The original songs as played on Radio New Vegas and Black Mountain Radio. Includes artists such as Frank Sinatra, Dean Martin, and The Ink Spots.

Because the Bing Crosby version of "Something gotta give" was not on Spotify I used the Sinatra version.

Source: http://fallout-new-vegas.info/tunes-on-the-radio

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edit: I took the liberty of adding some music you'll like quite the same to the end of this list. More to enjoy! If you've got any recommendations please let me knowin the comments below.