By Jonathan Stempel

NEW YORK (Reuters) - U.S. prosecutors on Thursday said Andrew Caspersen, the scion of a wealthy Wall Street family, should spend as long as 15-2/3 years in prison after he pleaded guilty to defrauding friends, family and a charity out of more than $38 million.

In papers filed with the federal court in Manhattan, prosecutors said Caspersen, 40, who had worked at a unit of investment banker Paul Taubman's PJT Partners Inc, abused the trust of his victims through his "long-running, significant and elaborate" fraud.

Prosecutors said the son of late Wall Street financier Finn M.W. Caspersen ran a Ponzi-like scheme from November 2014 to March 2016 to defraud more than one dozen investors, claiming he would use their funds to make loans to private equity firms.

Instead, prosecutors said Andrew Caspersen used money he raised to trade in his own accounts and pay earlier investors.

Though lawyers for Caspersen have said a "pathological" gambling disorder and mental health issues fueled their client's crimes, prosecutors said the 151- to 188-month prison term recommended under federal guidelines was justified.

The sentencing request came six days after Caspersen's lawyers said the Princeton University and Harvard Law School graduate's gambling addiction and efforts to rehabilitate himself were among the "powerful mitigating circumstances" justifying leniency.

Caspersen is scheduled to be sentenced in Manhattan on Nov. 4 by U.S. District Judge Jed Rakoff, a prominent critic of federal sentencing guidelines.

The judge told Caspersen at his July 6 plea hearing that he would consider the guidelines when imposing punishment, but that they "border on the irrational, and I like a sentence to be rational."

Caspersen has agreed not to appeal any prison term longer than 15-2/3 years. He also agreed to forfeit more than $45 million, though his lawyer has said he cannot afford that sum.

The case is U.S. v. Caspersen, U.S. District Court, Southern District of New York, No. 16-cr-00414.

(Reporting by Jonathan Stempel in New York; Additional reporting by Nate Raymond; Editing by Jonathan Oatis)