Counting with divisibility

Sets. $|A_2|=\lfloor1000/2\rfloor=500$, $|A_3|=333$, $|A_5|=200$.

Pairs. $|A_2\cap A_3|=\lfloor1000/6\rfloor=166$, $|A_2\cap A_5|=100$, $|A_3\cap A_5|=66$.

Triple. $|A_2\cap A_3\cap A_5|=\lfloor1000/30\rfloor=33$.

IE. $500+333+200-166-100-66+33=734$.

Conclusion. $734$ integers.