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243 (two hundred [and] forty-three) is the natural number following 242 and preceding 244. Additionally, 243 is: the only 3-digit number that is a fifth power (3 5). a perfect totient number. [1] the sum of five consecutive prime numbers (41 + 43 + 47 + 53 + 59). an 82-gonal 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.
A totient number is a value of Euler's totient function: that is, an m for which there is at least one n for which φ(n) = m. The valency or multiplicity of a totient number m is the number of solutions to this equation. [40] A nontotient is a natural number which is not a totient number. Every odd integer exceeding 1 is trivially a nontotient.
A highly totient number is an integer that has more solutions to the equation () =, where is Euler's totient function, than any integer smaller than it. The first few highly totient numbers are The first few highly totient numbers are
In mathematics, specifically number theory, a sparsely totient number is a natural number, n, such that for all m > n, > ()where is Euler's totient function.The first few sparsely totient numbers are:
The cototient of 8 is also 4, this time with these integers: 2, 4, 6, 8. There are exactly two numbers, 6 and 8, which have cototient 4. There are fewer numbers which have cototient 2 and cototient 3 (one number in each case), so 4 is a highly cototient number. (sequence A063740 in the OEIS)
In number theory, a totative of a given positive integer n is an integer k such that 0 < k ≤ n and k is coprime to n. Euler's totient function φ(n) counts the number of totatives of n. The totatives under multiplication modulo n form the multiplicative group of integers modulo n.
A cyclic number [1] [2] is a natural number n such that n and φ(n) are coprime. Here φ is Euler's totient function. An equivalent definition is that a number n is cyclic if and only if any group of order n is cyclic. [3] Any prime number is clearly cyclic. All cyclic numbers are square-free. [4] Let n = p 1 p 2 …