Definitions for nontotient
non·to·tient

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1. nontotientnoun

   An integer that is never a solution to Euler's totient function.

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1. Nontotient

   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 14, 26, 34, 38, 50, 62, 68, 74, 76, 86, 90, 94, 98, 114, 118, 122, 124, 134, 142, 146, 152, 154, 158, 170, 174, 182, 186, 188, 194, 202, 206, 214, 218, 230, 234, 236, 242, 244, 246, 248, 254, 258, 266, 274, 278, 284, 286, 290, 298, ... (sequence A005277 in the OEIS)Least k such that the totient of k is n are (0 if no such k exists) 1, 3, 0, 5, 0, 7, 0, 15, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 25, 0, 23, 0, 35, 0, 0, 0, 29, 0, 31, 0, 51, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 69, 0, 47, 0, 65, 0, 0, 0, 53, 0, 81, 0, 87, 0, 59, 0, 61, 0, 0, 0, 85, 0, 67, 0, 0, 0, 71, 0, 73, ... (sequence A049283 in the OEIS)Greatest k such that the totient of k is n are (0 if no such k exists) 2, 6, 0, 12, 0, 18, 0, 30, 0, 22, 0, 42, 0, 0, 0, 60, 0, 54, 0, 66, 0, 46, 0, 90, 0, 0, 0, 58, 0, 62, 0, 120, 0, 0, 0, 126, 0, 0, 0, 150, 0, 98, 0, 138, 0, 94, 0, 210, 0, 0, 0, 106, 0, 162, 0, 174, 0, 118, 0, 198, 0, 0, 0, 240, 0, 134, 0, 0, 0, 142, 0, 270, ... (sequence A057635 in the OEIS)Number of ks such that φ(k) = n are (start with n = 0) 0, 2, 3, 0, 4, 0, 4, 0, 5, 0, 2, 0, 6, 0, 0, 0, 6, 0, 4, 0, 5, 0, 2, 0, 10, 0, 0, 0, 2, 0, 2, 0, 7, 0, 0, 0, 8, 0, 0, 0, 9, 0, 4, 0, 3, 0, 2, 0, 11, 0, 0, 0, 2, 0, 2, 0, 3, 0, 2, 0, 9, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 17, ... (sequence A014197 in the OEIS)According to Carmichael's conjecture there are no 1's in this sequence. An even nontotient may be one more than a prime number, but never one less, since all numbers below a prime number are, by definition, coprime to it. To put it algebraically, for p prime: φ(p) = p − 1. Also, a pronic number n(n − 1) is certainly not a nontotient if n is prime since φ(p2) = p(p − 1). If a natural number n is a totient, it can be shown that n · 2k is a totient for all natural number k. There are infinitely many even nontotient numbers: indeed, there are infinitely many distinct primes p (such as 78557 and 271129, see Sierpinski number) such that all numbers of the form 2ap are nontotient, and every odd number has an even multiple which is a nontotient.

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1. Nontotient

   In number theory, a nontotient is a positive integer n which is not in the range of Euler's totient function φ, that is, for which φ(x) = n has no solution. 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 fifty even nontotients are An even nontotient may be one more than a prime number, but never one less, since all numbers below a prime number are, by definition, coprime to it. To put it algebraically, for p prime: φ = p − 1. Also, a pronic number n is certainly not a nontotient if n is prime since φ = p. Furthermore, a nontotient can't be expressed as the product of numbers of the form p - 1 and their powers.

How to pronounce nontotient?

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Numerology

1. Chaldean Numerology

   The numerical value of nontotient in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of nontotient in Pythagorean Numerology is: 2

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Nontotient
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Nontotient
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=nontotient