Puzzle 990. K n-values in AP with the same sigma(n)

Fred Schneider sent the following nice puzzle:

K n-values in AP with the same sigma(n)

1: 1 = sigma(1) => Trivial

2: 12 = sigma(6) = sigma(11) => Common difference: 5
3: 360 = sigma(267) = sigma(295) = sigma(323) => Common difference: 28

4: 119508480 = sigma(34560288) = sigma(36699180) = sigma(38838072) = sigma(40976964) => Common Difference: 2138892

5: 1666818611640000 =

sigma(1666818506570911) =

sigma(1666818512348641) =

sigma(1666818518126371) =

sigma(1666818523904101) =

sigma(1666818529681831)

=> Common Difference: 5777730

From CYU #35 at http://www.shyamsundergupta.com/canyoufind.htm:

The answer for 4 is the smallest known solution.

The answer for 5 is the only known solution. J. Wroblewski found this using a parametric equation(!)

Q1) Confirm this is the smallest answer for 4

Q2) Find a smaller solution to 5

Q3) Extend the list