Divisible by Seven

$2^n \equiv 2, 4, 1 \pmod{7}$

$4^n \equiv 4, 2, 1 \pmod{7}$

$1^n \equiv 1, 1, 1 \pmod{7}$

$\therefore 4^n + 2^n + 1^n \equiv 0, 0, 3 \pmod{7}$

Clearly $4^n + 2^n + 1^n$ is a not multiple of $7$ whenever $n$ is multiple of $3$

So subtract number of multiples of $3$ in the range $1 \le n \le 999$ i.e. $333$

$\therefore 999 - 333 = \boxed{666}$ .