6. A positive integer $n$, if it does not contain any perfect square factor greater than 1, is called a "simple number". Then, among the 1000 numbers $1,2, \cdots, 1000$, the number of simple numbers is $\qquad$.
6.508.

Notice that $1000<33^{2}$. If a number in the set $M=\{1,2, \cdots, 1000 \}$ is not a simple number, then it must contain one or more factors from the set
$$
A=\left\{2^{2}, 3^{2}, 5^{2}, 7^{2}, 11^{2}, 13^{2}, 17^{2}, 19^{2}, 23^{2}, 29^{2}, 31^{2}\right\}.
$$

Let $P(a)$ denote the number of multiples of $a^{2}$ in set $M$, i.e., $P(a)=\left[\frac{1000}{a^{2}}\right]$. Then
$$
\begin{array}{c}
P(2)=250, P(3)=111, P(5)=40, \\
P(7)=20, P(11)=8, P(13)=5, \\
P(17)=3, P(19)=2, \\
P(23)=P(29)=P(31)=1 ; \\
P(2 \times 3)=27, P(2 \times 5)=10, \\
P(2 \times 7)=5, P(2 \times 11)=2, \\
P(2 \times 13)=1, P(2 \times 17)=0, \\
P(3 \times 5)=4, P(3 \times 7)=2, P(3 \times 11)=0 ; \\
P(2 \times 3 \times 5)=1, P(2 \times 3 \times 7)=0 .
\end{array}
$$

Therefore, the number of simple numbers is
$$
\begin{aligned}
S= & 1000-[P(2)+P(3)+P(5)+ \\
& P(7)+P(11)+P(13)+P(17)+ \\
& P(19)+P(23)+P(29)+P(31)]+ \\
& {[P(2 \times 3)+P(2 \times 5)+P(2 \times 7)+} \\
& P(2 \times 13)+P(3 \times 5)+P(3 \times 7)]- \\
& P(2 \times 3 \times 5) \\
= & 508 .
\end{aligned}
$$