Generalizing values which Euler's-totient function does not take I was reading about Euler's totient function on wikipedia, and it eventually led me to this book on google:
Page 74 of the book, Prime numbers: the most mysterious figures in math
 By David G. Wells.
Anyway, the books lists many assertions without proof, only references which I can't find. One I could not solve for myself said that not all even numbers are values of $\phi(n)$. The sequence of even non-values of $\phi(n)$ starts:
$14, 26, 34, 38, 50, 62,\dots$
After thinking about it for a while, I've made little headway. Looking at 14 specifically, I suppose if such a solution $a$ to $\phi(x)=14$ were to exist, $(a,m_i)=1$ for $1\leq i\leq 14$, for some $m_i\lt a$ and so there must also exist inverses $\overline{a_i}$ such that $\overline{a_i}a\equiv 1 \pmod {m_i}$ for each $i$. I'm looking for some contradiction, possibly of the Chinese Remainder Theorem, to show such $a$ cannot exist. 
Is there some way to generalize which values are not taken by $\phi$, or at least explain why this is the case? I was hoping to see why $14$ is the least such integer such that this is true, but values $1$ to $13$ must be indeed taken. I suppose this would also explain why 26 is the next such value that is not taken, while $15$ to $25$ are.

From the comments to A005277 :
If p is prime then the following two statements are true. I. 2p is in the sequence iff 2p+1 is composite (p is not a Sophie Germain prime). II. 4p is in the sequence iff 2p+1 and 4p+1 are composite. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Dec 30 2005 
This covers most of your cases, 50 is covered by the next comment.
