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Topic: Highly composite number

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Composite number

	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 (7362 words)

	Wikipedia: Two
		Despite being a prime, two is also a highly composite number, because it has more divisors than one.
		Taking the square root of a number is such a common mathematical operation, that the spot on the root sign where the exponent would normally be written for cubic roots and other such roots, is left blank for square roots, as it is considered tacit.
		The number 2 is sometimes used as a shorthand for "to".
	www.factbook.org /wikipedia/en/t/tw/two.html (506 words)

	Highly composite number - Wikipedia, the free encyclopedia
		The sequence of highly composite numbers is a subset of the sequence of smallest numbers k with exactly n divisors (sequence A005179 in OEIS).
		Roughly speaking, for a number to be a highly composite it has to have prime factors as small as possible, but not too many of the same.
		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 vulgar fractions.
	en.wikipedia.org /wiki/Highly_composite_number (636 words)

	Six
		Six is the second smallest composite number, its proper divisors being 1, 2 and 3.
		A solid with six faces is a hexahedron (of which the cube is a special case).
		Number Six was the main character in the television series The Prisoner.
	www.ebroadcast.com.au /lookup/encyclopedia/nu/Number_6.html (155 words)

	PlanetMath: highly composite number
		The first several superior highly composite numbers are 2, 6, 12, 60, 120, 360.
		Alaoglu and P. Erdös, On highly composite and similar numbers.
		This is version 4 of highly composite number, born on 2003-06-11, modified 2006-12-08.
	planetmath.org /encyclopedia/HighlyCompositeNumber.html (84 words)

	PlanetMath: primorial
		Any highly composite number (with the exception of 1) can be expressed as a product of primorials in at least one way.
		highly cototeint numbers congruence conjectures by Lando47 on 2006-12-01 13:07:00
		Whit the exception of the small ones, all highly cototient numbres are congruent to -1 modulus a primorial.
	planetmath.org /encyclopedia/Primorial.html (262 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)

	Upto11.net - Wikipedia Article for 6 (number) (Site not responding. Last check: 2007-11-01)
		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.upto11.net /generic_wiki.php?q=6 (1040 words)

	Four
		Four is the smallest composite number, its proper divisors being 1 and 2.
		Three are not always sufficient; 7 for instance cannot be written as the sum of three squares.
		Four (四 pinyin si4) in considered an unlucky number in Chinese culture because it sounds like the word "death" (死 pinyin si3).
	www.ebroadcast.com.au /lookup/encyclopedia/fo/Four.html (186 words)

	Versatile Numbers-Versatile Economics
		The versatile numbers are 36, 24 and 12.
		The term "highly composite" might be descriptive to someone trained in mathematics, however, I believe the term “versatile” is simpler yet still descriptive, and should be used in order to communicate to the largest number of people the character and usefulness of these numbers.
		Versatile Numbers: 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840,...
	www.earth360.com /math-versatile.html (10098 words)

	Highly Composite Numbers (Site not responding. Last check: 2007-11-01)
		Highly composite numbers have sparked a number of interesting observations, some of which I will elaborate on here.
		In round numbers, for a given number of factors of H, H is minimized when the ratio of one plus the exponents of 2 and 3 is close to ln(3):ln(2), or about 1.585.
		Looking at Flammenkamp's table of HCNs, we see this exponent ratio fluctuate from 1 to more than 2, but the geometric mean of this ratio over all 1200 HCNs is 1.58946, which is very close to the expected value of 1.585.
	mcraeclan.com /mathhelp/BasicNumberFactorsHighlyComposite.htm (1545 words)

	Upto11.net - Wikipedia Article for 12 (number) (Site not responding. Last check: 2007-11-01)
		Twelve is a composite number, its proper divisors being 1, 2, 3, 4 and 6.
		The number twelve is often used as a sales unit in trade, and is often referred to as a dozen.
		In Greek mythology, the number of labours of Heracles (Hercules).
	www.upto11.net /generic_wiki.php?q=12 (941 words)

	Notable Properties of Specific Numbers at MROB
		Psychologically random numbers are usually odd and don't end in 5, because there is a natural psychological bias to thinking even numbers and numbers that end in 5 are "less random".
		This is an example of the type of property that is often reported for cult numbers like 23 and psychologically random numbers like 37, because it is often desirable to find as many properties of such numbers as possible.
		The smallest number with this property is 8, and it is perhaps of interest that 8 and 27 are themselves cubes.
	home.earthlink.net /~mrob/pub/math/numbers-4.html (2991 words)

	Wikipedia: Six
		Six is also a harmonic divisor number and a highly composite number.
		Bands with the number six in their name include Eve 6 and Sixpence None the Richer.
		Six similar coins can be arranged around a central seventh of the same kind so that each makes contact with the central one and touches both its neighbours without a gap.
	www.factbook.org /wikipedia/en/s/si/six.html (558 words)

	Prime number - ExampleProblems.com
		A natural number that is greater than one and is not a prime is called a composite number.
		Prime numbers are of fundamental importance in number theory.
		The prime number theorem says that the proportion of primes less than x is asymptotic to 1/ln x (in other words, as x gets very large, the likelihood that a number less than x is prime is inversely proportional to the number of digits in x).
	www.exampleproblems.com /wiki/index.php/Prime_number (3311 words)

	Highly composite numbers
		A natural number n is called highly composite, if it has more divisors than any smaller number.
		Here is a list of the first 1200 highly composite numbers computed 1991-10-31 on a HP 710/50 MHz.
		Because for the 97-th HCN we got the same, it seems that there is a HCN missing from Donald Siano's program!.
	wwwhomes.uni-bielefeld.de /achim/highly.html (605 words)

	composite number
		If a positive integer is not composite (4, 6, 8, 9, 10, 12,...) or one, then it is a prime number (2, 3, 5, 7, 11, 13, 17,...).
		But more basic to a mathematician is that this problem has always been central to number theory.
		Numbers that, for their size, have a lot of factors are sometimes referred to as highly composite numbers.
	www.daviddarling.info /encyclopedia/C/composite_number.html (158 words)

	Station Information - Two
		Two is also a highly composite number, even though it is prime rather than composite.
		Two is a Fibonacci number and a primorial, as well as its own factorial.
		See also: zero, one, two, three, four, integer, list of numbers.
	www.stationinformation.com /encyclopedia/t/tw/two.html (336 words)

	Superior highly composite number - Wikipedia, the free encyclopedia
		In mathematics, a superior highly composite number is a certain kind of natural number.
		Formally, a natural number n is called superior highly composite iff there is an ε > 0 such that for all natural numbers k ≥ 1,
		The first few superior highly composite numbers are 2, 6, 12, 60, 120, 360, 2520,...
	en.wikipedia.org /wiki/Superior_highly_composite_number (152 words)

	Some are born with the ability to tell a whole story with one picture and others the ability to paint a picture with a ...
		The Bernoulli numbers, named for the Swiss mathematician Jacob Bernoulli, were directly related to the coefficients of the Eulerian constant when stated in an infinite series.
		Ramanujan also worked with numbers that, as Hardy had put it, "were as far from prime numbers as possible." Where prime numbers have the fewest factors possible, itself and one, highly composite numbers had more prime factors than any number less than it.
		The first few highly composite numbers were 2, 4, 6, 12 24, 36, 48, 60, 120 and so on.
	www.math.ucla.edu /~rfioresi/hc41/Ramanujan.html (3495 words)

	Universal number names in SHOL numeration
		The universal number names in the SHOL* numeration
		The highly composite number: 10080, of course also highly composite in Base
		Similarly, the Golden ratio number φ ≈ B.
	hexadecimal.florencetime.net /universal_hexadecimal_number_names.htm (92 words)

	Why is the number 13 superstitious?
		Thirteen may be considered a "bad" number simply because it is one more than 12, which is a popularly used number in many cultures (possibly due to it being a highly composite number).
		According to another interpretation, the number 13 is unlucky because it is the number of full moons in a year.
		The fear of women's connection to the moon, as well as the association of the full moon with mental disorders has, according to this theory, caused the number to be seen as bad luck, and connected to supernatural forces.
	www.funtrivia.com /askft/Question73239.html (439 words)

	Number Theory (Site not responding. Last check: 2007-11-01)
		In a puzzle website, a "highly composite number" is one that has more factors than any smaller number.
		This is proved using the discriminant of a cleverly devised quadratic equation.
		AM-GM Inequality is that the arithmetic mean of a set of positive numbers is always less than or equal to their geometric mean.
	mcraefamily.com /MathHelp/BasicNumberTheory.htm (188 words)

	beebs1000's Xanga Site
		It is the square of 6 as well as a triangular number, making it a triangular square number, and also the only triangular number whose square root is also a triangular number.
		This number is the sum of a twin prime (17 + 19), and the sum of the cubes of the first three integers.
		The Saros number of the solar eclipse series which began on 1859 BC June 23 and ended on -561 August 11.
	www.xanga.com /beebs1000 (1483 words)

	Wikinfo \| Four
		The four Greek classical elements are fire, air, water, and earth.
		The number of strings on a violin, a viola, a cello and a double bass.
		Images, some of which are used under the doctrine of Fair use or used with permission, may not be available.
	www.wikinfo.org /wiki.php?title=four (354 words)

	The On-Line Encyclopedia of Integer Sequences
		Highly composite numbers, definition (1): where d(n), the number of divisors of n (A000005), increases to a record.
		Highly composite numbers are the product of primorials, A002110.
		J. Nicolas and G. Robin, Highly Composite Numbers by Srinivasa Ramanujan, The Ramanujan Journal, Vol.
	www.research.att.com /~njas/sequences/A002182 (429 words)

	Untitled Document
		The Partridge number of the 30-60-90 triangle is 4.
		Patrick found that the partridge number of a different shape is 6.
		The numbers after the title refers to the number of the puzzle in The Listener Crossword series.
	www.mathpuzzle.com /26Aug2002.htm (2543 words)

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