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The summatory of reciprocal totient function is defined as ():= ... The constant A = 1.943596... is sometimes known as Landau's totient constant. The sum ...
A perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers; if the sum equals n, then n is a perfect totient 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.
278 is equal to Φ(30). It is the sum of the totient function. [2] 278 is a nontotient number which means that it is an even number that doesn't follow Euler's totient function. [3] 278 is the smallest semiprime number that has an anagram that is also semiprime. The other number is 287. [4]
An average order of σ(n), the sum of divisors of n, is nπ 2 / 6; An average order of φ(n), Euler's totient function of n, is 6n / π 2; An average order of r(n), the number of ways of expressing n as a sum of two squares, is π; The average order of representations of a natural number as a sum of three squares is 4πn / 3;
In number theory, the gcd-sum function, [1] also called Pillai's arithmetical function, [1] is defined for every by = = (,)or equivalently [1] = (/)where is a divisor of and is Euler's totient function.
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
144, or twice 72, is also highly totient, as is 576, the square of 24. [8] While 17 different integers have a totient value of 72, the sum of Euler's totient function φ(x) over the first 15 integers is 72. [9] It also is a perfect indexed Harshad number in decimal (twenty-eighth), as it is divisible by the sum of its digits . [10]