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For last 5 test case, common method,to iterate from 1 to sqrt(n) to fetch all divisors, would fail with time out. Thus, we need an efficient way to find all divisors. Here's my method, hope this helps.
calculate all primes less than sqrt(8000000) +1
find all prime divisors and how many times each prime divisor shows up for n.
With the result in step 2, we can find all divisors less than sqrt(n) + 1 for n,
Iterate divisors we got from step 3, calculate how many solutions for n.
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Project Euler #135: Same differences
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For last 5 test case, common method,to iterate from 1 to sqrt(n) to fetch all divisors, would fail with time out. Thus, we need an efficient way to find all divisors. Here's my method, hope this helps.