A phenomenal computer-cavalryman

A brilliant cavalryman was once famous in France, which, regardless of the number of participants in the merry parade, was able to respond immediately, how many different ways the riders could have grouped into equal ranks, driving in pairs, pc three, after four, and there was no rider in any row, and no one was dismissed.
At that time, several dozen and several hundred people of knights and ladies would come together, and it has not happened, that the calculator would ever make a mistake in his judgment.
The king once summoned him during a parade of numerous armies, and said:
— W tym oddziale jest 1260 people. How many ways can they be put in equal rows?
— Na 34 ways, merciful lord.
— A w tamtym 7560? …
The task was a bit more difficult, so the bachelor thought for a long time, but soon he had the answer ready: on 62 ways!
— Jakże to robicie, Mr. Cavalier?
— Och, nothing easier: I am increasing each of the prime number divisors' exponents by one, I multiply and subtract two, because it is impossible to go downhill or all of them in one line.
Upon hearing such an explanation, the king reportedly turned pale and refrained from further questioning, because he felt, to bewildered him, and he did not want to let it show. Then he politely bid farewell to the bachelor and departed with his entourage as soon as possible, regardless, are they going goose”, or all in one row . ..
Find the number of divisors quickly, which at that time might have seemed something phenomenal, it is available today - with some practice - to many not at all phenomenal calculators.TMPCC47F-1This phenomenal cavalryman, however, excluded the "goose" ride and in one row, therefore his answer was 62.