2. How many natural numbers greater than one exist, the product of which with their smallest prime divisor does not exceed 100?
Answer: 33.

Sketch of the solution. The smallest prime divisor can be 2. These are the numbers: $2, 4, \ldots, 50$ (25 numbers). The smallest prime divisor can be 3. These are the numbers: 3, 9, 15, 21, 27, 33 (6 numbers). The smallest prime divisor can be 5. This number: 5 (1 number). The smallest prime divisor can be 7. This number: 7 (1 number). Since $11 \times 11=121>100$, there are no other prime divisors with this property. Total numbers: $25+5+1+1=33$.

Criteria. Correct answer only: 1 point.