Definition:Nontotient
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Definition
A nontotient is a positive even integer $n$ such that:
- $\nexists m \in \Z_{>0}: \map \phi m = n$
where $\map \phi m$ denotes the Euler $\phi$ function.
That is, a nontotient is a positive even integer which is not the totient of any positive integer.
Sequence
The sequence of nontotients begins:
- $14, 26, 34, 38, 50, 62, 68, 74, 76, 86, 90, 94, 98, 114, 118, 122, 124, 134, 142, 146, 152, 154, \ldots$
Also see
Linguistic Note
The word totient is pronounced to rhyme with quotient, that is: toe-shyent or toe-shent, according to taste.
The same applies to its various relatives: nontotient, cototient, noncototient, and so on.
Sources
- Weisstein, Eric W. "Nontotient." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Nontotient.html