What is "perfect number"

Perfect \Per"fect\, a. [OE. parfit, OF. parfit, parfet, parfait, F. parfait, L. perfectus, p. p. of perficere to carry to the end, to perform, finish, perfect; per (see Per-) + facere to make, do. See Fact.]

1. Brought to consummation or completeness; completed; not defective nor redundant; having all the properties or qualities requisite to its nature and kind; without flaw, fault, or blemish; without error; mature; whole; pure; sound; right; correct.

   My strength is made perfect in weakness.
   --2 Cor. xii. 9.

   Three glorious suns, each one a perfect sun.
   --Shak.

   I fear I am not in my perfect mind.
   --Shak.

   O most entire perfect sacrifice!
   --Keble.

   God made thee perfect, not immutable.
   --Milton.

2. Well informed; certain; sure.

   I am perfect that the Pannonains are now in arms.
   --Shak.

3. (Bot.) Hermaphrodite; having both stamens and pistils; -- said of flower.

   Perfect cadence (Mus.), a complete and satisfactory close in harmony, as upon the tonic preceded by the dominant.

   Perfect chord (Mus.), a concord or union of sounds which is perfectly coalescent and agreeable to the ear, as the unison, octave, fifth, and fourth; a perfect consonance; a common chord in its original position of keynote, third, fifth, and octave.

   Perfect number (Arith.), a number equal to the sum of all its divisors; as, 28, whose aliquot parts, or divisors, are 14, 7, 4, 2, 1. See Abundant number, under Abundant.
   --Brande & C.

   Perfect tense (Gram.), a tense which expresses an act or state completed.

   Syn: Finished; consummate; complete; entire; faultless; blameless; unblemished.

n. (context number theory English) A number that is the sum of all of its divisors except itself.

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum). Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself) i.e. σ(n) = 2n.

This definition is ancient, appearing as early as Euclid's Elements (VII.22) where it is called τέλειος ἀριθμός (perfect, ideal, or complete number). Euclid also proved a formation rule (IX.36) whereby q(q + 1)/2 is an even perfect number whenever q is what is now called a Mersenne prime—a prime of the form 2 − 1 for prime p. Much later, Euler proved that all even perfect numbers are of this form. This is known as the Euclid–Euler theorem.

It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist.

Perfect Number (; lit. Suspect X) is a 2012 South Korean mystery- drama film directed by Bang Eun-jin. Adapted from Keigo Higashino's novel The Devotion of Suspect X, it centers around a mild-mannered mathematics professor ( Ryoo Seung-bum) who plans the perfect alibi for the woman he secretly loves ( Lee Yo-won) when she unexpectedly murders her abusive ex-husband. Cho Jin-woong received a Best Supporting Actor nomination at the 49th Baeksang Arts Awards in 2013.