Once upon a time in Mathville

Number Theory Level 3

Once upon a time in Mathville, a planet in the distant galaxy of Mathematica, there were two students, Adarsh and Rajdeep, both of who went to the Mathlete School, the doors of which were open only to those who loved Math.

Anyway, they were discussing Number Theory just when Adarsh (the intelligent one) came up with a problem and decided to test it on Rajdeep (the brilliant one). Here's the question:

"I wrote down a list of natural numbers less than 1000 and none of any two numbers have a product divisible by 15. Tell me Rajdeep, what is the total maximum numbers I could have written down?"

Rajdeep answered almost instantly and was correct! What was the answer given by Rajdeep?

This problem hasn't been created solely by me, Rajdeep helped a lot!

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