In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter phi as or , and may also be called Euler's phi function. In other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal to 1. The integers k of this form are sometimes referred to as totatives of n.
111 is the natural number following 110 and preceding 112.
28 (twenty-eight) is the natural number following 27 and preceding 29.
72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozen.
81 (eighty-one) is the natural number following 80 and preceding 82.
39 (thirty-nine) is the natural number following 38 and preceding 40.
100 or one hundred is the natural number following 99 and preceding 101.
120, read as one hundred [and] twenty, is the natural number following 119 and preceding 121.
400 is the natural number following 399 and preceding 401.
2000 is a natural number following 1999 and preceding 2001.
8000 is the natural number following 7999 and preceding 8001.
In number theory, a nontotient is a positive integer n which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(x) = n has no solution x. In other words, n is a nontotient if there is no integer x that has exactly n coprimes below it. All odd numbers are nontotients, except 1, since it has the solutions x = 1 and x = 2. The first few even nontotients are
A highly totient number is an integer that has more solutions to the equation , where is Euler's totient function, than any integer below it. The first few highly totient numbers are
In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number. For example: 7 = 71, 9 = 32 and 64 = 26 are prime powers, while 6 = 2 × 3, 12 = 22 × 3 and 36 = 62 = 22 × 32 are not.
363 is the natural number following 362 and preceding 364.
183 is the natural number following 182 and preceding 184.
An Achilles number is a number that is powerful but not a perfect power. A positive integer n is a powerful number if, for every prime factor p of n, p2 is also a divisor. In other words, every prime factor appears at least squared in the factorization. All Achilles numbers are powerful. However, not all powerful numbers are Achilles numbers: only those that cannot be represented as mk, where m and k are positive integers greater than 1.
In number theory, 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 mathematics, a power of three is a number of the form 3n where n is an integer – that is, the result of exponentiation with number three as the base and integer n as the exponent.
The number 4,294,967,295 is an integer equal to 232 − 1. It is a perfect totient number. It follows 4,294,967,294 and precedes 4,294,967,296. It has a factorization of .
