I don't have time to solve this symbolically but I will tell you this:
so we only have finitely many numbers to check.
Scanning through we get and no numbers satisfy .
Hello all, I have questions about the function o(n) as well. o(n) is the sum of the divisors of n including n itself.
1a. First I need the find the n for which o(n) = 15, and then prove that n is unique. How do you accomplish this ?
1b. Similarly, how can I prove that no solutions exist to the equation o(n) = 17?
For the other problem try this:
and the other solution shows there is no such that .
This means if then must be a prime power, otherwise if where then which means , which is impossible.
So a prime power means . Thus which forces or . Next see that is the only option. Now you can find the exponent fairly easily.
This argument is a bit sloppy but I think I give enough info to piece it together.