Turboshaft engine, twin-engine helicopter equipped with such a turboshaft engine, and method for optimising the zero-power super-idle speed of such a twin-engine helicopter

A turboshaft engine comprising a gas generator that is capable of being rotated, and a free turbine that is rotated by gases of said gas generator, wherein said turboshaft engine comprises a device for spontaneously mechanically coupling said gas generator and said free turbine, comprising at least one free wheel that connects a first shaft which, together with said gas generator, has a reduction ratio K1, and a second shaft which, together with the free turbine, has a reduction ratio K2, said at least one free wheel being arranged such that said free turbine spontaneously drives said gas generator by means of said first and second shafts and said at least one free wheel as soon as a ratio of a rotational speed of said gas generator to a rotational speed of said free turbine is less than the ratio K2/K1, and

• wherein the turboshaft engine comprises a starter-generator that is rigidly connected to an intermediate shaft, and
• wherein said device for spontaneously mechanically coupling comprises two free wheels which connect said intermediate shaft to said first shaft, and to said second shaft, respectively, said two free wheels being arranged such that said free turbine spontaneously drives said gas generator by means of said first and second shafts and said two free wheels when said ratio of the rotational speed of said gas generator to the rotational speed of said free turbine is less than the ratio K2/K1.