As stated above, the Denons have HDMI passthrough. I'm not sure about the 1613 model, but I have other Denons and the HDMI passthrough is only on certain inputs. My models are older, so that may not apply to your 1613.
What I would recommend is actually getting a universal remote like a harmony that will turn on your cable box and AVR at the same time. You only have a single remote and it will turn on (and off) everything you want with a single button.