# 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

## March madness

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.