# Problem of the Month

• Everyone is welcome to participate, but only undergraduate OU students are eligible for the prizes.
• If there is more than one correct submission, the evaluation committee will select a winner.
• A complete solution to the problem must include a proof.
• Solutions to the Problem of the Month can be submitted in the Math Department's office (PHSC 423).
• Make sure that your submission includes your name and OU email.
• The deadline for submission is the last day of the month.

### March 2020

A positive integer $$m$$ is said to be mad if there exists a positive integer $$n$$ such that $$m=n^{d(n)}$$, where $$d(n)$$ is the number of positive integers that divide $$n$$. Find all mad numbers less than or equal to 2020. Note: When calculating $$d(n)$$, keep in mind that 1 and $$n$$ divide $$n$$. For example, $$d(12)=6$$, since the positive integers that divide 12 are 1, 2, 3, 4, 6 and 12.