Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/420

Examples of Numbers such that Divisor Count divides Phi divides Sigma
The number $420$ has the property that:
 * $\map {\sigma_0} {420} \divides \map \phi {420} \divides \map \sigma {420}$

where:
 * $\divides$ denotes divisibility
 * $\sigma_0$ denotes the divisor counting function
 * $\phi$ denotes the Euler $\phi$ (phi) function
 * $\sigma$ denotes the $\sigma$ (sigma) function.