A gaffe by Mayor Bloomberg turned into a round of laughs yesterday when the executive director of the Freelancers Union corrected confusion over her group’s name.

“Last year, we successfully advocated for reducing or eliminating the unincorporated business tax for some 17,000 freeloaders and contractors,” the mayor proclaimed at a downtown ceremony.

“And we, of course, meant freelancers,” interrupted Sara Horowitz.

“What’d I say?” asked the mayor.

“We won’t go there,” recommended Horowitz, generating laughter all around.