Question

How can one prove which even numbers are nontotient?

Answer 1

http://arxiv.org/abs/1412.3089

Answer 2

Take 50 as an example. How can one prove that no natural number n exists with phi(n) = 50 without using Schemmel totient functions, using just the following facts:
1. phi is a multiplicative function, i.e. phi(mn) = phi(m)phi(n) for all natural numbers m, n such that gcd(m, n) = 1
2. given that n = \[\prod_{i=1}^{r}p_i^{e_i}\] is the canonical prime factorization of n, phi(n) = \[\prod_{i=1}^{r}p_i ^{e_i}(1-\frac{ 1 }{ p_i })\]
3. Euler's theorem .