# Problem 127: abc-hits
The radical of n, rad(n), is the product of distinct prime factors of n.
For example, 504 = 23 × 32 × 7, so rad(504) = 2 × 3 × 7 = 42. We shall
define the triplet of positive integers (a, b, c) to be an abc-hit if:
GCD(a, b) = GCD(a, c) = GCD(b, c) = 1 a < b a + b = c rad(abc) < c
For example, (5, 27, 32) is an abc-hit, because: GCD(5, 27) = GCD(5, 32)
= GCD(27, 32) = 1 5 < 27 5 + 27 = 32 rad(4320) = 30 < 32 It turns
out that abc-hits are quite rare and there are only thirty-one abc-hits
for c < 1000, with ∑c = 12523. Find ∑c for c < 120000.