Rich? Want to be a U.S. senator? Welcome to Pennsylvania!

Rich, Republican and want to be a U.S. senator?

Pennsylvania might as well hang a welcome sign.

The presidential battleground state’s high-stakes race for an open Senate seat is seeing candidates with big bank accounts and big-time connections exchanging their blue-state mansions for decidedly purple Pennsylvania, and pursuing an opportunity they might never have at home.

Introducing Carla Sands, Mehmet Oz — best known as the host of TV’s “Dr. Oz Show” — and David McCormick, all three of whom seem prepared to spend millions of their own dollars to win a Senate seat.

Their arrival seems to be a testament to Republican optimism about winning in Pennsylvania, a bellwether state and one of the nation’s biggest presidential electoral prizes, backing Democrat Joe Biden in last year’s election and former President Donald Trump in 2016.

It’s also a test in an increasingly nationalized political environment of whether voters care about how deeply their representatives are tied to the state — or whether carpetbagging will be a pivotal issue in next year’s contest to replace retiring two-term Republican U.S. Sen. Pat Toomey.

“Every candidate comes with assets and liabilities,” said Charlie Dent, a former seven-term congressman from the Allentown area. “The question is, how big a liability it is and, at the end of the day, will it matter to voters more than any other issue?”

But, Dent said, “every one of those candidates will be doing everything they can to prove their Pennsylvania bonafides. They’ll spend a lot of time talking about their roots in Pennsylvania.”

The race is wide open, and has attracted Democratic contestants who have far more electoral experience than the Republican field. They include John Fetterman, the state’s lieutenant governor, and third-term U.S. Rep. Conor Lamb of suburban Pittsburgh.

For Republicans looking for a homer, they’ve got a few options.

A super PAC that supports one candidate, real estate investor Jeff Bartos, suggests the recent arrivals are treating Toomey’s seat like an “at-large” seat, not a Pennsylvania seat.

“These candidates are opportunists and elitist members of the ruling class, swooping in to a state they couldn’t be bothered to live in and don’t know,” said spokesperson David Abrams.

Still, the state Republican Party isn’t turning up its nose.

In a statement, chairman Lawrence Tabas said Republican candidates are emerging because electoral successes in 2021 “signal mass sobriety about the toxicity of Democrat leadership.”

Legally, they seem on solid ground.

To serve as a senator, a constitutional qualification is to be an inhabitant of the state when elected, but it’s a loose requirement.

The Senate has previously decided that someone elected to it must have some sort of residence in the state or at least an intention to establish a residence there, according to a Congressional Research Service analysis in 2015.

Sands, 61, a Pennsylvania native, spent the majority of the last four decades in California before taking a post as Trump’s ambassador to Denmark and selling her homes in Malibu and Bel Air.

She returned to the U.S. in early 2021, rented a condo overlooking the Susquehanna River with views of the state Capitol and began campaigning.

Oz, 61, gave a jolt to the race this week, declaring his candidacy and bringing unrivaled wealth and name recognition to the contest.

The longtime resident of Cliffside Park, New Jersey, claims he moved to Pennsylvania a year earlier, renting his in-laws’ home in suburban Philadelphia.

However, his social media posts from the past year are full of photos of him in his Cliffside Park home overlooking the Hudson River across from Manhattan, where he practices medicine and films his TV show.

A campaign aide has not answered questions about whether Oz actually sleeps at his in-laws’ home in suburban Philadelphia — where he is registered to vote — and makes the long commute to work in New York City.

Born in Cleveland, Oz’s main claim to Pennsylvania is that he went to medical school at the University of Pennsylvania in Philadelphia. He married a Pennsylvania native, and had his first two children there before moving to New Jersey.

In his pitch to Pennsylvania GOP officials, Oz stresses how he spent part of his boyhood in Wilmington, Delaware, often traveling across the nearby Pennsylvania line, not far from Philadelphia.

He’s already got the endorsement of one member of Congress, Rep. Guy Reschenthaler from southwestern Pennsylvania, and the GOP chairman of a big county came away impressed after speaking with Oz.

“This is not a vanity play for him, he really understands the issues,” Allegheny County Republican Party chair Sam DeMarco said.

McCormick, a Pennsylvania native, has not declared his candidacy or even spoken publicly about it. But he is meeting with Republican Party officials this week and next and bought a house near Pittsburgh, advisers say.

McCormick, 56, is the son of a former chancellor of the state university system, and grew up in Pennsylvania before leaving to attend West Point and serve in the Gulf War.

He spent some years in business in Pittsburgh before he left again in 2005 to take high-level jobs with the administration of then-President George W. Bush.

For more than a decade, he has lived in Connecticut, where he is CEO of one of the world’s largest hedge funds, Westport-based Bridgewater Associates.

Carpetbagger accusations have trickled into races in Pennsylvania in the past, but not like this, said party officials and campaign veterans.

“I’ve certainly never seen anything like this,” said Dave Ball, the chairman of the Washington County Republican Party.

As Ball and other Republicans take stock of the field, the intramural digs are starting.

U.S. Rep. Dan Meuser, who plans to endorse McCormick should he enter the race, took to Twitter to play up McCormick as a “great American who grew up in my district. Dave would be an America First/PA First Senator for and FROM PENNSYLVANIA!!”

In an interview, Meuser complained that Oz “is just coming in literally out of nowhere. I think Oz wants to be U.S. senator, but not a U.S. senator from Pennsylvania.”