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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.
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.
In 1736, Leonhard Euler published a proof of Fermat's little theorem [1] (stated by Fermat without proof), which is the restriction of Euler's theorem to the case where n is a prime number. Subsequently, Euler presented other proofs of the theorem, culminating with his paper of 1763, in which he proved a generalization to the case where n is ...
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,
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)
The first few values are 0, 1, 2, 4, 6, 10, 12, 18, 22, 28, 32 (sequence A002088 in the OEIS). Values for powers of 10 at (sequence A064018 in the OEIS ). Properties