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 $$a,b,c$$.

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