Integers whose Divisor Sum equals Half Phi times Divisor Count

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

where:
 * $\map \sigma n$ denotes the $\sigma$ function: the sum of the divisors of $n$
 * $\map \phi n$ denotes the Euler $\phi$ function: the count of positive integers smaller than of $n$ which are coprime to $n$
 * $\map \tau n$ denotes the divisor counting ($\tau$) function: the count of the divisors of $n$:

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

Proof
We have:

Also see

 * Integers whose Phi times Tau equal Sigma