How to show the top N value from Pivot Table and make the results appear in just 1 sheet when N change?

Joe

You can use the worksheet Change event to detect a change in a cell (containing N) then filter the pivot table based on that.

In the first attached file (and code below), I've put that value in B1. To prevent macro failure, I've also set data validation on that cell so you can only enter an integer between 1 and 200 (since there are currently only 195 countries) 

This code is behind Sheet2 (renamed Pivot in the second file) and I've added comments so you can see the steps (plus B1 is shown in bold, so you can change that if needed):

Private Sub Worksheet_Change(ByVal Target As Range)

' do nothing if a cell other than B1 changed
If Intersect(Target, Range("B1")) Is Nothing Then Exit Sub

' prevent pivot table filter changes re-triggering this procedure
Application.EnableEvents = False

With ActiveSheet.PivotTables("PivotTable1").PivotFields("Country name")
    'remove existing filter
    .ClearValueFilters
    ' apply a filter based on cell B1
    .PivotFilters.Add2 Type:=xlTopCount, _
    DataField:=ActiveSheet.PivotTables("PivotTable1"). _
    PivotFields("Sum of Amount"), Value1:=Target.Value

End With
' renable events
Application.EnableEvents = True

End Sub

REVISION:

Given your revised file (and question), I've moved the code in the sub  details (you copied from elsewhere I believe) to a standard module in the SECOND file below and modified it as below (with the event code above too). The Output sheet has only row 1 (at present) but when the button on the sheet renamed Pivot is clicked,  it will now collect the top N data (highest country first) and paste the detail into a single Output sheet (which is renamed to show when it was done) then show it. Comments are shown for your guidance:

Sub detail()
    Dim c As Range
    Dim LstRw As Long, Done As String
    
    'clear existing report detail but keep header row
    Sheet4.UsedRange.Offset(1, 0).Delete
    ' stop "want to save" alerts etc
    Application.DisplayAlerts = False
    ' loop through pivot
    With Sheet2.PivotTables("PivotTable1")
       For Each c In .DataBodyRange.Resize(, 1)
        'determine last row
          LstRw = Sheet4.Range("A" & Rows.Count).End(xlUp).Row
          'reveal data
          c.ShowDetail = True
          ' copy autoselected data (less headers) at end of Sheet4
          Selection.Offset(1, 0).Copy
          Sheet4.Range("A" & LstRw + 1).PasteSpecial Paste:=xlPasteAll
          ' delete the details sheet
          ActiveSheet.Delete
       Next c
    End With
    'renable
    Application.DisplayAlerts = True
    
    ' create text for time/date
    Done = Replace(Left(CStr(Time), 5), ":", "") & "hrs " & Replace(CStr(Date), "/", "-")
    
    'show output sheet and rename (with time/date)
    With Sheet4
        .Name = "Output " & Done
        .UsedRange.BorderAround (xlSolid)
        .Activate
        .Cells(2, 1).Select
    End With
    
    MsgBox "Here's the detail for the Top " & Sheet2.Range("B1") & " at " & Done
End Sub

Note that the Top N  pivot table is now sorted with the highest Amount value first (likewise for the Output detail).

Hope this solves your problem.