Here's a notebook with CellProlog and CellEpilog set up to automatically print perfect numbers in expanded form. One advantage is that Out[$Line] (or %) is equal to the actual integer and not some held or inactive form. And if you copy the output (either Copy/Paste or Cmd-Opt-L right below the output on a Mac), you get what you see (no hidden HoldForm[] and Defer[] is automatically stripped).

Note that this approach need not be applied via CellProlog. One can simply execute the following in a notebook:

$PrePrint = 
   Function[expr, 
     If[TrueQ[$expandPerfectNumbers] && PerfectNumberQ[expr],
       Defer[Plus[##]] & @@ Most@Divisors@expr, expr]];

In this case it will be set and apply to all notebooks until $PrePrint is unset with the following:

$PrePrint =.

Note that CellEpilog does the unsetting after every execution, so in effect, the expansion of perfect numbers happens only in the "Perfect Number Notebook" and not in other open notebooks. Also the SetOptions[EvaluationNotebook[],...] need only be executed once; when the notebook is saved, the options become persistent until explicitly reset. Note also that when CellEpilog unsets $PrePrint for all notebooks. A more careful implementation would use CellProlog to save the current value of $PrePrint and CellEpilog to restore it, if it already has a value. One might even try to compose the two, so that the user's $PrePrint would stay in effect in "Perfect Number Notebook." (I think I wouldn't do this. I would rather assert control over the notebook, so that I could be sure how it would behave.)

If all you want to do is to see the result then

Plus@@Map[HoldForm,Drop[Divisors[8128], -1]]

returns this

1+2+4+8+16+32+64+127+254+508+1016+2032+4064

But the appearance of that is different from what is behind the scene. You can use ReleaseHold to turn that into something you can then use in another calculation, but the sum will be immediately calculated when you do that