Substitute $a=dpqx$ $b=dpry$ $c=dqrz$ Where $gcd(a,b,c)=d$, $p$, $q$, $r$ are the common factors of $a,b$, $a,c$ and $b,c$, beside $d$, and $x,y,z$ the lone factors of $a,b,c$. we have that $n=[a,b]+[b,c]+[c,a]=\frac{ab}{gcd(a,b)}+\frac{cb}{gcd(c,b)}+\frac{ac}{gcd(a,c)}=dpqr(xy+yz+xz)=M(xy+yz+xz)$, where $x,y,z$ are coprime each 2, so we see that $n$ can't be a power of 2, because $(xy+yz+xz)$ is odd and also by substituting $y=z=1$, we have that $n=M(2x+1)$, so any number different from a power of $2$ can be written like this.