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- Nontotient abstract "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 fifty even nontotients are14, 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, 302 (sequence A005277 in OEIS)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).There are infinitely many nontotient numbers: indeed, there are infinitely many distinct primes p such that all numbers of the form 2ap are nontotient, and every odd number has a multiple which is a nontotient.".
- Nontotient wikiPageExternalLink C:TempObsTotientCototientValence.pdf.
- Nontotient wikiPageID "748422".
- Nontotient wikiPageRevisionID "562231734".
- Nontotient hasPhotoCollection Nontotient.
- Nontotient subject Category:Integer_sequences.
- Nontotient type Abstraction100002137.
- Nontotient type Arrangement107938773.
- Nontotient type Group100031264.
- Nontotient type IntegerSequences.
- Nontotient type Ordering108456993.
- Nontotient type Sequence108459252.
- Nontotient type Series108457976.
- Nontotient comment "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.".
- Nontotient label "Anti-indicateur".
- Nontotient label "Niettotiënt".
- Nontotient label "Nontotient".
- Nontotient label "Nontotiente".
- Nontotient label "Нетотиентное число".
- Nontotient label "ノントーティエント".
- Nontotient label "非歐拉商數".
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- Nontotient sameAs Nontotiente.
- Nontotient sameAs ノントーティエント.
- Nontotient sameAs Niettotiënt.
- Nontotient sameAs m.0380vc.
- Nontotient sameAs Q2048257.
- Nontotient sameAs Q2048257.
- Nontotient sameAs Nontotient.
- Nontotient wasDerivedFrom Nontotient?oldid=562231734.
- Nontotient isPrimaryTopicOf Nontotient.