"Mack the Knife" was introduced to the United States hit parade by Louis Armstrong in 1956, but the song is most closely associated with Bobby Darin, who recorded his version at Fulton Studios on West 40th Street, New York City, on December 19, 1958 (with Tom Dowd engineering the recording). Even though Darin was reluctant to release the song as a single, in 1959 it reached number one on the Billboard Hot 100 and number six on the Black Singles chart, and earned him a Grammy Award for Record of the Year. Dick Clark had advised Darin not to record the song because of the perception that, having come from an opera, it would not appeal to the rock and roll audience. In subsequent years, Clark recounted the story with good humor. Frank Sinatra, who recorded the song with Quincy Jones on his L.A. Is My Lady album, called Darin's the "definitive" version. Billboard ranked this version as the No. 2 song for 1959. Darin's version was No. 3 on Billboard's All Time Top 100. In 2003, the Darin version was ranked # 251 on Rolling Stone's "500 Greatest Songs of All Time" list. On BBC Radio 4's Desert Island Discs, pop mogul Simon Cowell named "Mack the Knife" the best song ever written. Darin's version of the song was featured in the movies Quiz Show and What Women Want. Both Armstrong and Darin's versions were inducted by the Library of Congress in the National Recording Registry in 2016.

Who sang mack the knife with frank sinatra? OK. Let's think. My stream of consciousness:
The relevant information to answer the above question is: Frank Sinatra, who recorded the song with Quincy Jones on his L.A. Is My Lady album, called Darin's the "definitive" version. The answer is Quincy Jones.