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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.
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.
183 is a perfect totient number, a number that is equal to the sum of its iterated totients. [ 1 ] Because 183 = 13 2 + 13 + 1 {\displaystyle 183=13^{2}+13+1} , it is the number of points in a projective plane over the finite field Z 13 {\displaystyle \mathbb {Z} _{13}} .
It is a perfect totient number. [3] 39 is the sum of five consecutive primes (3 + 5 + 7 + 11 + 13) and also is the product of the first and the last of those ...
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)
It is a perfect totient number, the smallest such number to be neither a power of three nor thrice a prime. Since 255 is the product of the first three Fermat primes, the regular 255-gon is constructible. In base 10, it is a self number. 255 is a repdigit in base 2 (11111111), in base 4 (3333), and in base 16 (FF).
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]