Integers whose Divisor Sum equals Half Phi times Divisor Count/Historical Note

Historical Note on Integers whose Sigma equals Half Phi times Tau
The intent of this result is unclear. Its statement by in his  of $1997$ was erroneous, but no indication was given as to where it originated.

The On-Line Encyclopedia of Integer Sequences suggests that this result may be intended as:
 * $\map \sigma n = \map \phi n \times \map j n$

where $\map j n$ is the count of $d \divides n$ such that $d \ge 3$ and $1 \le \dfrac n d \le d - 2$.

In such a case, the sequence begins:
 * $35, 105, 248, 418, 594, 744, 812, 1254, \ldots$

It is also possible that the result may also have been intended to be:
 * $\map \sigma n = \map \phi n \times \map k n$

where $\map k n$ is the count of $d \divides n$ such that $d < \sqrt n$.