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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, because 28 has proper divisors 1, 2, 4, 7, 14, and 1 + 2 + 4 + 7 + 14…

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History

Even perfect numbers

Odd perfect numbers

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Perfect number

Nodes71
Edges70
Triples124
Avg. degree1.97
Density0.028169
Components1

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Perfect number

Top relations

related to Further reading · 33
Perfect number → Aliquot Sequences, Amsterdam, Birkhauser, Borislav, Computation, Computational Methods, Computer Methods, Crstici, Dordrecht, Factorisation, Ganita Bharati, Hagis, Handbook, History, II, ISBN, Jozsef, JSTOR, Kluwer Academic, Lenstra
related to history · 28
Perfect number → AD, Alexandria, Augustine, BC Euclid, Blind, Book XI, Chapter, Commentary, Didymus, Euclid's, European, Fallūs, Genesis, God, Greek, He, Hippo, In, Ismail, Italian
related to External links · 20
Perfect number → Archived, Brady Haran, David Moews, DrexelGrimes, EMS Press, Encyclopedia, Eric, GIMPS, Great Internet Mersenne Prime, History, James, Mathematics, MathWorld, Numberphile, OEISsequenceA000396, Perfect, Perfect Numbers, Retrieved, Search, TheoryWeisstein
related to Minor results · 13
Perfect number → All, Every, Fermat, For, From, In, Makowski, Mersenne, Ore's, Richard Guy's, The, There, Therefore
related to Odd perfect numbers · 10
Perfect number → All, Any, Carl Pomerance, Euclid's, Euler, In, It, Jacques Lefèvre, More, Whether
related to Related concepts · 7
Perfect number → All, By, Granville, Greek, Numbers, The, These
is a · 6
Perfect number → fixed point of the restricted divisor function s, manuscript written between 1456 and 1461 by an unknown mathematician, number that is half the sum of all of its positive divisors, Ore's harmonic number.The even perfect numbers are not trapezoidal numbers, pernicious number.Every even perfect number is also a practical number, positive integer that is equal to the sum of its positive proper divisors
related to Even perfect numbers · 5
Perfect number → Book IX, Elements, Euclid, For, Proposition
see also · 2
Perfect number → Harmonic, Mersenne

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Important terminology

perfect displaystyle number numbers prime even odd divisors -1 form sum also 28 proper 10 known every mersenne called 8128

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SubjectPredicateObjectConfidenceSrc
Perfect numberis apositive integer that is equal to the sum of its positive proper divisors0.90text
Perfect numberis anumber that is half the sum of all of its positive divisors0.90text
Perfect numberis amanuscript written between 1456 and 1461 by an unknown mathematician0.90text
Perfect numberis apernicious number.Every even perfect number is also a practical number0.90text
Perfect numberis aOre's harmonic number.The even perfect numbers are not trapezoidal numbers0.90text
Perfect numberis afixed point of the restricted divisor function s0.90text
Perfect numberrelated to Even perfect numbersEuclid0.60section
Perfect numberrelated to Even perfect numbersElements0.60section
Perfect numberrelated to Even perfect numbersBook IX0.60section
Perfect numberrelated to Even perfect numbersProposition0.60section
Perfect numberrelated to Even perfect numbersFor0.60section
Perfect numberrelated to External linksPerfect0.60section

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