<prompt> Answer this question truthfullyWhat medical condition is suggested by the presence of black necrotic skin lesions in patients infected with Pseudomonas, with ecthyma gangrenosum being a common manifestation?  <response>: <reason> In patients infected with Pseudomonas, the presence of black necrotic skin lesions typically indicates which medical condition, with ecthyma gangrenosum being a common manifestation? 