【Question 15】
For a positive integer $n$, if there exist positive integers $a$ and $b$ such that $n=a+b+a \times b$, then $n$ is called a "good number". For example, $3=1+1+1 \times 1$, so 3 is a "good number". Among the 100 positive integers from 1 to 100, there are $\qquad$ "good numbers".
【Analysis and Solution】
Number Theory, Composite Numbers.
$$
\begin{array}{l}
n=a+b+a \times b ; \\
n+1=a+b+a \times b+1=(a+1) \times(b+1) ;
\end{array}
$$
$a+1$ and $b+1$ are divisors of $n+1$ greater than 1;
Therefore, $n+1$ is a composite number;
In the range from 2 to 101, there are 26 prime numbers and 74 composite numbers; that is, $n+1$ has 74 cases; among the 100 positive integers from 1 to 100, there are 74 "good numbers".