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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 few 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, ... (sequence A005277 in OEIS)Least k such that the totient of k is n are0, 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 OEIS)Greatest k such that the totient of k is n are0, 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 OEIS)Number of ks such that φ(k) = n are: 1, 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 OEIS)According to Carmichael's conjecture there are no 1's in this sequence except the zeroth term.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 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 a multiple which is a nontotient.".
- Nontotient wikiPageExternalLink C:TempObsTotientCototientValence.pdf.
- Nontotient wikiPageID "748422".
- Nontotient wikiPageLength "4255".
- Nontotient wikiPageOutDegree "45".
- Nontotient wikiPageRevisionID "704202881".
- Nontotient wikiPageWikiLink 114_(number).
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- Nontotient wikiPageWikiLink Carmichaels_totient_function_conjecture.
- Nontotient wikiPageWikiLink Category:Integer_sequences.
- Nontotient wikiPageWikiLink Coprime_integers.
- Nontotient wikiPageWikiLink Eulers_totient_function.
- Nontotient wikiPageWikiLink Journal_of_Number_Theory.
- Nontotient wikiPageWikiLink Number_theory.
- Nontotient wikiPageWikiLink PlanetMath.
- Nontotient wikiPageWikiLink Prime_number.
- Nontotient wikiPageWikiLink Pronic_number.
- Nontotient wikiPageWikiLink Range_(mathematics).
- Nontotient wikiPageWikiLink Sierpinski_number.
- Nontotient wikiPageWikiLink Springer_Science+Business_Media.
- Nontotient wikiPageWikiLinkText "Nontotient".
- Nontotient wikiPageWikiLinkText "nontotient number".
- Nontotient wikiPageWikiLinkText "nontotient".
- Nontotient wikiPageUsesTemplate Template:Cite_book.
- Nontotient wikiPageUsesTemplate Template:Cite_journal.
- Nontotient wikiPageUsesTemplate Template:Classes_of_natural_numbers.
- Nontotient wikiPageUsesTemplate Template:OEIS.
- Nontotient wikiPageUsesTemplate Template:Reflist.
- Nontotient wikiPageUsesTemplate Template:Totient.
- Nontotient wikiPageUsesTemplate Template:Wiktionary.
- Nontotient subject Category:Integer_sequences.
- Nontotient hypernym N.
- Nontotient type Band.
- Nontotient type Combinatoric.
- Nontotient type Integer.
- 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 "Nontotient".
- Nontotient sameAs Q2048257.
- Nontotient sameAs Nombro_kiu_ne_estas_valoro_de_eŭlera_φ_funkcio.
- Nontotient sameAs Anti-indicateur.
- Nontotient sameAs Nontóciens_számok.
- Nontotient sameAs Nontotiente.
- Nontotient sameAs ノントーティエント.
- Nontotient sameAs Niettotiënt.
- Nontotient sameAs m.0380vc.
- Nontotient sameAs Нетотиентное_число.
- Nontotient sameAs Q2048257.
- Nontotient sameAs 非歐拉商數.
- Nontotient wasDerivedFrom Nontotient?oldid=704202881.
- Nontotient isPrimaryTopicOf Nontotient.