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.
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).