Not always adorable!

Number Theory Level 4

A natural number $m$ is adorable if you can write it as sum of three natural numbers $m = a+b+c$ such that $(2 \mid a), (3 \mid b), (4 \mid c)$ .

Find the sum of all natural numbers which are not adorable.

Details and assumptions:

$a\mid b$ means $a$ divides $b$ , i.e. $b$ is divisible by $a$ .
As an explicit example, the number $11$ is adorable because $11 = 4+3+4$ , and $2\mid 4 ; 3\mid 3 , 4\mid 4$ . But the number $7$ is not adorable because you can't find such $a,b,c$ .