|
182 (number)
182 (one hundred ndeighty-two) is the natural number following 181 and preceding 183. In mathematics * 182 is an even number * 182 is a composite number, as it is a positive integer with a positive divisor other than one or itself * 182 is a deficient number, as the sum of its proper divisors, 154, is less than 182 * 182 is a member of the Mian–Chowla sequence: 1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, 123, 148, 182 * 182 is a nontotient number, as there is no integer with exactly 182 coprimes below it * 182 is an odious number * 182 is a pronic number, oblong number or heteromecic number, a number which is the product of two consecutive integers ( 13 × 14) * 182 is a repdigit in the D'ni numeral system ( 77), and in base 9 ( 222) * 182 is a sphenic number, the product of three prime factors * 182 is a square-free number * 182 is an Ulam number * Divisors of 182: 1, 2, 7, 13, 14, 26, 91, 182 In astronomy * 182 Elsa is a S-type main belt asteroid * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1 (number)
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proper Divisors
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder. Definition An integer is divisible by a nonzero integer if there exists an integer such that n=km. This is written as :m\mid n. Other ways of saying the same thing are that divides , is a divisor of , is a factor of , and is a multiple of . If does not divide , then the notation is m\not\mid n. Usually, is required to be nonzero, but is allowed to be zero. With this convention, m \mid 0 for every nonzero integer . Some definitions omit the requirement that m be nonzero. General Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4; they are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thue–Morse Sequence
In mathematics, the Thue–Morse sequence, or Prouhet–Thue–Morse sequence, is the binary sequence (an infinite sequence of 0s and 1s) obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far. The first few steps of this procedure yield the strings 0 then 01, 0110, 01101001, 0110100110010110, and so on, which are prefixes of the Thue–Morse sequence. The full sequence begins: :01101001100101101001011001101001.... The sequence is named after Axel Thue and Marston Morse. Definition There are several equivalent ways of defining the Thue–Morse sequence. Direct definition To compute the ''n''th element ''tn'', write the number ''n'' in binary. If the number of ones in this binary expansion is odd then ''tn'' = 1, if even then ''tn'' = 0. For this reason John H. Conway ''et al''. called numbers ''n'' satisfying ''tn'' = 1 ''odious'' (for ''odd'') numbers and numbers for which ''tn''&n ... [...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 : 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, ... Least ''k'' such that the totient of ''k'' is ''n'' are (0 if no such ''k'' exists) :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, 0, 0, 41, 0, 43, 0, 69, 0, 47, 0, 65, 0, 0, 0, 53, 0, 81, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
148 (number)
148 (one hundred ndforty-eight) is the natural number following 147 and before 149. In mathematics 148 is the second number to be both a heptagonal number and a centered heptagonal number (the first is 1). It is the twelfth member of the Mian–Chowla sequence, the lexicographically smallest sequence of distinct positive integers with distinct pairwise sums. There are 148 perfect graphs with six vertices, and 148 ways of partitioning four people into subsets, ordering the subsets, and selecting a leader for each subset. In other fields In the Book of Nehemiah 7:44 there are 148 singers, sons of Asaph, at the census of men of Israel upon return from exile. This differs from Ezra 2:41, where the number is given as 128. Dunbar's number is a theoretical cognitive limit to the number of people with whom one can maintain stable interpersonal relationships. Dunbar predicted a "mean group size" of 148, but this is commonly rounded to 150. See also * The year AD 148 or 148 BC _ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
123 (number)
123 (one hundred ndtwenty-three) is the natural number following 122 and preceding 124. In mathematics *123 is a Lucas number. It is the eleventh member of the Mian-Chowla sequence. *Along with 6, 123 is one of only two positive integers that is simultaneously two more than a perfect square and two less than a perfect cube (123 = 112 + 2 = 53 - 2). In religion The Book of Numbers says that Aaron died at the age of 123. In telephony *The emergency telephone number in Colombia *The telephone number of the speaking clock for the correct time in the United Kingdom *The electricity ( PLN) emergency telephone number in Indonesia *The medical emergency telephone number in Egypt *The Notation for national and international telephone numbers Recommendation ITU-T Recommendation E.123 defines a standard way to write telephone numbers, e-mail addresses, and web addresses In other fields 123 is also: * ''123'' (film), a 2002 Indian film *123 (interbank network), shared cash network ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
97 (number)
97 (ninety-seven) is the natural number following 96 and preceding 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), following 89 and preceding 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 <= 29. * The numbers 97, 907, 9007, 90007 and 900007 are all primes, and they are all s. However, 9000007 (read as ''nine million seven'') is |
81 (number)
81 (eighty-one) is the natural number following 80 and preceding 82. In mathematics 81 is: * the square of 9 and the fourth power of 3. * a perfect totient number like all powers of three. * a heptagonal number. * a centered octagonal number. * a tribonacci number. * an open meandric number. * the ninth member of the Mian-Chowla sequence. * a palindromic number in bases 8 (1218) and 26 (3326). * a Harshad number in bases 2, 3, 4, 7, 9, 10 and 13. * one of three non-trivial numbers (the other two are 1458 and 1729) which, when its digits (in decimal) are added together, produces a sum which, when multiplied by its reversed self, yields the original number: : 8 + 1 = 9 : 9 × 9 = 81 (although this case is somewhat degenerate, as the sum has only a single digit). The inverse of 81 is 0. recurring, missing only the digit "8" from the complete set of digits. This is an example of the general rule that, in base ''b'', :\frac = 0.\overline, omitting only the digit ''b'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
66 (number)
66 (sixty-six) is the natural number following 65 and preceding 67. Usages of this number include: In mathematics 66 is: *a sphenic number. *a triangular number. *a hexagonal number. *a semi-meandric number. *a semiperfect number, being a multiple of a perfect number. *an Erdős–Woods number, since it is possible to find sequences of 66 consecutive integers such that each inner member shares a factor with either the first or the last member. *palindromic and a repdigit in bases 10 (6610), 21 (3321) and 32 (2232) In science Astronomy *Messier object Spiral Galaxy M66, a magnitude 10.0 galaxy in the constellation Leo. *The New General Catalogue object NGC 66, a peculiar barred spiral galaxy in the constellation Cetus. * 66 Maja, a carbonaceous background asteroid from the central regions of the asteroid belt. Physics *The atomic number of dysprosium, a lanthanide. In computing 66 (more specifically 66.667) megahertz (MHz) is a common divisor for the front side bus (F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
45 (number)
45 (forty-five) is the natural number following 44 (number), 44 and followed by 46 (number), 46. In mathematics Forty-five is the smallest Parity (mathematics), odd number that has more divisors than n+1, and that has a larger sum of divisors than n+1. It is the sixth positive integer with a prime factorization of the form p^q, with and being Prime number, prime. Forty-five is the summation, sum of all single-digit decimal digits: 0+1+2+3+4+5+6+7+8+9=45. It is, equivalently, the ninth triangle number. Forty-five is also the fourth hexagonal number and the second polygonal number, hexadecagonal number, or 16-gonal number. It is also the second smallest triangle number (after 1 and 10) that can be written as the sum of two squares. Since the greatest prime factor of 45^+1=2026 is 1,013, which is much more than 45 twice, 45 is a Størmer number. In decimal, 45 is a Kaprekar number and a Harshad number. Forty-five is a oeis:A001003, little Schroeder number; the next suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
31 (number)
31 (thirty-one) is the natural number following thirty, 30 and preceding 32 (number), 32. It is a prime number. In mathematics 31 is the 11th prime number. It is a superprime and a Self number#Self primes, self prime (after 3, 5, and 7), as no integer added up to its base 10 digits results in 31. It is a lucky prime and a happy number; two properties it shares with 13 (number), 13, which is its dual emirp and permutable prime. 31 is also a primorial prime, like its twin prime, 29 (number), 29. 31 is the number of regular polygons with an odd number of sides that are known to be constructible polygon, constructible with compass and straightedge, from combinations of known Fermat primes of the form 22''n'' + 1. 31 is the third Mersenne prime of the form 2''n'' − 1. It is also the eighth Mersenne prime exponent, specifically for the number 2,147,483,647, which is the maximum positive value for a 32-bit Integer (computer science), signed binary integer in computing. After 3, it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21 (number)
21 (twenty-one) is the natural number following 20 and preceding 22. The current century is the 21st century AD, under the Gregorian calendar. In mathematics 21 is: * a composite number, its proper divisors being 1, 3 and 7, and a deficient number as the sum of these divisors is less than the number itself. * a Fibonacci number as it is the sum of the preceding terms in the sequence, 8 and 13. * the fifth Motzkin number. * a triangular number, because it is the sum of the first six natural numbers (1 + 2 + 3 + 4 + 5 + 6 = 21). * an octagonal number. * a Padovan number, preceded by the terms 9, 12, 16 (it is the sum of the first two of these) in the padovan sequence. * a Blum integer, since it is a semiprime with both its prime factors being Gaussian primes. * the sum of the divisors of the first 5 positive integers (i.e., 1 + (1 + 2) + (1 + 3) + (1 + 2 + 4) + (1 + 5)) * the smallest non-trivial example of a Fibonacci number whose digits are Fibonacci numbers and whose digit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
