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Topic: Almost perfect number

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	Perfect number - Definition, explanation
		In mathematics, a perfect number is defined as an integer which is the sum of its proper positive divisors, excluding itself.
		Six (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 deficient, and where it is greater, abundant.
	www.calsky.com /lexikon/en/txt/p/pe/perfect_number.php (590 words)

	Perfect number Summary
		In mathematics, a perfect number is defined as an integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors not including the number.
		Equivalently, a perfect number is a number that is half the sum of all of its positive divisors, or σ(n) = 2 n.
		By definition, a perfect number is a fixed point of the restricted divisor function s(n) = σ(n) − n, and the aliquot sequence associated with a perfect number is a constant sequence.
	www.bookrags.com /Perfect_number (1658 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.
		Quasiperfect numbers have a divisor sum of 2n+1; almost perfect numbers have a divisor sum of 2n-1.
		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)

	perfect number definition : Search Results : GoodSearch : Search the Internet with GoodSearch and support your favorite ...
		Well, the definition of a perfect number is: any number that is equal to the sum...
		numbers is perfect, using the definition of the...
		If is a prime number (see section 4.3 for definition of prime number.), then is a perfect number.
	www.goodsearch.com /Search.aspx?Keywords=perfect+number+definition&page=4 (287 words)

	Notable Properties of Specific Numbers at MROB
		Apart from the trivial cases of 0 and 1, 8 is the smallest number for which the sum of the digits of its cube is equal to the number: 8
		The largest number with this property is 27, and it is perhaps of interest that 8 and 27 are themselves cubes.
		Numbers that set records for number of factors are sometimes called "highly composite" numbers (Sloane's A002182).
	home.earthlink.net /~mrob/pub/math/numbers-3.html (2553 words)

	PlanetMath: top ten coolest numbers
		Specifically, the largest known collection of sociable numbers has cardinality 28, and though this might seem a silly feat in and of itself, the fact that sociable numbers and perfect numbers are so closely related may reveal something slightly more profound about 28 than it just being perfect.
		Also contributing to this number's rank on this list is the remarkable properties of the monster group itself, which has been realized (actually, was constructed as) a group of rotations in 196,883-dimensional space, representing in some sense a limit to the amount of symmetry such a space can possess.
		The issue of factorization in quadratic fields, and of number fields in general, is one of the principal driving forces of algebraic number theory, and to be able to pinpoint the end of perfect factorization in the quadratic case like this seems at least arguably fundamental.
	planetmath.org /encyclopedia/TopTenCoolestNumbers.html (2349 words)

	J - Abundance and Perfect Numbers
		Perfect numbers are the numbers whose sum of divisors are twice the number itself.
		For example 28 is a perfect number because the summation of the divisors of 28 is (1+2+4+7+14+28)=56=2*28.
		The first integer is the input number n and the second integer is the value of abun(n).
	acm.uva.es /p/v109/10914.html (212 words)

	Almost perfect number - Wikipedia, the free encyclopedia
		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.
		The only almost perfect numbers known are those of the form 2
		for some natural number k; however, it has not been shown yet that all almost perfect numbers are of this form.
	en.wikipedia.org /wiki/Almost_perfect_number (123 words)

	Sacred Number Theory: The Roots of Numerology
		The student of numbers should be cautioned, however, to understand that striving for balance is very different from striving for equality; the center of gravity is very rarely at the mid-point.
		The perfect nature of the six is born-out by the myths associated with this number.
		On the human level, the number is seen as a counterpart to the number five and is associated with the female.
	theunicornshoppe.com /articles/numbers.htm (1095 words)

	The thought that counts
		Each number had a certain significance attached to it; broadly, the Pythagoreans believed that the world was composed of a series of ten pairs of opposite corresponding to oddness or evenness in numbers - limited/unlimited, right/left, male/female, and so on.
		In Hebrew, as in Greek, numbers were represented by letters of the alphabet, and this may well have stimulated gematria, the Jewish art of turning names into numbers.
		Twelve, for instance, is a number of completeness: there are 12 months in the year, 12 signs of the zodiac, 12 tribes of Israel and, of course, 12 disciples Thirteen is a number of excess - it goes one beyond a number of completeness.
	members.fortunecity.com /templarser/number3.html (2749 words)

	perfect number : Search Results : GoodSearch : Search the Internet with GoodSearch and support your favorite charity or ...
		During this lesson students will learn the definition of a perfect number and use various methods for determining what numbers are perfect.
		A perfect number is defined to be one which is equal to the sum of its...
		parts is less than the number; and perfect numbers which have the property that...
	www.goodsearch.com /Search.aspx?Keywords=perfect+number&page=1 (287 words)

	DVD Review: Almost Normal
		Almost Normal provides an almost perfect example of a film left in the hands of the filmmakers, versus one taken over by the studio.
		A number of promising early scenes showcasing the mistreatment of minorities are quickly glossed over and forgotten about as the film degenerates into the realm of a mindless action thriller.
		Almost Normal most definitely deals with mature themes, and while the film is careful not to show anything overy explicit, there is quite a bit of strong language.
	www.dvddude.net /a_to_z/reviews/almostnormal.php (1567 words)

	About Almost Home Dachshund Rescue Society
		Almost Home Dachshund Rescue Society is a nationwide organization of volunteers that seeks to rescue abandoned, abused, neglected, and unwanted dachshunds and dachshund mixes, provide necessary veterinary and behavioral care for them, and place them in homes where they will be a perfect fit.
		A number of all-breed rescue groups that were founded after AHDRS now use "Almost Home" in their names, and some of their Web site addresses are similar to ours.
		Almost Home is committed to working with other national and regional rescue groups in placing and transporting dogs, as well as offering financial assistance when possible.
	www.almosthomerescue.org /about_ah/about_ah.htm (384 words)

	Almost perfect number - Art History Online Reference and Guide
		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.
		The only almost perfect numbers known are those of the form 2
		for some natural number k; however, it has not been shown yet that all almost perfect numbers are of this form.
	www.arthistoryclub.com /art_history/Almost_perfect_number (110 words)

	Perfect Number
		A "perfect" number is a number whose divisors sum to twice itself.
		Euclid was one of the first to study perfect numbers, although, due to the difficulty of finding such numbers, he only knew of the first four perfect numbers: 6, 28, 496, and 8128.
		In his book Perfect Numbers, Richard Shoemaker defines social numbers "as being a chain of numbers in which each number is equal to the sum of all the proper divisors of the preceding number, the last being considered as preceding the first number of the chain" (page 27).
	math.arizona.edu /~ura/001/gaberdiel.jw (6796 words)

	Perfect Hashing
		It is almost always faster than my perfect hash in -i mode, by 0..3 cycles per character (mostly depending on whether your machine has a barrelshift instruction).
		If perfect hashing is implemented as a special table for Pearson's hash (the usual implementation), minimal perfect hashing is not always possible, with probabilities given in the table below.
		This sorted-table minimal perfect hash might not even be slower than Pearson perfect hashing, since the sorted-table hash must do a comparison per bit of key, while the Pearson hash must do an operation for every character of the key.
	www.burtleburtle.net /bob/hash/perfect.html (2077 words)

	Notable Properties of Specific Numbers at MROB
		Number of fingers on the average human, and many other cultural properties resulting from that or indirectly through other cultural properties (the use of 10 as our base is considered a cultural property).
		Numbers that set records for number of factors are sometimes called "highly composite" numbers.
		numbers which "sound random" or are chosen more often when someone is asked to pick a random number.
	home.earthlink.net /~mrob/pub/numbers-2.html (2188 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.
		Also, any prime factor of a number also divides any exponential divisor of that number, so except for 1, which is augmented exponential perfect but not reduced exponential perfect, there cannot be any augmented or reduced exponential perfect numbers.
	djm.cc /amicable.html (2519 words)

	Occultists Worship Numbers
		Further, the number 6 + 21 = 27, another number of power, because it is formed by the multiplication of 3x9.
		When eleven is multiplied by the perfect number 3, the number 33 is produced, a number of tremendous occult importance.
		Numbers 11 and 22 are sacred primary occult numbers.
	www.cuttingedge.org /pages/seminar2/NUMBERS.htm (1216 words)

	Protestantism: Why 7 is the perfect number
		I`ve been a pastor for almost 30 years in the Lutheran Church and have studied not only the Reformation but also all major denominations including both traditional and Charismatic.
		The number 7 has been peceived as the perfect number because it is the number of completion...when God had finished His work of creation.
		You have come to God, the judge of all men, to the spirits of righteous men made perfect, 24 to Jesus the mediator of a new covenant, and to the sprinkled blood that speaks a better word than the blood of Abel.
	en.allexperts.com /q/Protestantism-3208/7-perfect-number.htm (329 words)

	Finding the Perfect Dog
		Meanwhile, the pet industry needs to move a lot of animals, so it promotes the idea that there's a Perfect Dog for everyone.
		It's the dog that instantly learns to pee outdoors, never menaces or frightens children, plays gently with other dogs, won't jump on the UPS guy, never rolls in gross things, eats only the appropriate food at the right time, and never chews anything not meant for him.
		The peddling of Perfect Dogs amounts to a multibillion dollar business in the United States.
	www.almosthomerescue.org /perfectdog/perfectdog.htm (915 words)

	Big Numbers - Astronomy for Kids
		This number is called an "exponent" and it tells you how to convert a number expressed in scientific notation to one that you are familiar with.
		In our top example, if you move the decimal point in the number to the right of the equals sign twelve places over (the exponent is 12), you will get the number to the left of the equals sign.
		When we start talking about a light year, which is almost six trillion miles, our eyes kind of glaze over and the number becomes a concept instead of a real number.
	www.dustbunny.com /afk/skywonders/bignumbers (880 words)

	Perfect number - Wikipedia, the free encyclopedia
		[1] Also, it has been conjectured that there are no odd Ore's harmonic numbers.
		If true, this would imply that there are no odd perfect numbers.
		Pace P. Nielsen, "An upper bound for odd perfect numbers," Integers, vol.
	en.wikipedia.org /wiki/Perfect_number (1476 words)

	Math Forum - Ask Dr. Math Archives: College Number Theory (Site not responding. Last check: 2007-09-23)
		Apparently almost any number can be made into a palindromic number by reversing the digits and adding and then repeating the steps until you get a palindromic number.
		An antifirst number is a number with more divisors than every number before it.
		Is it possible to find a formula that takes X (a large number) and creates another expression which equals X but is shorter in length than X? For example, take 390,625 which uses six characters.
	mathforum.org /library/drmath/sets/college_number_theory.html (965 words)

	Puzzle 111. Spoof odd Perfect numbers
		The method for finding such numbers is similar to the method for finding multiperfect numbers: Write down a small composite number (spoof prime factor) p and above it write down p+1.
		I have found number of solutions(29 which are less than 410^11) with 7 composite factors like 172368000=46891475*95.
		In return to my invitation Shyam asks to look for odd and completely spoof perfect numbers or at least bounds below which such a number can not exist; but he believes that there are none.
	www.primepuzzles.net /puzzles/puzz_111.htm (575 words)

	The Almost Perfect Definition
		There were 53 men and 53 women perfectionists and an equal number of non-perfectionists.
		However, this anxiety could be caused by any number things; it was not considered as unique and central to perfectionism.
		This discrepancy factor is now a part of the Almost Perfect Scale-Revised, an updated version being investigated by Slaney, Ashby, Joseph Trippi of Landy Jacobs & Associates consulting firm, and Penn State doctoral student Michael Mobley.
	www.rps.psu.edu /sep96/almost.html (2248 words)

	The Perfect Stall
		Now I use one of the lightweight electric tillers, such as what I recommended for use with Equidry, only it is not necessary to take off the sharp tines and replace them with blunt paddles.
		For the STP bed, the original tines are perfect.
		To work best (and to be healthier for your horses, no matter what bedding you use), at least one dimension of the stall must be 20 feet, and your horses should be outside at least 12 hours per day, preferably longer (for their own health).
	www.theperfectstall.com /blog (1052 words)

	Fibonacci (Site not responding. Last check: 2007-09-23)
		A perfect number is an integer for which the sum of its proper divisors is equal to the number itself.
		The sum of those numbers is 7, so 8 cannot be considered perfect.
		However, it is termed as being a deficient number because the sum (7) is less than the number itself (8).
	www.saintjoe.edu /~kbi4571/Fibonacci.html (370 words)

	ALMOST PERFECT by W. E. Peterson
		After agonizing over the definitions for a few months, I finally came to the conclusion that a goal was a desired result you could measure, while an objective was something desired that was easier to visualize or describe than to measure.
		By this definition, reaching $100 million in sales or scoring a touchdown were goals, because they involved reaching a particular number or c rossing a certain line.
		Although competitors are almost always civil and courteous to one another, at the same time they are at each other's throats.
	www.fitnesoft.com /AlmostPerfect/ap_chap08.shtml (5034 words)

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