Thought Process

I brute forced this problem with a few important tricks

1. Note that gcd(c, a) = gcd(a + b, a) = gcd(a, b) therefore if gcd(a, b) = 1 this implies that gcd(a, c) = gcd(b, c) = 1. This means we only need to check if the gcd of one pair is 1 instead of all 3.

2. Since a, b, c are pairwise co-prime then rad(a), rad(b), rad(c) are also pairwise co-prime, therefore rad(abc) = rad(a) * rad(b) * rad(c)

3. Using a sieve (Very similar to the sieve of Eratosthenes) we can precompute the rad of all numbers up till N. 

4. In our brute force search, we loop through possible a, and b and instead of first checking if gcd(a, b) = 1, we first check if rad(abc) > c  as this operation by step (3) is instant. Then we check the gcd condition for a valid abc-hit