors of a number is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors; in symbols, \sigma_1(n)=2n where \sigma_1 is the sum-of-divisors function. This definition is ancient, appearing as early as Euclid's Elements, Euclid's ''Elements'' (VII.22) where it is called (''perfect'', ''ideal'', or ''complete number''). Euclid also proved a formation rule (IX.36) whereby \frac is an even perfect number whenever q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Number Cuisenaire Rods 6 Exact
Perfect commonly refers to: * Perfection; completeness, and excellence * Perfect (grammar), a grammatical category in some languages Perfect may also refer to: Film and television * Perfect (1985 film), ''Perfect'' (1985 film), a romantic drama * Perfect (2018 film), ''Perfect'' (2018 film), a science fiction thriller * Perfect (Doctors), "Perfect" (''Doctors''), a 2004 television episode Literature * Perfect (Friend novel), ''Perfect'' (Friend novel), a 2004 novel by Natasha Friend * Perfect (Hopkins novel), ''Perfect'' (Hopkins novel), a young adult novel by Ellen Hopkins * Perfect (Joyce novel), ''Perfect'' (Joyce novel), a 2013 novel by Rachel Joyce * Perfect (Shepard novel), ''Perfect'' (Shepard novel), a Pretty Little Liars novel by Sara Shepard * ''Perfect'', a young adult science fiction novel by Dyan Sheldon Music * Perfect interval, in music theory * Perfect Records, a record label Artists * Perfect (musician) (born 1980), reggae singer * Perfect (Polish band) * P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
