There Can Be Infinitely Many

Number Theory Level 4

A positive integer \(n\) is called sacred if it is divisible by all odd integers \(a\) for which \(n \geq a^2\). Determine the sum of all sacred numbers.

As an arbitrary example, \(n=15\) is sacred because it is divisible by \(1\) and \(3\).

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.