Katy Perry -- '1984' Registered By Swedish Songwriter ... NOT Katy

We now know how Katy Perry's name ended up on the official registration of a song the media claims is a hit piece targeting Taylor Swift ... Katy had nothing to do with it, but a producer who once worked with her did.

The song -- "1984" -- was registered with BMI last September. When you go to the BMI site, it lists Katy as the artist and 4 producers/songwriters, including Dallas Austin and a guy named Andreas Carlsson.

The reason everyone's interested in the prospect of such a song ... Taylor got pissed off at Katy last September after 3 of Taylor's backup dancers bailed on Taylor to do backup for Katy. We broke the story ... the 3 dancers had worked with Katy long before and when they signed up with Taylor, they wanted a 30-day out if Katy launched a new tour. Katy had no beef with Taylor, but Taylor was bitter.

So when the story broke that Katy was attached to "1984" (the year she was born) -- a play on Taylor's "1989" album -- everyone thought it was a response to Taylor's song "Bad Blood," which is rumored to be about her feud with Katy.

But here's what we found out. "1984" was actually registered 5 days after we broke the story about the 3 dancers jumping ship. Sources tell us the management company BMG in Sweden registered the song at the behest of Andreas Carlsson. By the way, Carlsson co-wrote "Waking Up in Vegas," which Katy recorded.

Multiple sources familiar with the situation tell TMZ, Katy had no idea Carlsson registered the song.