An EyakTek building in Dulles. (Nikki Kahn/Post)

Strip away the shell companies and complex wire transfers, and what federal prosecutors on Tuesday called “one of the most brazen corruption schemes in the history of federal contracting” was really quite simple.

First, officials at the Army Corps of Engineers and technology company representatives got together and agreed to file inflated invoices for federal contracting services, prosecutors said.

Then they bought millions of dollars worth of BMWs, Rolex and Cartier watches, flat-screen televisions, first-class airline tickets and investment properties across the globe. Until they were arrested Tuesday, authorities said, they had their sights on another contract, one worth $780 million.

Four men — two program managers at the corps, a son of one of them and the director of contracts at a Dulles technology firm — were indicted on corruption-related charges that were made public Tuesday.

The arrests revealed what authorities described as one of the most audacious bribery scams they have investigated. With little oversight, corps officials and contractors easily manipulated an arcane and complex contracting system on a scale rarely seen, allowing them to fleece the government of about $20 million, authorities said.

“The scheme was staggering in scope,” said Ronald C. Machen Jr., U.S. attorney for the District of Columbia. “It surprised all of us.”

Authorities learned of the alleged scam this year while investigating another contracting fraud. Their attention soon centered on the actions of two corps program managers who specialized in contracting, Kerry F. Khan, 53, of Alexandria and Michael A. Alexander, 55, of Woodbridge, and their connections to Harold F. Babb, 60, director of contracting at a Virginia-based firm.

Khan; his 30-year-old son, Lee; Alexander; and Babb were charged with wire fraud, bribery and money laundering. After pleading not guilty to all charges, they were ordered held until a hearing scheduled for Thursday in the District’s federal court.

Attorneys for the men declined to comment or could not be reached Tuesday.

Babb, who lives in Sterling, worked for EyakTek, a company with offices in Dulles and Anchorage that could take advantage of its status as an Alaska native-owned company to obtain contracts of unlimited size without competition. A 2010 investigation by The Washington Post found that some native corporations regularly served as pass-through companies, securing contracts and then turning to larger, more established firms to do the work.

In this instance, prosecutors say, EyakTek obtained a contract from the corps to provide information technology and software security services. Because EyakTek often relies on subcontractors, it sought another firm for the job.

Starting in 2007, the two corps program managers and Babb began steering that work to a Chantilly-based firm identified in court papers as “Company A.” That company’s chief technology officer, called an “unindicted co-conspirator” in court papers, then began filing inflated invoices for work to EyakTek, which passed the bills to the government.

Rod Worl, chief executive of EyakTek’s parent company, the Eyak Corp., said the company was cooperating with investigators and does “not tolerate this type of conduct by anyone employed by or associated with an Eyak company.”

In total, prosecutors say, the conspirators inflated $25 million in work by about $20 million. They funneled the extra cash — which they called “overhead” — to themselves, prosecutors said.

Earlier this year, the men set their sights on another, possibly more lucrative corps contract worth about $780 million, prosecutors say.

In recent months, prosecutors said, the men had been working to install “certain employees” on the selection board to ensure that “Company A” got the contract. “Our biggest thing is being able to stack the board,” Babb told the chief technology officer during a March 25 meeting, according to the indictment. “That’s what I’m going to do. I’m trying to stack it in our favor.”

The conspirators also were working to ensure that the government’s statement of objectives for the work were tailored to favor that firm, prosecutors said.

In all, authorities said, Khan had been paid or promised $18 million. He allegedly used the money to buy three BMWs, home improvements, Rolex and Breitling watches, and high-end liquor and also passed money to family members. Prosecutors alleged that one of his relatives — in jail for an unrelated offense — blackmailed Khan and the others for several hundred thousand dollars to keep quiet about the fraud.

Alexander netted more than $1 million in actual and promised proceeds, prosecutors said, and Babb was paid or promised about $775,000. The EyakTek contracting director, apparently unhappy with his employer, had also been assured of a job at “Company A,” prosecutors alleged.

Peggy Gustafson, inspector general for the Small Business Administration, said that the crime was particularly egregious “not simply for the breadth and scope of their greed, but the brashness and disregard of the public trust” by the two corps employees.

Press officers of the Corps of Engineers did not return phone calls or e-mails seeking comment.