Thinking Cap

Problem 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.