id	title	challengeType	forumTopicId	dashedName
5900f3ec1000cf542c50fefe	Problem 127: abc-hits	5	301754	problem-127-abc-hits

--description--

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.

--hints--

euler127() should return 18407904.

assert.strictEqual(euler127(), 18407904);

function euler127() {

  return true;
}

euler127();

// solution required