How many strictly positive integers less than or equal to 120 are not divisible by 3, 5, or 7?

Proof. By induction (good luck

Translation of the problem statement:
How many strictly positive integers less than or equal to 120 are not divisible by 3, 5, or 7?

Proof. By induction (good luck)
Let's find the number of strictly positive integers less than or equal to 120 that are divisible by 3, 5, or 7. According to the inclusion-exclusion principle, this number is:

$$
40+24+17-8-5-3+1=66
$$

Thus, the number we are looking for is $120-66=54$.