Shina wrote a list of positive integers. Belle noticed that each number in the list and any sum of any quantity of distinct numbers from the list were square-free (that is, not divisible by any perfect square except, of course, 1).
What is the maximum quantity of numbers that Shina’s list can have?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!