
	Where results make sense

Topic: Highly totient number

Related Topics

24 (number)

Totient function

20 (number)

19 (number)

42 (number)

27 (number)

12 (number)

Integer

List of numbers

In the News (Mon 6 Oct 08)

Eli Manning

Josh Beckett

Sage Rosenfels

South Ossetia

Super League

Angelina Jolie

West Bengal

Wayne Rooney

Howard Stern

Beth Ostrosky

	TeluguPeople.com - Articles (Site not responding. Last check: 2007-11-04)
		22 is the number of partitions of 8.
		101 is the number of partitions of 13.
		231 is the number of partitions of 16.
	www.telugupeople.com /discussion/article.asp?id=24159 (16335 words)

	12 (number) - Encyclopedia, History, Geography and Biography
		Twelve is a composite number, the smallest number with exactly six divisors, its proper divisors being 1, 2, 3, 4 and 6.
		Twelve is the number of pitch classes in an octave, not counting the duplicated (octave) pitch.
		In Greek mythology, the number of labours of Heracles (Hercules).
	www.arikah.net /encyclopedia/12th (1547 words)

	Highly totient number - Wikipedia, the free encyclopedia
		The sequence of highly totient numbers is a subset of the sequence of smallest number k with exactly n solutions to φ(x) = k.
		The concept is somewhat analogous to that of highly composite numbers, and in the same way that 1 is the only odd highly composite number, it is also the only odd highly totient number (indeed, the only odd number to not be a nontotient).
		And just as there are infinitely many highly composite numbers, there are also infinitely many highly totient numbers, though the highly totient numbers get tougher to find the higher one goes, since calculating the totient function involves factorization into primes, something that becomes extremely difficult as the numbers get larger.
	en.wikipedia.org /wiki/Highly_totient_number (263 words)

	Numbers (Site not responding. Last check: 2007-11-04)
		1449 is a stella octangula number an automorphic number.
		840 is the smallest number divisble by 1
		630 is the number of degree 499 is the smallest number with the property 275 is the number of partitions of 28
	numbers.greatphonebook.net /numbers.html (1631 words)

	1000 (number) - Biocrawler (Site not responding. Last check: 2007-11-04)
		1001 - sphenic number, pentagonal number, pentatope number
		1440 - a highly totient number, square pyramidal number and a 481-gonal number.
		1540 - triangular number, hexagonal number, decagonal number, tetrahedral number
	www.biocrawler.com /encyclopedia/Thousand (929 words)

	Highly Composite Numbers (Site not responding. Last check: 2007-11-04)
		Highly composite numbers have sparked a number of interesting observations, some of which I will elaborate on here.
		Together, these two prime numbers "contribute" xy factors of H. Now, let's further suppose that the contribution of these two primes is a constant, a, and that xy=a.
		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.
	mcraefamily.com /MathHelp/BasicNumberFactorsHighlyComposite.htm (1545 words)

	PrimeFan's Listing of Esoteric Integer Sequences
		When a highly totient number is followed by that prime, that prime will obviously be the smallest totient answer for that particular highly totient number.
		Smallest composite number such that the previous n - 1 integers have the property that the list of smallest prime factors not in common with a smaller number of the set is the set of the first n prime numbers.
		Numbers that are quasi-strobogrammatic (read like a different number upside down, but still a valid one in the representational scheme) in base 10 written in ASCII using a Base 14 font such as Times New Roman or Courier New.
	www.geocities.com /primefan/EsotericIntegerSequences.html (4668 words)

	math lessons - Category:Number theory
		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)

	[No title] (Site not responding. Last check: 2007-11-04)
		A Summary of Important Facts and Theorems in Elementary Number Theory Michael Misamore, 2001 A note on notation Summations are written as: sigma(i = lower to upper, expression) where lower is the lower index of summation, upper is the terminal index, and expression is the form of the terms to be summed.
		Perfect Numbers --------------- We now introduce the notation sigma(n) as the sum of the divisors of n; that is, the sum of those integers less than or equal to n that divide n.
		Since we may independently choose which power of each distinct prime factor occurs in a divisor, the total number of divisors of n is tau(n) = pi(i = 1 to r, a_i + 1) since the number of ways to choose a given divisor is (a_1 + 1)(a_2 + 1)(a_3 + 1)...(a_r + 1).
	userpages.umbc.edu /~mmisam1/doc.elemnum.txt (4025 words)

	1000_(number) info here at en.after-gasoline-alley.info (Site not responding. Last check: 2007-11-04)
		1000 (number) In mathematics In mathematics The decimal representation for hundred is a one superseded by nine zeroes.
		The year 1000 is the meanest year of achievement of the number millennium AD.
		In the decimal enlargement of e the number allotment outright 10 digits expose in sequence starts at the 1729th decimal place.
	en.after-gasoline-alley.info /1000_(number) (462 words)

	Highly cototient number - Wikipedia, the free encyclopedia
		It has been suggested that highly cototient prime be merged into this article or section.
		In number theory, a branch of mathematics, a highly cototient number k is an integer that has more solutions to the equation
		Just as there are infinitely many highly composite numbers, there are also infinitely many highly cototient numbers.
	en.wikipedia.org /wiki/Highly_cototient_number (248 words)

	GNU Emacs Calc 2.02 Manual: Scientific Functions
		Calc's random number generator uses several methods to ensure that the numbers it produces are highly random.
		When Calc's random number generator is first invoked, it "seeds" the low-level random sequence using the time of day, so that the random number sequence will be different every time you use Calc.
		If the number is a non-integral real number, the generalized factorial is used, as defined by the Euler Gamma function.
	www.xemacs.org /Documentation/packages/html/calc_11.html (3946 words)

	Euler's totient function - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab2.netlab.uky.edu) (Site not responding. Last check: 2007-11-04)
		In number theory, the totient φ(n) of a positive integer n is defined to be the number of positive integers less than or equal to n and coprime to n.
		The totient is usually called the Euler totient or Euler's totient, after the Swiss mathematician Leonhard Euler, who studied it.
		The totient function is important mainly because it gives the size of the multiplicative group of integers modulo n.
	en.wikipedia.org.cob-web.org:8888 /wiki/Euler's_totient_function (737 words)

	How to find primes and prove primality (merged version)
		For example, to find all the odd primes less than or equal to 100 we first list the odd numbers from 3 to 100 (why even list the evens?) The first number is 3 so it is the first odd prime--cross out all of its multiples.
		Repeat with 7 and then since the first number left, 11, is larger than the square root of 100, all of the numbers left are primes.
		Though Carmichael number are 'rare' (only 2,163 are less that 25,000,000,000), it has recently been shown that there are infinitely many [AGP94].
	primes.utm.edu /prove/merged.html (6842 words)

	100000 (number) info here at en.my-widgets.com (Site not responding. Last check: 2007-11-04)
		If you look closely at resource boxes, youll 100000 (number) that they all contain an 100000 (number) link back to the authors website.
		This link is 100000 (number) up by popular 100000 (number) engines like 100000 (number) and Altavista, and actually helps to improve your sites ranking in 100000 (number) results.
		Of 100000 (number) the links on their own also generate traffic, as readers who like the content of your article are 100000 (number) to click on the link to see the rest of your site.
	en.my-widgets.com /100000_(number) (314 words)

	100000 - The real meaning from Timesharetalk wikipedia (Site not responding. Last check: 2007-11-04)
		One hundred thousand (100000) is the natural number following 99999 and preceding 100001.
		In piphilology, one hundred thousand is the current world record for the number of digits of pi memorized by a human being.
		107777 - smallest natural number requiring 16 syllables in American English, 18 in British English
	www.timesharetalk.co.uk /wiki.asp?k=100000 (294 words)

	Home > Ronkonkoma, New York, NY, 11749, Ronkonkoma Real Estate, Ronkonkoma Yellow Pages, Ronkonkoma Classifieds, ... (Site not responding. Last check: 2007-11-04)
		The number twelve is often used as a sales unit in trade, and is often referred to as a
		It is possible to construct a perfect circle divided into twelve sectors of 30 degrees each, using only a compass and straightedge.
		The number of the -2680 -1129 number of the -2360 -1062 The Church of Jesus Christ of Latter-day Saints, there is a twelve-tone technique (also dodecaphony) is a method of musical
	www.ronkonkomanyus.com /topic/12_(number) (487 words)

	GNU Emacs Calc 2.02 Manual - Scientific Functions
		See section Numeric Prefix Arguments, for a discussion of the effect of numeric prefix arguments on commands in this chapter which do not otherwise interpret a prefix argument.
		where m and @c{$\sigma$} s are both real numbers, the result uses a Gaussian distribution with mean m and standard deviation @c{$\sigma$} s.
		This method generates a pair of Gaussian random numbers at a time, so only every other call to
	www.math.utah.edu /docs/info/calc_9.html (3975 words)

	Mathematics Archives - Topics in Mathematics - Number Theory
		Elementary Number Theory, Lucas' Theorem, Pascal's triangle via cellular automata, Bernoulli numbers and polynomials, Theorems of Morley and Emma Lehmer and their generalizations, Some useful p-adic numbers
		Number theory, computer algebra system, algebraic number fields, software
		Divisibility and primes, Euclidean algorithm, Euler's theorem, Representation of numbers, Bertrand's postulate
	archives.math.utk.edu /topics/numberTheory (675 words)

	Donation Draw Happening THURSDAY Night! \| Gamers With Jobs
		The drawing will be held by "Random Number Generator" who is a lesser know but crucially important member of our team.
		It is a Harshad number in every base from binary to decimal.
		There are 49 solutions to the equation φ(x) = 720, more than any integer below it, making 720 a highly totient number.
	www.gamerswithjobs.com /node/27383 (1119 words)

	What's New on the Mathematics Archives
		GAP, Listing of all groups of order 64, presentations, elements with their orders, number of conjugacy classes, nilpotency class, centre and commutator subgroup, automorphism and inner automorphism group and the lower central series.
		Collection of articles, Zeno's Paradox of Motion, Archimedes and the Square Root of 3, Bertleson's Number, Euclid's Plan and Proposition 6, Legendre's Prime Number Conjecture, Mayan Numeration, The Dullness of 1729, The Helen of Mathematics, Berkeley and the Infidel, Newton's Birth Date and the Anni Mirabiles, etc.
		Mathwise modules are based on the SEFI (European Society for Engineering Education) syllabus, comprising mathematical topics taught in pre-university and first year university, together with a number of key topics in second-year university Science and Engineering courses.
	archives.math.utk.edu /whatsnew/mar00.html (3099 words)

	On sparsely totient numbers., D. W. Masser, P. Shiu
		On sparsely totient numbers., D. Masser, P. Shiu
		[1] L. Alaoglu and P. Erdos, On highly composite and similar numbers, Trans.
		[4] L.-K. Hua, Introduction to Number Theory, Springer-Verlag, Berlin-Heidelberg-New York 1982.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.pjm/1102702441 (113 words)

	Mathematical Food for Thought
		Math Books A list of math books that I highly recommend to problem solvers.
		Art of Problem Solving Forum The largest online math community in the world.
		By the looks of this problem, Euler’s Totient Theorem might come in handy again.
	wangsblog.com /jeffrey/?p=54 (262 words)

Try your search on: Qwika (all wikis)