Are there infinity many $n$ that can't be represented as sum of two composite numbers relatively prime to each other Let $a$ and $b$ be composite integers relatively prime to each other.

Can it be shown that
There are infinity many positive integers $n$ that can't be represented as
$$n=a+b$$

Example first $n$ which can represent $13=9+4$

Update Now posted to MO link
 A: http://oeis.org/A096076 is the sequence, "Not the sum of two relatively prime composite numbers." It's given as, 
$1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 36, 38, 40, 42, 45, 48, 50, 54, 56, 60, 66, 70, 72, 78, 80, 84, 90, 96, 105, 108, 110, 120, 126, 132, 138, 140, 150, 180, 210.$ 
It says, 
"Max Alekseyev showed that this sequence is finite; proof completed by several people to show that the list is complete." 
No proof is given, nor any link to a proof. 
A: Answer is given by GH from MO
Link for original answer
Following fedja's comment, the number of decomposition $n=a+b$ with $\gcd(a,b)=1$ equals $\varphi(n)$. Among these, there are at most $2\pi(n)$ decompositions in which $a$ or $b$ is prime, hence $n$ has a suitable decomposition when $\varphi(n)>2\pi(n)$. Now the well-known explicit lower bounds for $\varphi(n)$ and upper bounds for $\pi(n)$ imply an explicit finite list of exceptions. For more details, see the relevant Wikipedia articles (link1 and link2), or Rosser-Schoenfeld: Approximate formulas for some functions of prime numbers (1961).
Added. By (3.6) and (3.42) in the paper of Rosser and Schoenfeld, the inequality $\varphi(n)>2\pi(n)$ holds as long as
$$e^\gamma\log\log n+\frac{2.51}{\log\log n}<\frac{\log n}{2.52}.$$
In particular, $\varphi(n)>2\pi(n)$ holds for $n>10^7$.
