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118 (number)
118 (one hundred [and] eighteen) is the natural number following 117 (number), 117 and preceding 119 (number), 119. In mathematics There is no answer to the equation Euler's totient function, φ(''x'') = 118, making 118 a nontotient. Four expressions for 118 as the sum of three positive integers have the same product: :14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72 = 118 and :14 × 50 × 54 = 15 × 40 × 63 = 18 × 30 × 70 = 21 × 25 × 72 = 37800. 118 is the smallest number that can be expressed as four sums with the same product in this way. Because of its expression as , it is a Leyland number#Leyland_number_of_the_second_kind, Leyland number of the second kind. 118!! - 1 is a prime number, where !! denotes the double factorial (the product of even integers up to 118). In other fields * There are 118 known elements, the 118th element being oganesson. See also * 118 (other) References [...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] |
117 (number)
117 (one hundred [and] seventeen) is the natural number following 116 (number), 116 and preceding 118 (number), 118. In mathematics 117 is the smallest possible length of the longest edge of an integer Heronian tetrahedron (a tetrahedron whose edge lengths, face areas and volume are all integers). Its other edge lengths are 51, 52, 53, 80 and 84. 117 is a pentagonal number. In other fields 117 can be a substitute for the number 17 (number), 17, which is considered unlucky in Italy. When Renault exported the R17 to Italy, it was renamed R117. Chinese dragons are usually depicted as having 117 scales, subdivided into 81 associated with yin and yang, yang and 36 associated with yin and yang, yin. In the Danish language the number 117 ( da, hundredesytten) is often used as a Hyperbole, hyperbolic term to represent an arbitrary but large number. See also * 117 (other) References {{DEFAULTSORT:117 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
119 (number)
119 (one hundred ndnineteen) is the natural number following 118 and preceding 120. Mathematics * 119 is a Perrin number, preceded in the sequence by 51, 68, 90 (it is the sum of the first two mentioned). * 119 is the sum of five consecutive primes (17 + 19 + 23 + 29 + 31). * 119 is the sum of seven consecutive primes (7 + 11 + 13 + 17 + 19 + 23 + 29). * 119 is a highly cototient number. * 119 is the order of the largest cyclic subgroups of the monster group. * 119 is the smallest composite number that is 1 less than a factorial (120 is 5!). * 119 is a semiprime, and the third in the family. Telephony * 119 is an emergency telephone number in some countries * A number to report youth at risk in France * 119 is the emergency number in Afghanistan that belongs to police and interior ministry. * The South Korean emergency call number * The Chinese fire station call number * 119 is the number for the UK's NHS Test and Trace service (created in response to the of COVID-19 pand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Totient Function
In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In other words, it is the number of integers in the range for which the greatest common divisor is equal to 1. The integers of this form are sometimes referred to as totatives of . For example, the totatives of are the six numbers 1, 2, 4, 5, 7 and 8. They are all relatively prime to 9, but the other three numbers in this range, 3, 6, and 9 are not, since and . Therefore, . As another example, since for the only integer in the range from 1 to is 1 itself, and . Euler's totient function is a multiplicative function, meaning that if two numbers and are relatively prime, then . This function gives the order of the multiplicative group of integers modulo (the group of units of the ring \Z/n\Z). It is also used for defining the RSA e ... [...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] |
The Penguin Dictionary Of Curious And Interesting Numbers
''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, and a revised edition appeared in 1997 (). Contents The entries are arranged in increasing order of magnitude, with the exception of the first entry on −1 and ''i''. The book includes some irrational numbers below 10 but concentrates on integers, and has an entry for every integer up to 42. The final entry is for Graham's number. In addition to the dictionary itself, the book includes a list of mathematicians in chronological sequence (all born before 1890), a short glossary, and a brief bibliography. The back of the book contains eight short tables "for the benefit of readers who cannot wait to look for their own patterns and properties", including lists of polygonal numbers, Fibonacci numbers, prime numbers, factorials, decimal rec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leyland Number
In number theory, a Leyland number is a number of the form :x^y + y^x where ''x'' and ''y'' are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are : 8, 17, 32, 54, 57, 100, 145, 177, 320, 368, 512, 593, 945, 1124 . The requirement that ''x'' and ''y'' both be greater than 1 is important, since without it every positive integer would be a Leyland number of the form ''x''1 + 1''x''. Also, because of the commutative property of addition, the condition ''x'' ≥ ''y'' is usually added to avoid double-covering the set of Leyland numbers (so we have 1 References External links * {{DEFAULTSORT:Leyland Number Integer sequences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Factorial
In mathematics, the double factorial or semifactorial of a number , denoted by , is the product of all the integers from 1 up to that have the same parity (odd or even) as . That is, :n!! = \prod_^ (n-2k) = n (n-2) (n-4) \cdots. For even , the double factorial is :n!! = \prod_^\frac (2k) = n(n-2)(n-4)\cdots 4\cdot 2 \,, and for odd it is :n!! = \prod_^\frac (2k-1) = n(n-2)(n-4)\cdots 3\cdot 1 \,. For example, . The zero double factorial as an empty product. The sequence of double factorials for even = starts as : 1, 2, 8, 48, 384, 3840, 46080, 645120,... The sequence of double factorials for odd = starts as : 1, 3, 15, 105, 945, 10395, 135135,... The term odd factorial is sometimes used for the double factorial of an odd number. History and usage In a 1902 paper, the physicist Arthur Schuster wrote: states that the double factorial was originally introduced in order to simplify the expression of certain trigonometric integrals that arise in the derivation of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oganesson
Oganesson is a synthetic chemical element with the symbol Og and atomic number 118. It was first synthesized in 2002 at the Joint Institute for Nuclear Research (JINR) in Dubna, near Moscow, Russia, by a joint team of Russian and American scientists. In December 2015, it was recognized as one of four new elements by the Joint Working Party of the international scientific bodies IUPAC and IUPAP. It was formally named on 28 November 2016. The name honors the nuclear physicist Yuri Oganessian, who played a leading role in the discovery of the heaviest elements in the periodic table. It is one of only two elements named after a person who was alive at the time of naming, the other being seaborgium, and the only element whose eponym is alive today. Oganesson has the highest atomic number and highest atomic mass of all known elements. The radioactive oganesson atom is very unstable, and since 2005, only five (possibly six) atoms of the isotope oganesson-294 have been detected. Althou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
118 (other)
118 may refer to: *118 (number) * AD 118 *118 BC *118 (TV series) *118 (film) *118 (Tees) Corps Engineer Regiment *118 (Tees) Field Squadron, Royal Engineers See also *11/8 (other) 11/8 may refer to: *A time signature e.g.: "The Eleven" by the Grateful Dead *November 8 (month-day date notation) * August 11 (day-month date notation) *11 shillings and 8 pence in UK predecimal currency See also *118 (other) 118 may ref ... * Oganesson, synthetic chemical element with atomic number 118 {{Numberdis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
