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Topic: Highly abundant number

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	What's Special About This Number?
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is the number of planar partitions of 12.
	www.stetson.edu /~efriedma/numbers.html (7305 words)

	Springer Online Reference Works
		» Encyclopaedia of Mathematics » A »; Abundant number
		Dickson (1913, [a6]) called a non-deficient number primitive abundant if it is not a multiple of a smaller non-deficient number.
		Erdős [a7] stating that the sum of reciprocals of primitive abundant numbers converges.
	eom.springer.de /A/a130070.htm (740 words)

	Abundant number - Wikipedia, the free encyclopedia
		In mathematics, an abundant number or excessive number is a number n for which σ(n) > 2n.
		Marc Deléglise showed in 1998 that the natural density of abundant numbers is between 0.2474 and 0.2480.
		An abundant number which is not a semiperfect number is called a weird number; an abundant number with abundance 1 is called a quasiperfect number.
	en.wikipedia.org /wiki/Abundant_number (288 words)

	Highly abundant number - Wikipedia, the free encyclopedia
		In mathematics, a highly abundant number is a certain kind of natural number.
		The first few highly abundant numbers are 1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60,...
		All integer values of the factorial are highly abundant numbers, as are all colossally abundant numbers.
	en.wikipedia.org /wiki/Highly_abundant_number (108 words)

	Wikinfo \| Highly composite number
		Roughly speaking, the necessary conditions for a number to be a highly composite number are that it has prime factors that are as small as possible, but not too many of the same: e.g.
		Highly composite numbers higher than 6 are also abundant numbers.
		Many of these numbers are used in traditional systems of measurement, and tend to be used in engineering designs, due to their ease of use in calculations involving fractions.
	www.wikinfo.org /wiki.php?title=Highly_composite_number (405 words)

	Colossally abundant number - Wikipedia, the free encyclopedia
		In mathematics, a colossally abundant number (sometimes abbreviated as CA) is a certain kind of natural number.
		The first few colossally abundant numbers are 2, 6, 12, 60, 120, 360, 2520, 5040,...
		Keith Briggs on colossally abundant numbers and the Riemann hypothesis
	en.wikipedia.org /wiki/Colossally_abundant_number (235 words)

	Superabundant number - Wikipedia, the free encyclopedia
		In mathematics, a superabundant number (sometimes abbreviated as SA) is a certain kind of natural number.
		The first few superabundant numbers are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120,...
		It can also be shown that all superabundant numbers are Harshad numbers.
	en.wikipedia.org /wiki/Superabundant_number (163 words)

	Brazil - Wikipedia, the free encyclopedia
		These figures may be a serious undercounting of the actual numbers of immigrants, since the spouses were often not counted; there were large numbers of illegals never counted; the family names were changed to hide national origins; and Brazilian record-keeping was slipshod.
		Poverty in Brazil is most visually represented by the various favelas, a great number of slums in the country's metropolitan areas and in upcountry remote regions with low rates of economic and social development.
		Italian and German immigrants came in large numbers and their influences are felt closer to the South of Brazil.
	en.wikipedia.org /wiki/Brazil (4949 words)

	Math Forum Discussions
		abundant number n such that n > n_0, n has a prime factor > m.
		This contradicts the assumption that n is highly abundant.
		Theorem 2: The largest highly abundant number that is odd is 3.
	www.mathforum.org /kb/thread.jspa?threadID=79666&messageID=372995 (403 words)

	Colossally abundant number - Encyclopedia, History, Geography and Biography
		Formally, a number n is colossally abundant iff there is an ε > 0 such that for all k > 1,
		Colossally abundant numbers are related to the Riemann hypothesis.
		Colossally abundant number, Properties, Relation to the Riemann hypothesis, See also and Integer sequences.
	www.arikah.com /encyclopedia/Colossally_abundant_number (143 words)

	Highly abundant number - Encyclopedia, History, Geography and Biography
		Highly abundant number - Encyclopedia, History, Geography and Biography
		This encyclopedia, history, geography and biography article about Highly abundant number contains research on
		Highly abundant number, See also and Integer sequences.
	www.arikah.com /encyclopedia/Highly_abundant_number (124 words)

	The On-Line Encyclopedia of Integer Sequences
		Colossally abundant numbers: n for which there is a positive exponent epsilon such that sigma(n)/n^{1 + epsilon} >= sigma(k)/k^{1 + epsilon} for all k > 1, so that n attains the maximum value of sigma(n)/n^{1 + epsilon}.
		All superabundant, colossally abundant, highly composite and superior highly composite numbers are Niven/Harshad numbers.
		abundant numbers = A002093, A002182, A005101, A006038, A004394; colossally abundant numbers = A004490, highly abundant numbers = A002093, superabundant numbers = A004394.
	www.research.att.com /~njas/sequences/A004490 (206 words)

	The Number Four and the Covenant
		Thus, the number four is symbolic of the square and it conveys a message of building, of exactness, and of trueness.
		The symbology of the number four and of the square is ancient.
		Of all the numbers, it is the number four that best demonstrates an intrinsic capacity for stability; three can be lacking, whereas five is superfluous.
	members.aol.com /DrNewKnee/numbers/4.htm (2988 words)

	Short-eared Owl Fact Sheet
		Their breeding sites, the number of wintering birds, the number of nesting pairs, and the number of eggs or young may change from year to year based on the food supply.
		When food is abundant they may form large communal roosts of up to 200 birds in sheltered sites ranging from conifers to stump piles to abandoned quarries.
		Northern populations are believed to be highly migratory, and there is a marked increase in the number of birds in New York in the fall and spring.
	www.dec.state.ny.us /website/dfwmr/wildlife/endspec/seowfs.html (999 words)

	Lake information report: Minnesota DNR
		Northern pike were less abundant, but larger than in the 1989 survey; however, both the number of pike and their size were above average for this lake type.
		Largemouth bass numbers and size from electrofishing were below average for the area and their growth was slow; however, the lake is difficult to sample and bass may be more abundant than these results indicate.
		In contrast, bluegill were highly abundant in the 2001 survey and higher than all previous surveys.
	www.dnr.state.mn.us /lakefind/showreport.html?downum=71006900 (490 words)

	China - QuickSeek Encyclopedia (Site not responding. Last check: 2007-10-21)
		China is composed of a vast variety of highly different landscapes, with mostly plateaus and mountains in the west, and lower lands on the east.
		In terms of numbers, however, the pre-eminent ethnic group in China is the Han, which is a group so diverse in its culture and language that some conceive of it as a larger overarching group bringing together many smaller, distinct ethnic groups sharing common traits in language and culture.
		Falun Gong - exact numbers unknown (claimed not to be a "religion", though from a scholarly perspective is a spiritual practice.
	china.quickseek.com (11242 words)

	The Number Seven and Sanctification
		In nearly all cultures the number seven is regarded as lucky, magical, mystical, or enchanted.
		Since the number seven symbolizes perfection, and since the number six is symbolic of man, man was created one less than perfection.
		The second diaspora began 70 A.D. The double occurrence of the number seventy in relationship to the diaspora again implies that this was a consequence for failure of sabbath observance.
	users.aol.com /DrNewKnee/numbers/7.htm (2446 words)

	Voices from Africa
		Given the Masai's large open tracts of land, abundant plant and animal wildlife, and their rich and much-romanticised culture, it was almost inevitable that they would be targeted by large-scale tourism.
		Often overlooked is the fact that ecotourism is a highly consumer- centred activity catering to the lifestyles of the new urbanized middle-class societies.
		As a result, the forest is still dense and rich in biodiversity, with abundant wild flora and fauna, plants which serve as herbal medicines, sufficient water sources, and pastures on which to raise healthy cattle.
	www.unsystem.org /ngls/documents/publications.en/voices.africa/number6/vfa6.12.htm (2272 words)

	Earthtoys - Emagazine
		Even though many fuel cell related stocks are down 70 to 90 percent from their peak in early 2000 they still have fairly large market caps and therefore could still be judged to be overvalued.
		There are a number of problems that must be solved involving storing the hydrogen effectively (cost, weight, space and safety) to fit in an automobile that are not factors in a building or home.
		He was the contributing editor for the past 17 years to the Photovoltaic Insider Report, the leading publication in PV that was directed at industrial subscribers, such as major energy companies, utilities and governments around the world.
	www.earthtoys.com /emagazine.php?issue_number=05.02.01&article=hydrogen (2078 words)

	Perfect Number (Site not responding. Last check: 2007-10-21)
		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.
		A 'deficient' number is, as one might guess, a number whose proper divisors sum to less than twice itself.
		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)

	Coral Reef - MSN Encarta
		Because their skeletons are made of limestone, corals leave clear and abundant fossils.
		Reefs are highly productive resources for human beings.
		A number of important groups of marine plants known as algae also lay down limestone.
	encarta.msn.com /encyclopedia_761572186/Coral_Reef.html (1448 words)

	math lessons - Category:Number theory (Site not responding. Last check: 2007-10-21)
		Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers and contains many open problems that are easily understood even by non-mathematicians.
		More generally, the field has come to be concerned with a wider class of problems that arose naturally from the study of integers.
		Number theory may be subdivided into several fields according to the methods used and the questions investigated.
	www.mathdaily.com /lessons/Category:Number_theory (102 words)

	WHO \| Avian influenza frequently asked questions
		The role of migratory birds in the spread of highly pathogenic avian influenza is not fully understood.
		In the past, highly pathogenic viruses have been isolated from migratory birds on very rare occasions involving a few birds, usually found dead within the flight range of a poultry outbreak.
		The severity of disease and the number of deaths caused by a pandemic virus vary greatly, and cannot be known prior to the emergence of the virus.
	www.who.int /entity/csr/disease/avian_influenza/avian_faqs/en (3533 words)

	EPA-MAIA - Maryland Case Study (Site not responding. Last check: 2007-10-21)
		The large number of plots constituting the composite sample and the fixed count of 100 organisms for establishing IBI scores appears to characterize a stream segment fairly accurately.
		The number of plots sampled in each stream segment, and the number of organisms subsampled for identification in the lab, affects the precision in estimates of species richness and in particular the likelihood of detecting rare species.
		However, the total number of fish captured with two passes was highly correlated with the total from three passes (Figure 3-19).
	www.epa.gov /emfjulte/tpmcmaia/html/biomd3d.html (2742 words)

	AT&T Worldnet Service - Directory
		These are numbers where an expression can be given using the operations of addition and squaring, using the digits of a number in order, which gives the original number.
		Uses gematria to calculate the number of the beast, and evaluates what it may mean w/r specific Hebrew words and names in the Bible adding up to 666.
		Published as math.NT/0006089, this note investigates numbers that are normal to no base whatsoever, and writes down explicitly such a number.
	www.att.net /cgi-bin/webdrill?catkey=gwd/Top/Science/Math/Recreations/Specific_Numbers (679 words)

	Highly abundant number
		The special issues of highly gifted children are examined and a series of recommendations for the placement and education of highly gifted children in full inclusion classrooms are made.
		Reviews the occurrences of the number forty in the Bible, where it is second to the number seven in its frequency of occurrence.
		It is highly irritating to the skin, eyes, nose, throat, and lungs and it is a carcinogen.
	www.omniknow.com /common/wiki.php?in=en&term=Highly_abundant_number (1742 words)

	Superior Highly Composite Number -- from Wolfram MathWorld
		A superior highly composite number is a positive integer
		The first few superior highly composite numbers are 2, 6, 12, 60, 120, 360, 2520, 5040, 55440,...
		SEE ALSO: Abundant Number, Colossally Abundant Number, Highly Composite Number, Round Number, Smooth Number.
	mathworld.wolfram.com /SuperiorHighlyCompositeNumber.html (140 words)

	ATP Project Brief - 00-00-5940
		The company intends to develop a standard process with a limited number of steps for producing all these devices on the same integrated circuit wafer, while maintaining the required performance in each device.
		In addition to size and cost reductions, the proposed front end is expected to offer up to a 10-fold increase in efficiency, thereby extending the life of batteries or other power sources.
		The ultimate objective is to combine the passive component chip with an active signal-processing chip to make a receiver that operates at 0.4 to 2.5 gigahertz, encompassing the frequencies used by cell phones.
	jazz.nist.gov /atpcf/prjbriefs/prjbrief.cfm?ProjectNumber=00-00-5940 (395 words)

	Checks on Population Growth
		An alternative to limiting the number of offspring per pair of parents is to limit the number of parents.
		The house finch, Carpodacus mexicanus, — native to western North America — is a recent immigrant to the eastern United States where it is parasitized by a mycoplasma that reduces the lifespan and fecundity of the birds.
		Producing smaller numbers of larger lizards, they were more successful at leaving surviving offspring to lay the groundwork for the next boom year.
	users.rcn.com /jkimball.ma.ultranet/BiologyPages/P/Populations2.html (3620 words)

	The Search for Extraterrestrial Intelligence: Scientific American
		It is possible that the number of individual steps required for the evolution of intelligence and technology is so large and improbable that not all inhabited planets evolve technical civilizations It is also possible-some would say likely-that civilizations tend to destroy themselves at about our level of technological development.
		It is obviously a highly uncertain exercise to attempt to estimate the number of such civilizations.
		The number of other plausible and available communication channels is not large, so that determining the right one should not be too difficult.
	www.sciam.com /article.cfm?articleID=000B35F3-A4B2-1C59-B882809EC588ED9F&pageNumber=3&catID=9 (793 words)

	SCREEN IT! ARTISTIC REVIEW: LUCKY NUMBER SLEVIN
		And while it has its share of design flaws -- including trying a bit too hard to be clever in a way that ultimately draws attention to itself -- this crime caper turns out to be a fairly entertaining diversion for viewers who don't mind the Tarantino-esque blend of violence, bloodshed, language and more.
		The film starts out with a number of quick murders before settling in on Bruce Willis appearing in a wheelchair and commenting on the Kansas City Shuffle that, in this case, has been in the making for twenty years.
		Slathered in abundant hip style, the it looks great and moves along at a good clip, thus allowing the terrific cast -- that also includes Stanley Tucci and Robert Forster -- to have fun running with the material and their slightly over the top characters.
	www.screenit.com /ourtake/2006/lucky_number_slevin.html (958 words)

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