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358 (number)
300 (three hundred) is the natural number following 299 and preceding 301. In Mathematics 300 is a composite number and the 24th triangular number. It is also a second hexagonal number. Integers from 301 to 399 300s 301 302 303 304 305 306 307 308 309 310s 310 311 312 313 314 315 315 = 32 × 5 × 7 = D_ \!, rencontres number, highly composite odd number, having 12 divisors. It is a Harshad number, as it is divisible by the sum of its digits. It is a Zuckerman number, as it is divisible by the product of its digits. 316 316 = 22 × 79, a centered triangular number and a centered heptagonal number. 317 317 is a prime number, Eisenstein prime with no imaginary part, Chen prime, one of the rare primes to be both right and left-truncatable, and a strictly non-palindromic number. 317 is the exponent (and number of ones) in the fourth base-10 repunit prime. 318 319 319 = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hebrew Numerals
The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. The system was adapted from that of the Greek numerals sometime between 200 and 78 BCE, the latter being the date of the earliest archeological evidence. The current numeral system is also known as the ''Hebrew alphabetic numerals'' to contrast with earlier systems of writing numerals used in classical antiquity. These systems were inherited from usage in the Aramaic and Phoenician scripts, attested from in the Samaria Ostraca. The Greek system was adopted in Hellenistic Judaism and had been in use in Greece since about the 5th century BCE. In this system, there is no notation for zero, and the numeric values for individual letters are added together. Each unit (1, 2, ..., 9) is assigned a separate letter, each tens (10, 20, ..., 90) a separate letter, and the first four hundreds (100, 200, 300, 400) a separate letter. The later hundreds (500, 600, 700, 8 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Happy Number
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because the sequence starting with 4^2=16 and 1^2+6^2=37 eventually reaches 2^2+0^2=4, the number that started the sequence, and so the process continues in an infinite cycle without ever reaching 1. A number which is not happy is called sad or unhappy. More generally, a b-happy number is a natural number in a given number base b that eventually reaches 1 when iterated over the perfect digital invariant function for p = 2. The origin of happy numbers is not clear. Happy numbers were brought to the attention of Reg Allenby (a British author and senior lecturer in pure mathematics at Leeds University) by his daughter, who had learned of them at school. However, they "may have originated in Russia" . Happy numbers and perfect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sparsely Totient Number
In mathematics, specifically number theory, a sparsely totient number is a natural number, ''n'', such that 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'', then \liminf P(n)/\lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentagonal Number
A pentagonal number is a figurate number that extends the concept of triangular number, triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotational symmetry, rotationally symmetrical. The ''n''th pentagonal number ''pn'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex (geometry), vertex. For instance, the third one is formed from outlines comprising 1, 5 and 10 dots, but the 1, and 3 of the 5, coincide with 3 of the 10 – leaving 12 distinct dots, 10 in the form of a pentagon, and 2 inside. ''p''n is given by the formula: :p_n = =\binom+3\binom for ''n'' ≥ 1. The first few pentagonal numbers are: 1 (number), 1, 5 (number), 5, 12 (number), 12, 22 (number), 22, 35 (number), 35, 51 (number), 51, 70 (number), 70, 92 (number), 92, 117 (nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Coefficient
In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the term in the polynomial expansion of the binomial power ; this coefficient can be computed by the multiplicative formula : \binom nk = \frac, which using factorial notation can be compactly expressed as : \binom = \frac. For example, the fourth power of is : \begin (1 + x)^4 &= \tbinom x^0 + \tbinom x^1 + \tbinom x^2 + \tbinom x^3 + \tbinom x^4 \\ &= 1 + 4x + 6 x^2 + 4x^3 + x^4, \end and the binomial coefficient \tbinom =\tfrac = \tfrac = 6 is the coefficient of the term. Arranging the numbers \tbinom, \tbinom, \ldots, \tbinom in successive rows for gives a triangular array called Pascal's triangle, satisfying the recurrence relation : \binom = \binom + \binom . The binomial coefficients occur in many areas of mathematics, and espe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentatope Number
In number theory, a pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row , either from left to right or from right to left. It is named because it represents the number of 3-dimensional unit spheres which can be packed into a pentatope (a 4-dimensional tetrahedron) of increasing side lengths. The first few numbers of this kind are: : 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001, 1365 Pentatope numbers belong to the class of figurate numbers, which can be represented as regular, discrete geometric patterns. Formula The formula for the th pentatope number is represented by the 4th rising factorial of divided by the factorial of 4: :P_n = \frac = \frac . The pentatope numbers can also be represented as binomial coefficients: :P_n = \binom , which is the number of distinct quadruples that can be selected from objects, and it is read aloud as " plus three choose four". Properties Two of every three ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highly Cototient Number
In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above 1 and has more solutions to the equation :x - \phi(x) = k than any other integer below k and above 1. Here, \phi is Euler's totient function. There are infinitely many solutions to the equation for :k = 1 so this value is excluded in the definition. The first few highly cototient numbers are:. : 2, 4, 8, 23, 35, 47, 59, 63, 83, 89, 113, 119, 167, 209, 269, 299, 329, 389, 419, 509, 629, 659, 779, 839, 1049, 1169, 1259, 1469, 1649, 1679, 1889, ... Many of the highly cototient numbers are odd. The concept is somewhat analogous to that of highly composite numbers. Just as there are infinitely many highly composite numbers, there are also infinitely many highly cototient numbers. Computations become harder, since integer factorization becomes harder as the numbers get larger. Example The cototient of x is defined as x - \phi(x), i.e. the number of positive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refactorable Number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n with \tau(n)=\sigma_0(n)=\prod_^(e_i+1) for n=\prod_^np_i^. The first few refactorable numbers are listed in as :1 (number), 1, 2 (number), 2, 8 (number), 8, 9 (number), 9, 12 (number), 12, 18 (number), 18, 24 (number), 24, 36 (number), 36, 40 (number), 40, 56 (number), 56, 60 (number), 60, 72 (number), 72, 80 (number), 80, 84 (number), 84, 88 (number), 88, 96 (number), 96, 104 (number), 104, 108 (number), 108, 128 (number), 128, 132 (number), 132, 136 (number), 136, 152 (number), 152, 156 (number), 156, 180 (number), 180, 184 (number), 184, 204 (number), 204, 225 (number), 225, 228 (number), 228, 232 (number), 232, 240 (number), 240, 248 (number), 248, 252 (number), 252, 276 (number), 276, 288 (number), 288, 296 (number), 296, ... For example, 18 has 6 divisors (1 and 18, 2 and 9, 3 and 6) and is divisible by 6. Ther ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Totient Number
In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, one applies the totient function to a number ''n'', apply it again to the resulting totient, and so on, until the number 1 is reached, and adds together the resulting sequence of numbers; if the sum equals ''n'', then ''n'' is a perfect totient number. Examples For example, there are six positive integers less than 9 and relatively prime to it, so the totient of 9 is 6; there are two numbers less than 6 and relatively prime to it, so the totient of 6 is 2; and there is one number less than 2 and relatively prime to it, so the totient of 2 is 1; and , so 9 is a perfect totient number. The first few perfect totient numbers are : 3, 9, 15, 27, 39, 81, 111, 183, 243, 255, 327, 363, 471, 729, 2187, 2199, 3063, 4359, 4375, ... . Notation In symbols, one writes :\varphi^i(n) = \begin \varphi(n), &\text i = 1 \\ \varphi(\varphi^(n)), &\text i \geq 2 \end for th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lucas Number
The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci sequence. Individual numbers in the Lucas sequence are known as Lucas numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences. The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values. This produces a sequence where the ratios of successive terms approach the golden ratio, and in fact the terms themselves are roundings of integer powers of the golden ratio. The sequence also has a variety of relationships with the Fibonacci numbers, like the fact that adding any two Fibonacci numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. The first few Lucas numbers are : 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Untouchable Number
In mathematics, an untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer. That is, these numbers are not in the image of the aliquot sum function. Their study goes back at least to Abu Mansur al-Baghdadi (circa 1000 AD), who observed that both 2 and 5 are untouchable. Examples * The number 4 is not untouchable, as it is equal to the sum of the proper divisors of 9: 1 + 3 = 4. * The number 5 is untouchable, as it is not the sum of the proper divisors of any positive integer: 5 = 1 + 4 is the only way to write 5 as the sum of distinct positive integers including 1, but if 4 divides a number, 2 does also, so 1 + 4 cannot be the sum of all of any number's proper divisors (since the list of factors would have to contain both 4 and 2). * The number 6 is not untouchable, as it is equal to the sum of the proper divisors of 6 itself: 1 + 2 + 3&nb ... [...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] |
