Numbers such that Divisor Count divides Phi divides Divisor Sum/Mistake

Source Work

 * The Dictionary
 * $210$
 * $210$

Mistake

 * $\phi \left({210}\right) = 48$ is a factor of $\sigma \left({210}\right) = 576$, and $d \left({210}\right) = 16$ divides both. The sequence of numbers with both these properties starts: $1 \quad 3 \quad 15 \quad 30 \quad 35 \quad 52 \quad 70 \quad 78 \quad 105 \quad 140 \quad 168 \quad 190 \quad 210 \ldots$

The list is incorrect. $52$ does not have this property:

and neither $6$ nor $24$ divide $98 = 2 \times 7^2$.

Instead it appears that $56$ is the correct number here:

The list should be:
 * $1, 3, 15, 30, 35, 56, 70, 78, 105, 140, 168, 190, 210$