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Self Number
In number theory, a self number or Devlali number in a given number base b is a natural number that cannot be written as the sum of any other natural number n and the individual digits of n. 20 is a self number (in base 10), because no such combination can be found (all n 1 F_b : \mathbb \rightarrow \mathbb to be the following: :F_(n) = n + \sum_^ d_i. where k = \lfloor \log_ \rfloor + 1 is the number of digits in the number in base b, and :d_i = \frac is the value of each digit of the number. A natural number n is a b-self number if the preimage of n for F_b is the empty set. In general, for even bases, all odd numbers below the base number are self numbers, since any number below such an odd number would have to also be a 1-digit number which when added to its digit would result in an even number. For odd bases, all odd numbers are self numbers.Sándor & Crstici (2004) p.384 The set of self numbers in a given base b is infinite and has a positive asymptotic density: when b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Number Theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory can often be understood through the study of Complex analysis, analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
42 (number)
42 (forty-two) is the natural number that follows 41 and precedes 43. Mathematics 42 is a pronic number, an abundant number as well as a highly abundant number, a practical number, an admirable number, and a Catalan number. The 42-sided ''tetracontadigon'' is the largest such regular polygon that can only tile a vertex alongside other regular polygons, without tiling the plane. 42 is the magic constant of the smallest non-trivial magic cube, a 3 \times 3 \times 3 cube with entries of 1 through 27, where every row, column, corridor, and diagonal passing through the center sums to forty-two. 42 can be expressed as the sum of three cubes:80,435,758,145,817,515^3 + 12,602,123,297,335,631^3 + (-80,538,738,812,075,974)^3 = 42. Technology * Magic numbers used by programmers: ** In TIFF (Tag Image File Format), the second 16-bit word of every file is 42, "an arbitrary but carefully chosen number that further identifies the file as a TIFF file". ** In the reiser4 fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
176 (number)
176 (one hundred ndseventy-six) is the natural number following 175 and preceding 177. In mathematics 176 is an even number and an abundant number. It is an odious number, a self number, a semiperfect number, and a practical number. 176 is a cake number, a happy number, a pentagonal number, and an octagonal number In mathematics, an octagonal number is a figurate number. The ''n''th octagonal number ''o'n'' is the number of dots in a pattern of dots consisting of the outlines of regular octagons with sides up to ''n'' dots, when the octagons are overlai .... 15 can be partitioned in 176 ways. The Higman–Sims group can be constructed as a doubly transitive permutation group acting on a geometry containing 176 points, and it is also the symmetry group of the largest possible set of equiangular lines in 22 dimensions, which contains 176 lines. References External links Number Facts and Trivia: 176The Number 176The Positive Integer 176 Number Gossip: 176 {{D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
165 (number)
165 (one hundred ndsixty-five) is the natural number following 164 and preceding 166. In mathematics 165 is: *an odd number, a composite number, and a deficient number. *a sphenic number. *a tetrahedral number. *the number of prime knots with 10 crossings. *the sum of the sums of the divisors of the first 14 positive integers. *a self number in base 10. *a 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 ''palin ... in binary (101001012) and bases 14 (BB14), 32 (5532) and 54 (3354). *a unique period in base 2. References External links Number Facts and Trivia: 165The Number 165The Positive Integer 165 Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
154 (number)
154 (one hundred ndfifty-four) is the natural number following 153 and preceding 155. In mathematics 154 is a nonagonal number. Its factorization makes 154 a sphenic number. There is no integer with exactly 154 coprimes below it, making 154 a noncototient, nor is there, in base 10, any integer that added up to its own digits yields 154, making 154 a self number 154 is the sum of the first six factorials, if one starts with 0! and assumes that 0!=1. With just 17 cuts, a pancake can be cut up into 154 pieces ( Lazy caterer's sequence). The distinct prime factors of 154 add up to 20, and so do the ones of 153, hence the two form a Ruth-Aaron pair. 154! + 1 is a factorial prime A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). The first 10 factorial primes (for ''n'' = 1, 2, 3, 4, 6, 7, 11, 12, 14) are : : 2 (0! + 1 or 1! + 1) .... References * Wells, D. '' The Penguin Diction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
143 (number)
143 (one hundred ndforty-three) is the natural number following 142 and preceding 144. It is one less than a gross. In media * On '' Mister Rogers' Neighborhood'': "Transformations", 143 is used to mean "I love you". 1 meaning I for 1 letter, 4 meaning Love for the 4 letters, and 3 meaning You for the 3 letters. Reportedly, Fred Rogers maintained his weight at exactly for the last thirty years of his life, and associated the number with the phrase "I love you". * Jake Shimabukuro released the song "143" based on his experience in high school when 143 was sent on a pager to indicate "I Love You". * Sal Governale of '' The Howard Stern Show'' had a long running saga on the show about his wife who had an emotional friend. He discovered the severity of their relationship when he read their text messages and emails which included "143", shorthand for "I love you". * " Case 143", song by Stray Kids. In popular culture *143. A popular pager number to communicate "I love you" (b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
132 (number)
132 (one hundred ndthirty-two) is the natural number following 131 and preceding 133. It is 11 dozens. In mathematics 132 is the sixth Catalan number. With twelve divisors total where 12 is one of them, 132 is the 20th refactorable number, preceding the triangular 136. 132 is an oblong number, as the product of 11 and 12 whose sum instead yields the 9th prime number 23; on the other hand, 132 is the 99th composite number. Adding all two- digit permutation subsets of 132 yields the same number: :12 + 13 + 21 + 23 + 31 + 32 = 132. 132 is the smallest number in decimal with this property, which is shared by 264, 396 and 35964 (see digit-reassembly number). The number of irreducible trees with fifteen vertices is 132. In a 15 \times 15 toroidal board in the ''n''–Queens problem, 132 is the count of non-attacking queens, with respective indicator of 19 and multiplicity of 1444 = 382 (where, 2 × 19 = 38).I. Rivin, I. Vardi and P. Zimmermann (1994)The n-queens p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
121 (number)
121 (one hundred ndtwenty-one) is the natural number following 120 and preceding 122. In mathematics ''One hundred ndtwenty-one'' is * a square (11 times 11) * the sum of the powers of 3 from 0 to 4, so a repunit in ternary. Furthermore, 121 is the only square of the form 1 + p + p^2 + p^3 + p^4, where ''p'' is prime (3, in this case). * the sum of three consecutive prime numbers (37 + 41 + 43). * As 5! + 1 = 121, it provides a solution to Brocard's problem. There are only two other squares known to be of the form n! + 1. Another example of 121 being one of the few numbers supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form x^-4 (with being 2 and 5, respectively).Wells, D., '' The Penguin Dictionary of Curious and Interesting Numbers'', London: Penguin Group. (1987): 136 * It is also a star number, a centered tetrahedral number, and a centered octagonal number. * In decimal, it is a Smith number since its digits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
110 (number)
110 (one hundred ndten) is the natural number following 109 and preceding 111. In mathematics 110 is a sphenic number and a pronic number. Following the prime quadruplet (101, 103, 107, 109), at 110, the Mertens function reaches a low of −5. 110 is the sum of three consecutive squares, 110 = 5^2 + 6^2 + 7^2. RSA-110 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. In base 10, the number 110 is a Harshad number and a self number. In other fields 110 is also: * 1-1-0, the emergency telephone number used to reach police services in Iran, Germany, Estonia, China, Indonesia, and Japan. Also used to reach the fire and rescue services in Norway and Turkey. * A percentage in the expression "To give 110%", meaning to give a little more effort than one's maximum effort * Lowest number to not be considered a favourite by anyone among 44,000 people surveyed in a 2014 online poll and subsequently adopted by British television show '' QI ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
108 (number)
108 (one hundred ndeight) is the natural number following 107 and preceding 109. In mathematics 108 is: *an abundant number. *a semiperfect number. *a tetranacci number. *the hyperfactorial of 3 since it is of the form 1^1 \cdot 2^2 \cdot 3^3. *divisible by the value of its φ function, which is 36. *divisible by the total number of its divisors (12), hence it is a refactorable number. *the angle in degrees of the interior angles of a regular pentagon in Euclidean space. *palindromic in bases 11 (9911), 17 (6617), 26 (4426), 35 (3335) and 53 (2253) *a Harshad number in bases 2, 3, 4, 6, 7, 9, 10, 11, 12, 13 and 16 *a self number. *an Achilles number because it is a powerful number but not a perfect power. *a largely composite number because its number of divisors is 12 and no smaller number has more than 12 divisors. *nine dozen, or three quarters of a gross. There are 108 free polyominoes of order 7. The equation 2\sin\left(\frac\right) = \phi results in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
97 (number)
97 (ninety-seven) is the natural number following 96 (number), 96 and preceding 98 (number), 98. It is a prime number and the only prime in the nineties. In mathematics 97 is: * the 25th prime number (the largest two-digit prime number in Base 10, base 10), following 89 (number), 89 and preceding 101 (number), 101. * a Proth prime and a Pierpont prime as it is 3 × 25 + 1. * the eleventh member of the Mian–Chowla sequence. * a self number in base 10, since there is no integer that added to its own digits, adds up to 97. * the smallest odd prime that is not a cluster prime. * the highest two-digit number where the sum of its digits is a square. * the number of primes less than 29. * The numbers 97, 907, 9007, 90007 and 900007 are all primes, and they are all happy primes. However, 9000007 (read as ''nine million seven'') is composite number, composite and has the factorization 277 (number), 277 × 32491. * an emirp with 79 (number), 79. * an isolated p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
86 (number)
86 (eighty-six) is the natural number following 85 (number), 85 and preceding 87 (number), 87. In mathematics 86 is: * nontotient and a noncototient. * the 25th distinct semiprime and the 13th of the form (2.q). * together with 85 (number) , 85 and 87 (number), 87, forms the middle semiprime in the 2nd cluster of three consecutive semiprimes; the first comprising 33 (number), 33, 34 (number), 34, 35 (number), 35. * an Erdős–Woods number, since it is possible to find sequences of 86 consecutive integers such that each inner member shares a factor with either the first or the last member. * a happy number and a self number in base 10. * with an aliquot sum of 46 (number), 46; itself a semiprime, within an aliquot sequence of seven members (86,46 (number), 46,26 (number), 26,16 (number), 16,15 (number), 15,9 (number), 9,4 (number), 4,3 (number), 3,1 (number), 1,0) in the Prime 3 (number), 3-aliquot tree. It appears in the Padovan sequence, preceded by the terms 37, 49, 65 (it is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
