I'm doing a Number Theory question, and if someone could offer a hint, that would be greatly appreciated;
The question is: Find the sum of the perfect square divisors of the smallest integer with exactly 6 perfect square divisors.
- My method so far has been simply listing out pairs of possible exponents that are multiples of 2, and listing them out, or using combinations to calculate the total number of combinations. Obviously, this brute-force method is not working out well, and if anyone could provide a hint, that would be greatly appreciated.
- I know how to find the product of all divisors, but not their sum. Furthermore, how would one "target" only perfect square divisors? Perhaps complementary counting?