26) Let $S=\{1,2, \cdots, 21002\}$ for any $a, b \in S$ (where $a, b$ can be the same), we always have $a b \notin S$, find the maximum value of $|S|$.
Solve $|. S|_{\text {max }}=1958$.
First. $1 \in S$. Otherwise, let $a=b=1$. Then $a \cdot b \cdot a b \in S$, which contradicts the problem's condition!

Next. If $a \in\{2,3,4, \pi, 6: \| \in S$, then in the following pairs, the two numbers cannot both belong to $S$.
$$
\begin{array}{c}
(1 \cdot a) \cdot(2 \cdot 2 a) \cdot \cdots \cdot(a-1 \cdot(a-1) a) \\
(a+1 \cdot(a+1) a) \cdot(a+2 \cdot(a+2) a), \cdots, \\
(2 a-1 \cdot(2 a-1) a)
\end{array}
$$
$$
(44 a+1 \cdot(44 a+1) a) \cdot(44 a+2 \cdot(44 a+2) a), \cdots$.
$$
(4 \overline{5} a-1 \cdot(4 \overline{5} a-1) a) \text {. }
$$

From the above, $(a-1) a \leqslant(45 \times 6-1) \times 645^{2}-2025>2002$, so $a b \notin S$. At this point, $|S|=1958$.

In summary, the maximum value of $|S|$ is 1958.