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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.
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.
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 ...
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 is defined as (), i.e. the number of positive integers less than or equal to that have at least one prime factor in common with .For example, the cototient of 6 is 4 since these four positive integers have a prime factor in common with 6: 2, 3, 4, 6.
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. [41] A nontotient is a natural number which is not a totient number. Every odd integer exceeding 1 is trivially a nontotient.
In number theory, the totient summatory function is a summatory function of Euler's totient function defined by ():= = (),.It is the number of ordered pairs of coprime integers (p,q), where 1 ≤ p ≤ q ≤ n.