Definition:Noncototient
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Definition
A noncototient is a positive integer $n$ such that:
- $\nexists m \in \Z_{>0}: m - \map \phi m = n$
where $\map \phi m$ denotes the Euler $\phi$ function.
That is, a noncototient is a positive integer which is not the cototient of any positive integer.
Sequence
The sequence of noncototients begins:
- $10, 26, 34, 50, 52, 58, 86, 100, 116, 122, 130, 134, 146, 154, 170, 172, 186, 202, \ldots$
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
- 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $10$