The lecherous millionaire is a hypothetical character who offers to pay for a woman's sick child's medical treatment in return for sexual favours. It's meant as a philosophy thought experiment to illustrate the concept of coercion.
I'm not thinking in terms of philosophy however, but rather about law. Assume that the lecherous millionaire is sincere: if the woman says yes he will keep his word to pay the medical bills, while if the woman declines he'll let her go without further comment. Does the lecherous millionaire violate any laws by making this offer? If the woman accepts, can she later claim rape? What about lesser charges like sexual harassment?
My guess is it's not rape - if the woman doesn't want sex, she can walk away - but I'm not sure about sexual harassment.
If the country matters, assume it is in the US (however I'm interested in all countries, and especially so if this situation has happened before).