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- Noncototient abstract "In mathematics, a noncototient is a positive integer n that cannot be expressed as the difference between a positive integer m and the number of coprime integers below it. That is, m − φ(m) = n, where φ stands for Euler's totient function, has no solution for m. The cototient of n is defined as n − φ(n), so a noncototient is a number that is never a cototient.It is conjectured that all noncototients are even. This follows from a modified form of the Goldbach conjecture: if the even number n can be represented as a sum of two distinct primes p and q, then It is expected that every even number larger than 6 is a sum of distinct primes, so probably no odd number larger than 5 is a noncototient. The remaining odd numbers are covered by the observations and .The first few noncototients are:10, 26, 34, 50, 52, 58, 86, 100, 116, 122, 130, 134, 146, 154, 170, 172, 186, 202, 206, 218, 222, 232, 244, 260, 266, 268, 274, 290, 292, 298, 310, 326, 340, 344, 346, 362, 366, 372, 386, 394, 404, 412, 436, 466, 470, 474, 482, 490, 518, 520 (sequence A005278 in OEIS)Erdős (1913-1996) and Sierpinski (1882-1969) asked whether there exist infinitely many noncototients. This was finally answered in the affirmative by Browkin and Schinzel (1995), who showed every member of the infinite family is an example. Since then other infinite families, of roughly the same form, have been given by Flammenkamp and Luca (2000).".
- Noncototient wikiPageExternalLink Noncototient.html.
- Noncototient wikiPageID "758718".
- Noncototient wikiPageRevisionID "587431794".
- Noncototient hasPhotoCollection Noncototient.
- Noncototient subject Category:Integer_sequences.
- Noncototient type Abstraction100002137.
- Noncototient type Arrangement107938773.
- Noncototient type Group100031264.
- Noncototient type IntegerSequences.
- Noncototient type Ordering108456993.
- Noncototient type Sequence108459252.
- Noncototient type Series108457976.
- Noncototient comment "In mathematics, a noncototient is a positive integer n that cannot be expressed as the difference between a positive integer m and the number of coprime integers below it. That is, m − φ(m) = n, where φ stands for Euler's totient function, has no solution for m. The cototient of n is defined as n − φ(n), so a noncototient is a number that is never a cototient.It is conjectured that all noncototients are even.".
- Noncototient label "Anticoïndicateur".
- Noncototient label "Noncototient".
- Noncototient label "Noncototiente".
- Noncototient label "非互補歐拉商數".
- Noncototient sameAs Anticoïndicateur.
- Noncototient sameAs Noncototiente.
- Noncototient sameAs m.038xzd.
- Noncototient sameAs Q1172925.
- Noncototient sameAs Q1172925.
- Noncototient sameAs Noncototient.
- Noncototient wasDerivedFrom Noncototient?oldid=587431794.
- Noncototient isPrimaryTopicOf Noncototient.