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	Perfect number - Wikipedia, the free encyclopedia
		In mathematics, a perfect number is defined as an integer which is the sum of its proper positive divisors, excluding itself.
		Numbers where the sum is less than twice the number itself are called deficient, and where it is greater than twice the number, abundant.
		A pair of numbers which are the sum of each other's proper divisors are called amicable, and larger cycles of numbers are called sociable.
	en.wikipedia.org /wiki/Perfect_number (779 words)

	Encyclopedia: Perfect number (Site not responding. Last check: 2007-10-22)
		Another interesting fact is that the reciprocals of the factors of a perfect number add up to 2: Monzy lara is so dumb, i freakin hate her her name should be monzerella cheese, or stupid ass, of a number x is the number which, when multiplied by x, yields 1.
		In mathematics, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors.
		In mathematics, an almost perfect number (sometimes also called slightly defective number) is a natural number n such that the sum of all divisors of n (the divisor function σ(n)) is equal to 2n _ 1.
	www.nationmaster.com /encyclopedia/Perfect-number (1492 words)

	6 (number) article - 6 (number) 1 3 5 8 >> List numbers Integers 10 20 30 40 50 60 70 - What-Means.com (Site not responding. Last check: 2007-10-22)
		Six is also a unitary perfect number, a harmonic divisor number and a highly composite number.
		The number of feet below ground level a coffin is traditionally buried; thus, the phrase "six feet under" means that a person (or thing, or concept) is dead.
		The number of similar coins that can be arranged around a central seventh coin of the same kind so that each coin makes contact with the central one and touches both its neighbors without a gap; see also Sphere packing.
	www.what-means.com /encyclopedia/Six (845 words)

	Perfect number -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		In mathematics, a perfect number is defined as an (Any of the natural numbers (positive or negative) or zero) integer which is the sum of its proper positive (The number by which a dividend is divided) divisors, excluding itself.
		Six ((The cardinal number that is the sum of five and one) 6) is the first perfect number, because 1, 2 and 3 are its proper positive divisors and 1 + 2 + 3 = 6.
		Numbers where the sum is less than the number itself are called (Click link for more info and facts about deficient) deficient, and where it is greater, (Click link for more info and facts about abundant) abundant.
	www.absoluteastronomy.com /encyclopedia/p/pe/perfect_number.htm (810 words)

	Unitary perfect number - Wikipedia, the free encyclopedia
		dividing the sum of the unitary divisors of an odd number (where d(n) is the number* of distinct divisors of n).
		One gets this because the sum of all the unitary divisors is a multiplicative function and one has the sum of the unitary divisors of a power of a prime p
		One gets easily from this that an odd unitary perfect number must have only one distinct prime factor, and it is not hard to show that a power of prime cannot be a unitary perfect number, since there are not enough divisors.
	en.wikipedia.org /wiki/Unitary_perfect_number (242 words)

	Straight Dope Staff Report: What's the story on perfect numbers?
		Perfect numbers are a holdover from the days of the Pythagoreans, when mathematicians were mystics as much as anything else and put a lot more stock in coincidence.
		There are also amicable numbers, sociable numbers, harmonic numbers, hyperperfect numbers, infinitary perfect numbers, unitary perfect numbers, super unitary perfect numbers, superperfect numbers, sublime numbers, and weird numbers--all of which satisfy some quirky condition or another.
		For example, sublime numbers have a perfect number of divisors, and the sum of their divisors is itself perfect.
	www.straightdope.com /mailbag/mperfectnumbers.html (683 words)

	Unitary perfect number -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		A unitary perfect number is an (Any of the natural numbers (positive or negative) or zero) integer which is the sum of its positive proper unitary divisors, not including the number itself.
		Thus, (The cardinal number that is the product of ten and six) 60 is a unitary perfect number, because its unitary divisors, 1, 3, 4, 5, 12, 15 and 20 are its proper unitary divisors, and 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60.
		One gets this because the sum of all the unitary divisors is a (Click link for more info and facts about Multiplicative function) Multiplicative function and one has the sum of the unitary divisors of a power of a prime p
	www.absoluteastronomy.com /encyclopedia/u/un/unitary_perfect_number.htm (271 words)

	60 (number) - Encyclopedia, History, Geography and Biography
		Sixty is a composite number with divisors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, making it also a highly composite number.
		This number is the sum of a pair of twin primes (29 + 31), as well as the sum of four consecutive primes (11 + 13 + 17 + 19).
		The Saros number of the solar eclipse series which began on -1020 May 18 and ended on 260 June 26.
	www.arikah.com /encyclopedia/Sixty (447 words)

	Directory - Science: Math: Number Theory: Factoring: Perfect Numbers (Site not responding. Last check: 2007-10-22)
		Perfect Numbers · cached · A detailed history of the quest for perfect numbers, from Euclid to their present-day Mersenne discoveries.
		On a Generalization of Perfect Numbers · cached · J. Pe introduces perfect numbers relative to an arithmetical function f.
		Perfect Numbers · cached · Harry J. Smith's pages of the mathematics behind perfect numbers, aliquot sequences and Mersenne numbers.
	www.incywincy.com /default?p=400130 (334 words)

	6 (number) - Indopedia, the Indological knowledgebase
		In cricket, a "sixer" is a shot in which the ball clears the boundary without bouncing.
		The number of sides on a cube, hence the highest number on a standard die.
		The highest number on one end of a standard domino.
	www.indopedia.org /Six.html (1024 words)

	6 (number) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		The next perfect number is (The cardinal number that is the sum of twenty-seven and one) 28.
		The next highly composite number is (The cardinal number that is the sum of eleven and one) 12.
		The number of sides on a cube, hence the highest number on a standard (A device used for shaping metal) die.
	www.absoluteastronomy.com /encyclopedia/6/6/6_(number).htm (2235 words)

	Perfect number (Site not responding. Last check: 2007-10-22)
		The fifth perfect number has 8 digits, thus debunking the first assumption.
		(That the last digit of any even perfect number must be a 6 or an 8 is not difficult to show.)
		Also, it must have at least 8 distinct prime factors (and at least 11 if it is not divisible by 3), and it must have at least one prime factor greater than 10
	www.sciencedaily.com /encyclopedia/perfect_number (638 words)

	Perfect number - Definition up Erdmond.Com
		One of these assumptions was that since 2, 3, 5, and 7 are precisily the first four primes, the fifth perfect number would be obtained when ''n'' = 11, the fifth prime.
		(That the last digit of any even perfect number must be a 6 or an 8 is not difficult to show.) It's true that ''n'' should be a prime but it does not mean that 2''n'' − 1 is automatically a prime.
		Nowadays, prime_numbers generated by the formula 2''n'' − 1 are known as Mersenne_primes, after the seventeenth-century monk, Marin_Mersenne, who studied number theory and perfect numbers.
	www.erdmond.com /Perfect_number.html (489 words)

	Perfect, amicable and sociable numbers
		For a number n, we define s(n) to be the sum of the aliquot parts of n, i.e., the sum of the positive divisors of n, excluding n itself: so, for example, s(8)=1+2+4=7, and s(12)=1+2+3+4+6=16.
		A perfect number is a cycle of length 1 of s, i.e., a number whose positive divisors (except for itself) sum to itself.
		However the sum of unitary divisors, bi-unitary divisors, or infinitary divisors of a number is always even, unless the number is a power of 2.
	djm.cc /amicable.html (2519 words)

	Open Directory - Science: Math: Number Theory: Factoring: Perfect Numbers (Site not responding. Last check: 2007-10-22)
		Odd Perfect Numbers - Missing Values - Status of various factorisations that would extend the known area of non-existence of odd perfect numbers, by Kevin Hare.
		On a Generalization of Perfect Numbers - J. Pe introduces perfect numbers relative to an arithmetical function f.
		Perfect Numbers - A detailed history of the quest for perfect numbers, from Euclid to their present-day Mersenne discoveries.
	dmoz.org /Science/Math/Number_Theory/Factoring/Perfect_Numbers (339 words)

	The Kaprekar Numbers
		The (decimal) n-Kaprekar numbers are defined and are shown to be in one-one correspondence with the unitary divisors of 10
		The even perfect numbers are shown to be Kaprekar numbers in the binary base.
		The universal Kaprekar number 1 corresponds to the unitary divisor 1 of 10
	www.maths.tcd.ie /EMIS/journals/JIS/VOL3/iann2a.html (1251 words)

	Superconducting Quantum Computing: Christopher Altman (Site not responding. Last check: 2007-10-22)
		SQUID qubit biased at one-half flux is set to a distinct state, the unitary algorithm is performed, and its its state is projected by classical measurement.
		Unitary matrix transformations are reversible, requiring zero energy to change states or gate operations.
		The task of the algorithm designer is to first find the unitary matrix for the given computing problem and then map the matrix into a sequential product of smaller matrix operations that can be implemented relatively easily.
	artilect.org /altman/squid.html (843 words)

	On-line Mathematics Dictionary
		A number puzzle in which an indicated arithmetical operation has some or all of its digits replaced by letters or symbols and where the restoration of the original digits is required.
		A practical number is a positive integer m such that every natural number n not exceeding m is a sum of distinct divisors of m.
		A rational number is a number that is the ratio of two integers.
	cage.rug.ac.be /~hvernaev/glossary/glossary.html (1541 words)

	number system -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-22)
		The most elementary representation of numbers is the tally or unitary…
		The most elementary representation of numbers is the tally or unitary systemof...
		number of the form x + yi, in which x and y are real numbers and i is the imaginary unit such that i2 = -1.
	www.britannica.com /eb/article-9056491?tocId=9056491&query=real (796 words)

	Tables of Aliquot Cycles
		Note 1: All powers of 2 are augmented perfect numbers; no other augmented perfect numbers are known.
		Note 2: Multiplying all members of an exponential aliquot cycle by a squarefree number prime to all the members of the cycle yields a new exponential aliquot cycle.
		For sociable numbers all cycles with the member preceeding the largest member below the limit are known.
	amicable.homepage.dk /tables.htm (200 words)

	Read about 60 (number) at WorldVillage Encyclopedia. Research 60 (number) and learn about 60 (number) here! (Site not responding. Last check: 2007-10-22)
		The Saros number of the solar eclipse series which began on -1020
		The Saros number of the lunar eclipse series which began on
		in geometry, the number of seconds in a minute, and the number of minutes in a
	encyclopedia.worldvillage.com /s/b/60_%28number%29 (307 words)

	Post a Follow-Up to: (Site not responding. Last check: 2007-10-22)
		For unitary states, like the Philippines, the uniform LG system is advantageous in the sense that general policies and standards can easily be formulated in relation to certain local government levels.
		Somehow, in spite of their autonomy, local governments still have to follow national laws and standards and it would be a lot easier to benchmark in a uniform local government system.
		However, such systems must always have a minimum number of qualities which must be common to them no matter what form they take.
	www.decentralization.ws /forum/aspBoardPost.asp?Id=12 (302 words)

	Prime Curios!: 313
		313 is the smallest number to appear exactly 3 times in itself factorial (313!).
		The only 3-digit palindromic prime which is not the sum of consecutive composite numbers.
		313, 313 - 2, 313 - 23, 313 - 235 & 313 - 2357 are all prime numbers.
	primes.utm.edu /curios/page.php?short=313 (444 words)

	Unitary Perfect Number Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-22)
		Looking For unitary perfect number - Find unitary perfect number and more at Lycos Search.
		Find unitary perfect number - Your relevant result is a click away!
		Look for unitary perfect number - Find unitary perfect number at one of the best sites the Internet has to offer!
	www.karr.net /encyclopedia/Unitary_perfect_number (440 words)

	Read about 90 (number) at WorldVillage Encyclopedia. Research 90 (number) and learn about 90 (number) here! (Site not responding. Last check: 2007-10-22)
		Because 90 is the sum of its unitary divisors (excluding itself), it is a
		Also, in a right triangle, the angle opposing the hypotenuse measures 90 degrees, with the other two angles adding up to 90 for a total of 180 degrees.
		The Saros number of the solar eclipse series which began on 134 BC
	encyclopedia.worldvillage.com /s/b/90_%28number%29 (224 words)

	Yugas
		Four is the number "which affords an arithmetical division between unity and seven, as it surpasses the former by the same number (three), as it is itself surpassed by the seven, since four is by as many numbers above one, as seven is above four" (SD 2:582).
		The number four is considered feminine on the planes of matter; it is considered to be masculine and energic only on the highest plane of abstraction.
		When 4320 is halved the result is 2160, which multiplied by 12 is the number of years in one turning of the precessional cycle; again 2160 is the period of the so-called Messianic cycle.
	www.experiencefestival.com /yugas (2254 words)

	Number 14 (Site not responding. Last check: 2007-10-22)
		While there are a number of issues that arise in these processes such as capacity questions and questions of representation, this form of governance remains a priority and there is a process to ensure that this evolves so as to become increasingly more effective.
		A large number of these wards are marginal for both the ANC and the DA and victory or defeats are often determined by the efficacy of mobilisation.
		However, the ANC increased the number of voters it mobilised from 544 in December 2000 to 775 on 21 November 2001.
	www.anc.org.za /ancdocs/pubs/umrabulo/umrabulo14/umrhabulo14.html (17529 words)

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