What does ICAO database "engine count c" mean?
I don't know the exact ICAO phraseology, but it certainly seems to describe an aircraft that has two engines combined to a single driveshaft.

Soloy has trademarked the 'Dual Pac', a pair of turboprops driving a single shaft through a gearbox. All of the Soloy aircraft there use this powerplant.



The Fairey Gannet was a (super cool) anti-submarine aircraft designed in the late 40s. It was powered by the Armstrong Siddeley Double Mamba which you could argue was the direct predecessor of the Dual Pac, albeit using a presumably very different gearbox to drive the contra-rotating prop. One half of the Double Mamba could be shut down in flight, and both props would continue to be driven: 


  The Double Mamba engine could be run with one Mamba stopped to conserve fuel and extend endurance for cruise flight. The contra-rotating propellers meant that when only half of the Double Mamba was running there were no thrust asymmetry problems.