Find all positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
which satisfy the following tow conditions:
(a)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
has at least four different positive divisors;
(b) for any divisors
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
and
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
satisfying
![1<a<b<n](/media/m/c/9/9/c99675a28d8f2c0e488d3fd17b43109f.png)
, the number
![b-a](/media/m/0/d/2/0d22343dd6a1face9ee3b3cb3dd64eaf.png)
divides
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
.
%V0
Find all positive integers $n$ which satisfy the following tow conditions:
(a) $n$ has at least four different positive divisors;
(b) for any divisors $a$ and $b$ of $n$ satisfying $1<a<b<n$, the number $b-a$ divides $n$.