Puzzle of the Week #322 - Number Hunt

I have a number, let’s call it n. n doesn’t have any repeated prime factors. For every prime number p, p divides into n IF AND ONLY IF p-1 also divides into n.

For instance, if 23 divides into n, then 22 does also, and if 59 doesn’t divide into n, then neither does 58.

What is the value of n?