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218 (number)
218 (two hundred ndeighteen) is the natural number following 217 and preceding 219. In mathematics *Mertens function(218) = 3, a record high. *218 is nontotient and also noncototient. *218 is the number of inequivalent ways to color the 12 edges of a cube using at most 2 colors, where two colorings are equivalent if they differ only by a rotation of the cube. *There are 218 nondegenerate Boolean functions of 3 variables. *The number of surface points on a 73 cube. In other fields *218 is the current number of votes in the US House of Representatives a party or coalition needs to win in order to achieve a majority. *The years 218 and 218 BC __NOTOC__ Year 218 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Scipio and Longus (or, less frequently, year 536 ''Ab urbe condita''). The denomination 218 BC for this year has been ... *Area code 218, for northern Minnesota. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
217 (number)
217 (two hundred ndseventeen) is the natural number following 216 and preceding 218. In mathematics 217 is a centered hexagonal number, a 12-gonal number, a centered 36-gonal number, a Fermat pseudoprime to base 5, and a Blum integer. It is both the sum of two positive cubes and the difference of two positive consecutive cubes in exactly one way: 217 = 6^3 + 1^3 = 9^3 - 8^3. When written in binary, it is a non-repetitive Kaprekar number. OEIS It is also the sum of all the s of . See also *217
Year 217 (R ...
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219 (number)
219 (two hundred ndnineteen) is the natural number following 218 and preceding 220. In mathematics *219 is a happy number. *Mertens function(219) = 4, a record high. *There are 219 partially ordered sets on four labeled elements. *219 is the smallest number that can be represented as a sum of four positive cubes in two different ways.. *There are 219 different space group In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it uncha ...s, discrete and full-dimensional sets of symmetries of three-dimensional space or of crystal structures. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mertens Function
In number theory, the Mertens function is defined for all positive integers ''n'' as : M(n) = \sum_^n \mu(k), where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive real numbers as follows: : M(x) = M(\lfloor x \rfloor). Less formally, M(x) is the count of square-free integers up to ''x'' that have an even number of prime factors, minus the count of those that have an odd number. The first 143 ''M''(''n'') values are The Mertens function slowly grows in positive and negative directions both on average and in peak value, oscillating in an apparently chaotic manner passing through zero when ''n'' has the values :2, 39, 40, 58, 65, 93, 101, 145, 149, 150, 159, 160, 163, 164, 166, 214, 231, 232, 235, 236, 238, 254, 329, 331, 332, 333, 353, 355, 356, 358, 362, 363, 364, 366, 393, 401, 403, 404, 405, 407, 408, 413, 414, 419, 420, 422, 423, 424, 425, 427, 428, ... . Because the Möbius function only ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotient if there is no integer ''x'' that has exactly ''n'' coprimes below it. All odd numbers are nontotients, except 1, since it has the solutions ''x'' = 1 and ''x'' = 2. The first few even nontotients are : 14, 26, 34, 38, 50, 62, 68, 74, 76, 86, 90, 94, 98, 114, 118, 122, 124, 134, 142, 146, 152, 154, 158, 170, 174, 182, 186, 188, 194, 202, 206, 214, 218, 230, 234, 236, 242, 244, 246, 248, 254, 258, 266, 274, 278, 284, 286, 290, 298, ... Least ''k'' such that the totient of ''k'' is ''n'' are (0 if no such ''k'' exists) :1, 3, 0, 5, 0, 7, 0, 15, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 25, 0, 23, 0, 35, 0, 0, 0, 29, 0, 31, 0, 51, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 69, 0, 47, 0, 65, 0, 0, 0, 53, 0, 81, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noncototient
In mathematics, a noncototient is a positive integer ''n'' that cannot be expressed as the difference between a positive integer ''m'' and the number of coprime integers below it. That is, ''m'' − φ(''m'') = ''n'', where φ stands for Euler's totient function, has no solution for ''m''. The ''cototient'' of ''n'' is defined as ''n'' − φ(''n''), so a noncototient is a number that is never a cototient. It is conjectured that all noncototients are even. This follows from a modified form of the slightly stronger version of the Goldbach conjecture: if the even number ''n'' can be represented as a sum of two distinct primes ''p'' and ''q,'' then :pq - \varphi(pq) = pq - (p-1)(q-1) = p+q-1 = n-1. \, It is expected that every even number larger than 6 is a sum of two distinct primes, so probably no odd number larger than 5 is a noncototient. The remaining odd numbers are covered by the observations 1=2-\phi(2), 3 = 9 - \phi(9) and 5 = 25 - ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f:\^k \to \, where \ is known as the Boolean domain and k is a non-negative integer called the arity of the function. In the case where k=0, the function is a constant element of \. A Boolean function with multiple outputs, f:\^k \to \^m with m>1 is a ''vectorial'' or ''vector-valued'' Boolean function (an S-box in symmetric cryptography). There are 2^ different Boolean functions with k arguments; equal to the number of different truth tables with 2^k entries. Every k-ary Boolean function can be expressed as a propositional formula in k variables x_1,...,x_k, and two propositional formulas are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
US House Of Representatives
The United States House of Representatives, often referred to as the House of Representatives, the U.S. House, or simply the House, is the lower chamber of the United States Congress, with the Senate being the upper chamber. Together they comprise the national bicameral legislature of the United States. The House's composition was established by Article One of the United States Constitution. The House is composed of representatives who, pursuant to the Uniform Congressional District Act, sit in single member congressional districts allocated to each state on a basis of population as measured by the United States Census, with each district having one representative, provided that each state is entitled to at least one. Since its inception in 1789, all representatives have been directly elected, although universal suffrage did not come to effect until after the passage of the 19th Amendment and the Civil Rights Movement. Since 1913, the number of voting representatives ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
218 BC
__NOTOC__ Year 218 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Scipio and Longus (or, less frequently, year 536 ''Ab urbe condita''). The denomination 218 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Hispania *Second Punic War :* Fall of Saguntum to Hannibal of Carthage :* Hannibal sets out with around 40,000 men and 50 elephants from New Carthage ( Cartagena) to northern Spain and then into the Pyrenees where his army meets with stiff resistance from the Pyrenean tribes. This opposition and the desertion of some of his Spanish troops greatly diminishes his numbers, but he reaches the river Rhône facing little resistance from the tribes of southern Gaul. :* A Roman army under the consul Publius Cornelius Scipio is transported by sea to Massilia (modern Marseille) to prevent Hanniba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
