Definition:Nontotient

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

• Euler Phi Function is Even for Argument greater than 2

• Definition:Totient

• Definition:Cototient
• Definition:Noncototient

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