Calling them “far and away the most culpable” of the parents who have admitted their guilt in the college admissions scandal, federal prosecutors recommended Tuesday that a judge sentence four parents to prison terms ranging from 18 to 26 months, heavier penalties than any handed down in the case so far.

The four parents — Douglas Hodge, the former chief executive of Pimco; Michelle Janavs, heiress to a frozen foods fortune; Manuel Henriquez, a Bay Area venture capitalist, and his wife, Elizabeth — will be sentenced in federal court in Boston in the next two months.

Beneath the threat of new charges, the four admitted late last year that they rigged their children’s college entrance exams, misrepresented them as top-notch athletes and, in the process, conspired with William “Rick” Singer, the Newport Beach consultant at the center of the scandal, to commit fraud and money laundering.

Despite positions of wealth and influence that conferred on them and their children “extreme, almost unfathomable privilege,” prosecutors wrote in a memo, the four conspired with Singer 14 times over 11 years, to the benefit of nine children and at a cost of $1.6 million, collectively.

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