Use the DateTime.DayOfWeek property.
https://msdn.microsoft.com/en-US/library/system.datetime.dayofweek(v=vs.110).aspx
static public List<string> GetDates(DateTime start_date, DateTime end_date)
{
List<string> days_list = new List<string>();
for (DateTime date = start_date; date <= end_date; date = date.AddDays(1))
{
if (date.DayOfWeek == DayOfWeek.Sunday || date.DayOfWeek == DayOfWeek.Saturday)
days_list.Add(date.ToShortDateString());
}
return days_list;
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