Integers whose Divisor Sum equals Half Phi times Divisor Count

Theorem
The following positive integers $n$ have the property where:
 * $\sigma \left({n}\right) = \dfrac {\phi \left({n}\right) \times \tau \left({n}\right)} 2$

where:
 * $\sigma \left({n}\right)$ denotes the $\sigma$ function: the sum of the divisors of $n$
 * $\phi \left({n}\right)$ denotes the Euler $\phi$ function: the count of positive integers smaller than of $n$ which are coprime to $n$
 * $\tau \left({n}\right)$ denotes the $\tau$ function: the count of the divisors of $n$:

These positive integers are:
 * $35, 105, \ldots$

Proof
We have: