7. Given a composite number $k(1<k<100)$. If the sum of the digits of $k$ is a prime number, then the composite number $k$ is called a "pseudo-prime". The number of such pseudo-primes is . $\qquad$
7.23.

Let $S(k)$ denote the sum of the digits of $k$, and $M(p)$ denote the set of composite numbers with a pseudo-prime $p$.

When $k \leqslant 99$, $S(k) \leqslant 18$, so there are 7 prime numbers not exceeding 18, which are $2, 3, 5, 7, 11, 13, 17$.
The composite numbers with a pseudo-prime of 2 are $M(2)=\{20\}$.
Similarly, $M(3)=\{12,21,30\}$,
$$
\begin{array}{l}
M(5)=\{14,32,50\}, \\
M(7)=\{16,25,34,52,70\}, \\
M(11)=\{38,56,65,74,92\}, \\
M(13)=\{49,58,76,85,94\}, \\
M(17)=\{98\} .
\end{array}
$$

Thus, there are 23 pseudo-primes in total.