(In reply to Some were discovered....
by Dej Mar)
I got the same set of values in my search, but some of the results are interesting:
I used a search limit of 1600>=a,b,c. I found 87 sets with c>=b>=a>=1 which yeild an integer n.
The solution breakdown for n is:
n=1: 22; n=2: 14; n=3: 13; n=4: 5; n=5: 11
n=6: 11; n=7: 0; n=8: 5; n=9: 6; n=10+: 0
More interesting were a few of the large finds:
a:12, b:18, c:150, n:1
a:12, b:150, c:1458, n:1
a:16, b:72, c:968, n:1
a:18, b:48, c:726, n:1
a:20, b:25, c:405, n:1
a:25, b:45, c:980, n:1
This suggests that there may be no limit to what values a,b,c can take to yield an integer.