Katy is on the cover of the latest issue of Vogue, she mentions Madonna in the interview:
…Nevertheless, “I miss references all the time,” she admits. “Amy Grant was our Madonna. We knew about Madonna and Marilyn Manson in my family because we picketed their concerts.” At a Manson concert in Santa Barbara, she handed out pamphlets titled How to Find God. She ended up going in to watch the performance with her youth pastor and, to her surprise, found it “really interesting and weird—I got it. But my house was church on Sunday morning, church on Sunday night, church on Wednesday evening; you don’t celebrate Halloween; Jesus gives you your Christmas presents; we watch Bill O’Reilly on TV. That was my whole childhood and youth and early teens. I still have conditioned layers dropping off of me by the day.”

Later in the interview, she says about Madonna: “She did the art of evolution so well.”

Katy Perry on Madonna

Vogue