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Seventy-four (ship), 74-gun
74 (seventy-four) is the natural number following 73 and preceding 75. In mathematics 74 is: * the twenty-first distinct semiprime and the eleventh of the form (2.''q''), where q is a higher prime. * with an aliquot sum of 40, within an aliquot sequence of three composite numbers (74, 40, 50, 43, 1,0) to the Prime in the 43-aliquot tree. * a palindromic number in bases 6 (2026) and 36 (2236). * a 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 nontotie .... * the number of collections of subsets of that are closed under union and intersection. * φ(74) = φ(σ(74)). There are 74 different non-Hamiltonian polyhedra with a minimum number of vertices. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [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] |
73 (number)
73 (seventy-three) is the natural number following 72 (number), 72 and preceding 74 (number), 74. In English, it is the smallest natural number with twelve letters in its spelled out name. It is the 21st prime number and the fourth star number. It is also the eighth twin prime, with 71 (number), 71. In mathematics 73 is the 21st prime number, and emirp with 37 (number), 37, the 12th prime number. It is also the eighth twin prime, with 71 (number), 71. It is the largest minimal Primitive root modulo n, primitive root in the first 100,000 primes; in other words, if is one of the first one hundred thousand primes, then at least one of the numbers 2, 3, 4, 5, 6, ..., 73 is a primitive root modulo . 73 is also the smallest factor of the first Composite number, composite generalized Fermat number in decimal: 10^+1=10,001=73\times 137, and the smallest prime Modular arithmetic#Congruence, congruent to 1 modulo 24 (number), 24, as well as the only prime repunit in octal (1118). It is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
75 (number)
75 (seventy-five) is the natural number following 74 (number), 74 and preceding 76 (number), 76. __TOC__ In mathematics 75 is a self number because there is no integer that added up to its own digits adds up to 75. It is the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number, as well as a nonagonal number. It is also the fourth ordered Bell number, and a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 7 (number), 7, 5 (number), 5, 12 (number), 12, 17 (number), 17, 29 (number), 29, 46 (number), 46, 75... 75 is the count of the number of weak orderings on a set of four items. Excluding the infinite sets, there are 75 uniform polyhedra in the third dimension, which incorporate Star polyhedron, star polyhedra as well. Inclusive of 7 families of Prism (geometry), prisms and antiprism, antiprisms, there are also 75 uniform polyhedron compound, uniform compound polyhedra. References Integers {{N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes, since they include two primes, or second numbers, by analogy with how "prime" means "first". Alternatively non-prime semiprimes are called almost-prime numbers, specifically the "2-almost-prime" biprime and "3-almost-prime" triprime Examples and variations The semiprimes less than 100 are: Semiprimes that are not square numbers are called discrete, distinct, or squarefree semiprimes: The semiprimes are the case k=2 of the k- almost primes, numbers with exactly k prime factors. However some sources use "semiprime" to refer to a larger set of numbers, the numbers with at most two prime factors (including unit (1), primes, and semiprimes). These are: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliquot Sum
In number theory, the aliquot sum of a positive integer is the sum of all proper divisors of , that is, all divisors of other than itself. That is, s(n)=\sum_ d \, . It can be used to characterize the prime numbers, perfect numbers, sociable numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number. Examples For example, the proper divisors of 12 (that is, the positive divisors of 12 that are not equal to 12) are , and 6, so the aliquot sum of 12 is 16 i.e. (). The values of for are: :0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22, 11, 14, 1, 36, 6, 16, 13, 28, 1, 42, 1, 31, 15, 20, 13, 55, 1, 22, 17, 50, 1, 54, 1, 40, 33, 26, 1, 76, 8, 43, ... Characterization of classes of numbers The aliquot sum function can be used to characterize several notable classes of numbers: *1 is the only number whose aliquot sum is 0. *A number is prime if and only if its aliquot sum is 1. *The aliquot sum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
40 (number)
40 (forty) is the natural number following 39 and preceding 41. Though the word is related to ''four'' (4), the spelling ''forty'' replaced ''fourty'' during the 17th century and is now the standard form. Mathematics 40 is an abundant number. Swiss mathematician Leonhard Euler noted 40 prime numbers generated by the quadratic polynomial n^ + n + 41, with values n = 0,1,2,...,39. These forty prime numbers are the same prime numbers that are generated using the polynomial n^ - n + 41 with values of n from 1 through 40, and are also known in this context as ''Euler's "lucky" numbers''. Forty is the only integer whose English name has its letters in alphabetical order. In religion The number 40 is found in many traditions without any universal explanation for its use. In Jewish, Christian, Islamic, and other Middle Eastern traditions it is taken to represent a large, approximate number, similar to " umpteen". Sumerian Enki ( /ˈɛŋki/) or Enkil (Sumerian: dEN.KI(G) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliquot Sequence
In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0. Definition and overview The aliquot sequence starting with a positive integer can be defined formally in terms of the sum-of-divisors function or the aliquot sum function in the following way: \begin s_0 &= k \\ pts_n &= s(s_) = \sigma_1(s_) - s_ \quad \text \quad s_ > 0 \\ pts_n &= 0 \quad \text \quad s_ = 0 \\ pts(0) &= \text \end If the condition is added, then the terms after 0 are all 0, and all aliquot sequences would be infinite, and we can conjecture that all aliquot sequences are convergent, the limit of these sequences are usually 0 or 6. For example, the aliquot sequence of 10 is because: \begin \sigma_1(10) -10 &= 5 + 2 + 1 = 8, \\ pt\sigma_1(8) - 8 &= 4 + 2 + 1 = 7, \\ pt\sigma_1(7) - 7 &= 1, \\ pt\sigma_1(1) - 1 &= 0. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
50 (number)
50 (fifty) is the natural number following 49 and preceding 51. In mathematics Fifty is the smallest number that is the sum of two non-zero square numbers in two distinct ways. 50 is a Stirling number of the first kind and a Narayana number. In science * The fifth magic number in nuclear physics In religion * The traditional number of years in a jubilee period.Leviticus 25:10 * The Solemnity of Pentecost is celebrated fifty days from and including Easter Sunday. The Greek word pentekoste means fiftieth, hence the name. * The fifty Hail Mary during the meditation of the mysteries of the life of Jesus and the Virgin Mary of the Holy Rosary * In Hindu tantric tradition, the number 50 holds significance as the 50 Rudras in the Malinīvijayottara correlate with the 50 phonemes of Sanskrit, as well as with the 50 severed heads worn around goddess Kali's head. The mantra ''Aham'' ("I am"), as laid out in the Vijñāna Bhairava represents the first अ(a) and last ह(h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
43 (number)
43 (forty-three) is the natural number following 42 (number), 42 and preceding 44 (number), 44. Mathematics 43 is a prime number, and a twin prime of 41 (number), 41. 43 is the smallest prime that is not a Chen prime. 43 is also a Wagstaff prime, and a Heegner number. 43 is the fourth term of Sylvester's sequence. 43 is the largest prime which divides the order of the Janko group J4, Janko group J4. Netherlands, Dutch mathematician Hendrik Lenstra wrote a mathematical research paper discussing the properties of the number, titled ''Ode to the number 43.'' Notes Further reading Hendrik Lenstra, Lenstra, Hendrik (2009)''Ode to the number 43'' (In Dutch). Nieuw Archief voor Wiskunde, Nieuw Arch. Wiskd. Amsterdam, NL: Koninklijk Wiskundig Genootschap (5) 10, No. 4: 240-244. {{Integers, zero Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1 (number)
1 (one, unit, unity) is a number, numeral, and glyph. It is the first and smallest positive integer of the infinite sequence of natural numbers. This fundamental property has led to its unique uses in other fields, ranging from science to sports, where it commonly denotes the first, leading, or top thing in a group. 1 is the unit of counting or measurement, a determiner for singular nouns, and a gender-neutral pronoun. Historically, the representation of 1 evolved from ancient Sumerian and Babylonian symbols to the modern Arabic numeral. In mathematics, 1 is the multiplicative identity, meaning that any number multiplied by 1 equals the same number. 1 is by convention not considered a prime number. In digital technology, 1 represents the "on" state in binary code, the foundation of computing. Philosophically, 1 symbolizes the ultimate reality or source of existence in various traditions. In mathematics The number 1 is the first natural number after 0. Each natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Palindromic Number
A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16361) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term ''palindromic'' is derived from palindrome, which refers to a word (such as ''rotor'' or ''racecar'') whose spelling is unchanged when its letters are reversed. The first 30 palindromic numbers (in decimal) are: : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, ... . Palindromic numbers receive most attention in the realm of recreational mathematics. A typical problem asks for numbers that possess a certain property ''and'' are palindromic. For instance: * The palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, ... . * The palindromic square numbers are 0, 1, 4, 9, 121, 484, 676, 10201, 12321, ... . In any base there are infinitely many palindromic numbers, since ... [...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 this sequence: : 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, ... The least value of ''k'' such that the totient of ''k'' is ''n'' are (0 if no such ''k'' exists) are this sequence: :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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
