Oliva, a Somers resident and senior adviser to Astorino, filed paperwork with the Federal Election Commission earlier in January.
Six people have indicated their desire to run for the nomination so far, and the winner would face off against incumbent Democrat Sean Patrick Maloney in the election.
The 18th district includes all of Orange and Putnam counties, as well as parts of southern Dutchess County and northeastern Westchester County.
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