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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 number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758: Extravagant numbers: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ... A number that has fewer digits than the number of digits in its prime factorization (including ...
Thus, a highly totient number is a number that has more ways of being expressed as a product of this form than does any smaller number. The concept is somewhat analogous to that of highly composite numbers , and in the same way that 1 is the only odd highly composite number, it is also the only odd highly totient number (indeed, the only odd ...
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.
Every number in a reduced residue system modulo n is a generator for the additive group of integers modulo n. A reduced residue system modulo n is a group under multiplication modulo n . If { r 1 , r 2 , ... , r φ( n ) } is a reduced residue system modulo n with n > 2, then ∑ r i ≡ 0 mod n {\displaystyle \sum r_{i}\equiv 0\!\!\!\!\mod n} .
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:
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.