# Number Theory #2

Number Theory Level 5

$$N$$ is a positive integer that satisfies the following:

$$1$$) $$a < b < c$$ where $$a,b,c$$ are positive integers,

$$2$$) $$a|b$$, $$b|c$$,

$$3$$) $$N=a+b+c$$.

Find the sum of all possible values of $$N$$ that cannot satisfy the above conditions.

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