Highly cototient number

A highly cototient number is a natural number \( n \) such that the equation \( x - \varphi(x) = n \) has more solutions than any smaller positive integer \( m \). Here, \( \varphi(x) \) is the Euler's totient function, which counts the number of integers up to \( x \) that are relatively prime to \( x \).