“When you testified, you disclaimed any criminal responsibility,” the judge said, adding, “Although a defendant has a right to testify in his own defense, giving false testimony must be punished.”

Federal prosecutors in Manhattan had cited Mr. Skelos’s testimony at the retrial — “he lied repeatedly,” the government wrote — to argue that he deserved an even greater sentence than he received after his first trial.

A prosecutor, Thomas A. McKay, expressed sympathy for Mr. Skelos’s family, but said the senator knew he was putting his family in jeopardy by breaking the law.

“He did it anyway,” Mr. McKay said.

He also noted that the former senator continued to collect a pension of nearly $100,000 a year, “paid for by the victims of his crime: the people of New York.”

Mr. Skelos’s lawyers had argued that the he had already been severely punished by his fall from grace and the public scrutiny that followed. In seeking leniency, they described a broken man, one who had sunk deep into depression and had come to rely on alcohol to finish each day.

Indeed, while the trial captivated Albany mostly for its tale of a longtime power player’s fall, it also revealed, in stark detail, the deterioration of a once-unshakable bond between father and son.

In the years since Mr. Skelos’s arrest, the two men went from sharing multiple phone calls a day to barely speaking at all. While Mr. Skelos had once filled the role of loving, watchful father — a role that, by his own account, had led to the actions that brought him to trial — by the time of their sentencing, Adam Skelos was estranged from his father and had reconnected with his biological parents.