One remark attributed to Mr. Bloomberg went like this: “If women wanted to be appreciated for their brains, they’d go to the library instead of to Bloomingdale’s.” Another line, purportedly Mr. Bloomberg’s sales pitch for his eponymous computer terminal, said the machine will “do everything,” including oral sex, although a cruder term was used.

“I guess,” Mr. Bloomberg was quoted as saying, “that puts a lot of you girls out of business.”…

Lawsuits portrayed the early days of his company as a frat house, with employees bragging about sexual exploits. Even after entering politics, Mr. Bloomberg’s cavalier attitude caused trouble: In 2012, the mayor, while admiring a woman at a party, urged two guests to “look at the ass on her.” Just last year, he cast doubt on harassment allegations against Charlie Rose, the disgraced CBS anchor. “I don’t know how true all of it is,” Mr. Bloomberg told The New York Times.