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138 (number)
138 (one hundred [and] thirty-eight) is the natural number following 137 (number), 137 and preceding 139 (number), 139. Mathematics 138 is a sphenic number, an Ulam number, an abundant number, and a square-free congruent number. References [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
137 (number)
137 (one hundred [and] thirty-seven) is the natural number following 136 (number), 136 and preceding 138 (number), 138. Mathematics 137 is: * the 33rd prime number; the next is 139 (number), 139, with which it comprises a twin prime, and thus 137 is a Chen prime. * an Eisenstein prime with no imaginary part and a real part of the form 3n - 1. * the fourth Stern prime. * a Pythagorean prime: a prime number of the form 4n+1, where n=34 (137=4\times 34+1) or the sum of two squares 11^+4^ = (121+16). * a combination of three terms 4^+3^-2^ = (64+81-8), cube of 4 + Triangular number T4+T2 on each cube face (along 3 axes) - peaks (single 6th peak as free link) * a strong prime in the sense that it is more than the arithmetic mean of its two neighboring primes. * a strictly non-palindromic number and a primeval number. * a factor of 10001 (the other being 73 (number), 73) and the repdigit 11111111 (= 10001 × 1111). * using two radii to divide a circle according to the golden ratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
139 (number)
139 (one hundred [and] thirty-nine) is the natural number following 138 (number), 138 and preceding 140 (number), 140. In mathematics 139 is the 34th prime number. It is a twin prime with 137 (number), 137. Because 141 (number), 141 is a semiprime, 139 is a Chen prime. 139 is the smallest prime before a prime gap of length 10. This number is the sum of five consecutive prime numbers (19 (number), 19 + 23 (number), 23 + 29 (number), 29 + 31 (number), 31 + 37 (number), 37). It is the smallest factorization, factor of 64079 (number), 64079 which is the smallest Lucas number with prime index which is not prime. It is also the smallest factor of the first nine terms of the Euclid–Mullin sequence, making it the tenth term. 139 is a happy number and a strictly non-palindromic number. References External links Psalm 139 {{DEFAULTSORT:139 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphenic Number
In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers. Definition A sphenic number is a product ''pqr'' where ''p'', ''q'', and ''r'' are three distinct prime numbers. In other words, the sphenic numbers are the square-free 3- almost primes. Examples The smallest sphenic number is 30 = 2 × 3 × 5, the product of the smallest three primes. The first few sphenic numbers are : 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, ... The largest known sphenic number at any time can be obtained by multiplying together the three largest known primes. Divisors All sphenic numbers have exactly eight divisors. If we express the sphenic number as n = p \cdot q \cdot r, where ''p'', ''q'', and ''r'' are distinct primes, then the set of divisors of ''n'' will be: :\left\. The converse does not hold. F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ulam Number
In mathematics, the Ulam numbers comprise an integer sequence devised by and named after Stanislaw Ulam, who introduced it in 1964. The standard Ulam sequence (the (1, 2)-Ulam sequence) starts with ''U''1 = 1 and ''U''2 = 2. Then for ''n'' > 2, ''U''''n'' is defined to be the smallest integer that is the sum of two distinct earlier terms in exactly one way and larger than all earlier terms. Examples As a consequence of the definition, 3 is an Ulam number (1 + 2); and 4 is an Ulam number (1 + 3). (Here 2 + 2 is not a second representation of 4, because the previous terms must be distinct.) The integer 5 is not an Ulam number, because 5 = 1 + 4 = 2 + 3. The first few terms are :1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47, 48, 53, 57, 62, 69, 72, 77, 82, 87, 97, 99, 102, 106, 114, 126, 131, 138, 145, 148, 155, 175, 177, 180, 182, 189, 197, 206, 209, 219, 221, 236, 238 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abundant Number
In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4, for example. Definition An ''abundant number'' is a natural number for which the Divisor function, sum of divisors satisfies , or, equivalently, the sum of proper divisors (or aliquot sum) satisfies . The ''abundance'' of a natural number is the integer (equivalently, ). Examples The first 28 abundant numbers are: :12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, ... . For example, the proper divisors of 24 are 1, 2, 3, 4, 6, 8, and 12, whose sum is 36. Because 36 is greater than 24, the number 24 is abundant. Its abundance is 36 − 24&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square-free
{{no footnotes, date=December 2015 In mathematics, a square-free element is an element ''r'' of a unique factorization domain ''R'' that is not divisible by a non-trivial square. This means that every ''s'' such that s^2\mid r is a unit of ''R''. Alternate characterizations Square-free elements may be also characterized using their prime decomposition. The unique factorization property means that a non-zero non-unit ''r'' can be represented as a product of prime elements :r=p_1p_2\cdots p_n Then ''r'' is square-free if and only if the primes ''pi'' are pairwise non-associated (i.e. that it doesn't have two of the same prime as factors, which would make it divisible by a square number). Examples Common examples of square-free elements include square-free integers and square-free polynomials. See also *Prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number grea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Congruent Number
In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. A more general definition includes all positive rational numbers with this property. The sequence of (integer) congruent numbers starts with :5, 6, 7, 13, 14, 15, 20, 21, 22, 23, 24, 28, 29, 30, 31, 34, 37, 38, 39, 41, 45, 46, 47, 52, 53, 54, 55, 56, 60, 61, 62, 63, 65, 69, 70, 71, 77, 78, 79, 80, 84, 85, 86, 87, 88, 92, 93, 94, 95, 96, 101, 102, 103, 109, 110, 111, 112, 116, 117, 118, 119, 120, ... For example, 5 is a congruent number because it is the area of a (20/3, 3/2, 41/6) triangle. Similarly, 6 is a congruent number because it is the area of a (3,4,5) triangle. 3 and 4 are not congruent numbers. The triangle sides demonstrating a number is congruent can have very large numerators and denominators, for example 263 is the area of a triangle whose two shortest sides are 16277526249841969031325182370950195/2303229894605810399672144140263708 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yang Hui Magic Circle
Yang may refer to: * Yang, in yin and yang, one half of the two symbolic polarities in Chinese philosophy * Korean yang, former unit of currency of Korea from 1892 to 1902 * YANG, a data modeling language for the NETCONF network configuration protocol Geography * Yang County, in Shaanxi, China * Yangzhou (ancient China), also known as Yang Prefecture * Yang (state), ancient Chinese state * Yang, Iran, a village in Razavi Khorasan Province * Yang River (other) People * Yang, one of the names for the Karen people in the Thai language *Yang di-Pertuan Agong, the constitutional monarch of Malaysia * Andrew Yang, American Politician and Co-Founder of the Forward Party (United States), Forward Party. * Yang (surname) (楊), a Chinese surname * Yang (surname 陽), a Chinese surname * Yang (surname 羊), a Chinese surname * Yang (Korean surname) * Yang Rong (businessman) (, born 1957), Chinese businessman Fictional characters * Cristina Yang, on the TV show ''Grey's Anatomy' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
