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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:
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 \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