The K―N inverse scattering problem is solved for a model which assumes that the Λ(1405) is an elementary particle rather than a virtual bound state of the K―N system. This model points to a consistent explanation of the kaonic-hydrogen data and the K―N scattering results. It is found that the K―N interaction form factor determined from the real part of the elastic K―N phase shifts has reasonable behavior and a range that is consistent with that of the K―N interaction.