chore(i8n,learn): processed translations
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Mrugesh Mohapatra
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---
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id: 5900f3ec1000cf542c50fefe
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title: 问题127:abc-hits
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title: 'Problem 127: abc-hits'
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challengeType: 5
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videoUrl: ''
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forumTopicId: 301754
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dashedName: problem-127-abc-hits
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---
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# --description--
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n,rad(n)的基数是n的不同素因子的乘积。例如,504 = 23×32×7,因此rad(504)= 2×3×7 = 42.如果出现以下情况,我们将正整数(a,b,c)的三元组定义为abc-hit:GCD( a,b)= GCD(a,c)= GCD(b,c)= 1 a <ba + b = c rad(abc)<c例如,(5,27,32)是abc-hit,因为:GCD(5,27)= GCD(5,32)= GCD(27,32)= 1 5 <27 5 + 27 = 32 rad(4320)= 30 <32事实证明abc-hits是非常罕见的c <1000只有31次abc命中,Σc= 12523。查找Σc表示c <120000。
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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.
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We shall define the triplet of positive integers (a, b, c) to be an abc-hit if:
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GCD(a, b) = GCD(a, c) = GCD(b, c) = 1
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a < b
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a + b = c
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rad(abc) < c
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For example, (5, 27, 32) is an abc-hit, because:
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GCD(5, 27) = GCD(5, 32) = GCD(27, 32) = 1
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5 < 27
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5 + 27 = 32
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rad(4320) = 30 < 32
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It turns out that abc-hits are quite rare and there are only thirty-one abc-hits for c < 1000, with ∑c = 12523.
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Find ∑c for c < 120000.
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# --hints--
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`euler127()`应该返回18407904。
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`euler127()` should return 18407904.
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```js
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assert.strictEqual(euler127(), 18407904);
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