An integer $n > 0$ is called a nontotient if $N_{\phi}(n) = 0$ where $N_{\phi}$ is the totient valence function. This is the case of any odd integer greater than 1. This is also the case of twice a prime that isn't a Sophie Germain prime, one more than a prime, an oblong number that is the product of a prime and one more or less than that prime, etc.

Sloane's OEIS lists even values in A005277 and all values together in A007617.