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420 (number)
420 (four hundred ndtwenty) is the natural number following 419 and preceding 421. In mathematics 420 is: *the sum of four consecutive primes (101 + 103 + 107 + 109). *the sum of the first 20 positive even numbers. *a zero of the Mertens function and is sparsely totient. *a pronic number. *the smallest number divisible by the numbers 1 to 7, and as a consequence of that it is a Harshad number in every base from 2 to 10 except base 5. *a 141- gonal number. *a balanced number. In other fields *420 is a slang term that refers to the consumption of cannabis. April 20th is commonly celebrated as a holiday dedicated to the drug, due to the numerical form of the day being 4/20. *420 is the country calling code for Czech Republic The Czech Republic, or simply Czechia, is a landlocked country in Central Europe. Historically known as Bohemia, it is bordered by Austria to the south, Germany to the west, Poland to the northeast, and Slovakia to the southeast. The .... R ... [...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] |
419 (number)
400 (four hundred) is the natural number following 399 and preceding 401. Mathematical properties 400 is the square of 20. 400 is the sum of the powers of 7 from 0 to 3, thus making it a repdigit in base 7 (1111). A circle is divided into 400 grads, which is equal to 360 degrees and 2π radians. (Degrees and radians are the SI accepted units). 400 is a self number in base 10, since there is no integer that added to the sum of its own digits results in 400. On the other hand, 400 is divisible by the sum of its own base 10 digits, making it a Harshad number. Other fields Four hundred is also * The Four Hundred (oligarchy) of ancient Athens. * An HTTP status code for a bad client request. * The Four Hundred (sometimes The Four Hundred Club) a phrase meaning the wealthiest, most famous, or most powerful social group (see, e.g., Ward McAllister), leading to the generation of such lists as the Forbes 400. * The Atari 400 home computer. * A former limited stop bus route whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
421 (number)
400 (four hundred) is the natural number following 399 and preceding 401. Mathematical properties 400 is the square of 20. 400 is the sum of the powers of 7 from 0 to 3, thus making it a repdigit in base 7 (1111). A circle is divided into 400 grads, which is equal to 360 degrees and 2π radians. (Degrees and radians are the SI accepted units). 400 is a self number in base 10, since there is no integer that added to the sum of its own digits results in 400. On the other hand, 400 is divisible by the sum of its own base 10 digits, making it a Harshad number. Other fields Four hundred is also * The Four Hundred (oligarchy) of ancient Athens. * An HTTP status code for a bad client request. * The Four Hundred (sometimes The Four Hundred Club) a phrase meaning the wealthiest, most famous, or most powerful social group (see, e.g., Ward McAllister), leading to the generation of such lists as the Forbes 400. * The Atari 400 home computer. * A former limited stop bus route which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root Of A Function
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) ''vanishes'' at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. A "zero" of a function is thus an input value that produces an output of 0. A root of a polynomial is a zero of the corresponding polynomial function. The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree, and that the number of roots and the degree are equal when one considers the complex roots (or more generally, the roots in an algebraically closed extension) counted with their multiplicities. For example, the polynomial f of degree two, defined by f(x)=x^2-5x+6 has the two roots (or zeros) that are 2 and 3. f(2)=2^2-5\times 2+6= 0\textf(3)=3^2-5\times 3+6=0. If the function maps real numbers to real numbers, then it ... [...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] |
Sparsely Totient Number
In mathematics, a sparsely totient number is a certain kind of natural number. A natural number, ''n'', is sparsely totient if for all ''m'' > ''n'', :\varphi(m)>\varphi(n) where \varphi is Euler's totient function. The first few sparsely totient numbers are: 2, 6, 12, 18, 30, 42, 60, 66, 90, 120, 126, 150, 210, 240, 270, 330, 420, 462, 510, 630, 660, 690, 840, 870, 1050, 1260, 1320, 1470, 1680, 1890, 2310, 2730, 2940, 3150, 3570, 3990, 4620, 4830, 5460, 5610, 5670, 6090, 6930, 7140, 7350, 8190, 9240, 9660, 9870, ... . The concept was introduced by David Masser and Peter Man-Kit Shiu in 1986. As they showed, every primorial is sparsely totient. Properties * If ''P''(''n'') is the largest prime factor 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 ''n'', th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pronic Number
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n(n+1).. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,. or rectangular numbers; however, the term "rectangular number" has also been applied to the composite numbers. The first few pronic numbers are: : 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462 … . Letting P_n denote the pronic number n(n+1), we have P_ = P_. Therefore, in discussing pronic numbers, we may assume that n\geq 0 without loss of generality, a convention that is adopted in the following sections. As figurate numbers The pronic numbers were studied as figurate numbers alongside the triangular numbers and square numbers in Aristotle's ''Metaphysics'', and their discovery has been attributed much earlier to the Pythagoreans.. As a kind of figurate number, the pronic numbers are somet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harshad Number
In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit ' (joy) + ' (give), meaning joy-giver. The term "Niven number" arose from a paper delivered by Ivan M. Niven at a conference on number theory in 1977. Definition Stated mathematically, let be a positive integer with digits when written in base , and let the digits be a_i (i = 0, 1, \ldots, m-1). (It follows that a_i must be either zero or a positive integer up to .) can be expressed as :X=\sum_^ a_i n^i. is a harshad number in base if: :X \equiv 0 \bmod . A number which is a harshad number in every number base is called an all-harshad number, or an all-Niven number. There are only four all-harshad numbers: 1, 2, 4, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygonal Number
In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots are thought of as alphas (units). These are one type of 2-dimensional figurate numbers. Definition and examples The number 10 for example, can be arranged as a triangle (see triangular number): : But 10 cannot be arranged as a square (geometry), square. The number 9, on the other hand, can be (see square number): : Some numbers, like 36, can be arranged both as a square and as a triangle (see square triangular number): : By convention, 1 is the first polygonal number for any number of sides. The rule for enlarging the polygon to the next size is to extend two adjacent arms by one point and to then add the required extra sides between those points. In the following diagrams, each extra layer is shown as in red. Triangular numbers : Square numbers : Polygons with higher numbers of sides, such as pentagons and hexagons, can also be constructe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
420 (cannabis Culture)
420, 4:20 or 4/20 (pronounced four-twenty) is cannabis culture slang for marijuana and hashish consumption, especially smoking around the time 4:20 pm (16:20). It also refers to cannabis-oriented celebrations that take place annually on April 20 (4/20 in U.S. form). At locations in the United States where cannabis is legal, cannabis dispensaries will often offer discounts on their products on April 20. Origins In 1971, five high school students in San Rafael, California, used the term "4:20" in connection with a plan to search for an abandoned cannabis crop, based on a treasure map made by the grower. Calling themselves the Waldos, because their typical hang-out spot "was a wall outside the school", the five students—Steve Capper, Dave Reddix, Jeffrey Noel, Larry Schwartz, and Mark Gravich—designated the Louis Pasteur statue on the grounds of San Rafael High School as their meeting place, and 4:20 pm as their meeting time. The Waldos referred to this plan with the phra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cannabis (drug)
Cannabis, also known as marijuana among List of names for cannabis, other names, is a psychoactive drug from the cannabis plant. Native to Central or South Asia, the cannabis plant has been used as a drug for both Recreational marijuana, recreational and Entheogenic use of cannabis, entheogenic purposes and in various traditional medicines for centuries. Tetrahydrocannabinol (THC) is the main psychoactive component of cannabis, which is one of the 483 known compounds in the plant, including at least 65 other cannabinoids, such as cannabidiol (CBD). Cannabis can be used by Cannabis smoking, smoking, Vaporizer (inhalation device), vaporizing, Cannabis edible, within food, or Tincture of cannabis, as an extract. Cannabis has various effects of cannabis, mental and physical effects, which include euphoria, altered states of mind and Cannabis and time perception, sense of time, difficulty concentrating, Cannabis and memory, impaired short-term memory, impaired motor skill, body mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
April 20
Events Pre-1600 * 1303 – The Sapienza University of Rome is instituted by a bull of Pope Boniface VIII. 1601–1900 * 1653 – Oliver Cromwell dissolves England's Rump Parliament. * 1657 – English Admiral Robert Blake destroys a Spanish silver fleet, under heavy fire from the shore, at the Battle of Santa Cruz de Tenerife. * 1657 – Freedom of religion is granted to the Jews of New Amsterdam (later New York City). * 1752 – Start of Konbaung–Hanthawaddy War, a new phase in the Burmese Civil War (1740–57). * 1770 – The Georgian king, Erekle II, abandoned by his Russian ally Count Totleben, wins a victory over Ottoman forces at Aspindza. * 1775 – American Revolutionary War: The Siege of Boston begins, following the battles at Lexington and Concord. * 1789 – George Washington arrives at Grays Ferry, Philadelphia, while en route to Manhattan for his inauguration. * 1792 – France declares war against the " King of Hunga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
