Classification of 14, 15, and 20 as friendly or solitary

Determine for each n in {14, 15, 20} whether there exists a positive integer m ≠ n with abundancy index I(m) = I(n), or prove that n is solitary.

Background

Beyond the case of 10, the paper notes that several other integers also have unresolved friendly/solitary status. In particular, the integers 14, 15, and 20 are mentioned as having unknown status, reflecting wider gaps in the classification of friendly and solitary numbers.

This underscores the broader context in which the paper’s bounds fit and highlights additional concrete instances where the classification problem remains open.