Calls from this number (720-456-3695) show up on Caller ID as coming from Comenity, a Columbus, OH-based bank that handles accounts for several catalog-shopping companies (Eddie Bauer, Woman Within, Ashro, etc.).
Callers will typically not leave a msg. if the call is taken by an answering machine.  Some phones will allow you to block calls from this number (and others; see below).
Some other numbers associated with Comenity Bank (and may be robo-calls from a Call Center) are:
  303-255-5045
  614-212-7505
  614-212-7550
  614-729-6034
  614-729-6040
  614-754-4131
  913-563-5504
Complaints about Comenity's collection techniques (including harrassing phone calls) should be directed to the Columbus, OH Better Business Bureau : http//www.bbb.org/centralohio/get-consumer-help/

I don't know what company it is. Sounds like debt collector that is not mine.

Called every day without leaving messages

Keep getting calls from this number.  When answered only get a recording, "This is not a sales call.  This call is important, please stay on the line and an agent will be with you shortly".  It then hangs-up.

Commenity Capital