freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-127-abc-hits.md

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 = 2^3 × 3^2 × 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:

1. GCD(a, b) = GCD(a, c) = GCD(b, c) = 1
2. a < b
3. a + b = c
4. rad(abc) < c

For example, (5, 27, 32) is an abc-hit, because:

1. GCD(5, 27) = GCD(5, 32) = GCD(27, 32) = 1
2. 5 < 27
3. 5 + 27 = 32
4. 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 \sum{c} = 12523.

Find \sum{c} for c < 120000.

--hints--

abcHits() should return 18407904.

assert.strictEqual(abcHits(), 18407904);

--seed--

--seed-contents--

function abcHits() {

  return true;
}

abcHits();

--solutions--

// solution required