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

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

The intent of this result is unclear. Its statement by David Wells in his Curious and Interesting Numbers, 2nd ed. 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:

$\map {\sigma_1} n = \map \phi n \times \map j n$

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:

$\map {\sigma_1} n = \map \phi n \times \map k n$

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