Integers whose Ratio between Sigma and Phi is Square

Theorem

The sequence of integers whose $\sigma$ value divided by its Euler $\phi$ value is a square begins:

$1, 14, 30, 105, 248, 264, 418, 714, 1485, 3080, \ldots$

Proof

 $\displaystyle \map \phi {714}$ $=$ $\displaystyle 192$ $\phi$ of $714$ $\displaystyle \map \sigma {714}$ $=$ $\displaystyle 1728$ $\sigma$ of $714$ $\displaystyle \map \sigma {714} / \map \phi {714}$ $=$ $\displaystyle 1728 / 192$ $\displaystyle$ $=$ $\displaystyle 9$ $\displaystyle$ $=$ $\displaystyle 3^2$