4. Between 1 and 200, how many numbers have the sum of all their distinct prime factors equal to 16? (For example: The distinct prime factors of 12 are $2$ and $3$, and their sum is $2+3=5$)
【Analysis】Since $2+3+5+7=17>16$, the number sought can have at most 3 different prime factors. And since 16 is even, if it is decomposed into the sum of 3 primes, one of them must be 2.
$1 、 16=2+3+11$, there are $66 、 132 、 198$ for a total of 3
2、 $16=3+13$, there are $39 、 117$ for a total of 2
3、 $16=5+11$, there is 55 for a total of 1
In summary, there are 6 in total.