--- id: 5900f3781000cf542c50fe8b title: 问题12:高度可分的三角数 challengeType: 5 videoUrl: '' dashedName: problem-12-highly-divisible-triangular-number --- # --description-- 通过添加自然数生成三角数的序列。所以第7个三角形数字是1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.前十个术语是: 1,3,6,10,15,21,28,36,45,55 ...... 让我们列出前七个三角形数字的因子: **1:** 1 **3:** 1,3 **6:** 1,2,3,6 **10:** 1,2,5,10 **15:** 1,3,5,15 **21:** 1,3,7,21 **28:** 1,2,4,7,14,28 我们可以看到28是第一个超过五个除数的三角形数。超过`n`除数的第一个三角形数的值是多少? # --hints-- `divisibleTriangleNumber(5)`应该返回28。 ```js assert.strictEqual(divisibleTriangleNumber(5), 28); ``` `divisibleTriangleNumber(23)`应该返回630。 ```js assert.strictEqual(divisibleTriangleNumber(23), 630); ``` divisibleTriangleNumber `divisibleTriangleNumber(167)`应该返回1385280。 ```js assert.strictEqual(divisibleTriangleNumber(167), 1385280); ``` divisibleTriangleNumber `divisibleTriangleNumber(374)`应该返回17907120。 ```js assert.strictEqual(divisibleTriangleNumber(374), 17907120); ``` divisibleTriangleNumber `divisibleTriangleNumber(500)`应该返回76576500。 ```js assert.strictEqual(divisibleTriangleNumber(500), 76576500); ``` # --seed-- ## --seed-contents-- ```js function divisibleTriangleNumber(n) { return true; } divisibleTriangleNumber(500); ``` # --solutions-- ```js function divisibleTriangleNumber(n) { if (n === 1) return 3; let counter = 1; let triangleNumber = counter++; while (noOfFactors(triangleNumber) < n) { triangleNumber += counter++; } return triangleNumber; } function noOfFactors(num) { const primeFactors = getPrimeFactors(num); let prod = 1; for(let p in primeFactors) { prod *= (primeFactors[p] + 1) } return prod; } function getPrimeFactors(num) { let n = num; let primes = {}; let p = 2; let sqrt = Math.sqrt(num); function checkAndUpdate(inc) { if (n % p === 0) { const curr = primes[p]; if (curr) { primes[p]++ } else { primes[p] = 1; } n /= p; } else { p += inc; } } while(p === 2 && p <= n) { checkAndUpdate(1); } while (p <= n && p <= sqrt) { checkAndUpdate(2); } if(Object.keys(primes).length === 0) { primes[num] = 1; } else if(n !== 1) { primes[n] = 1; } return primes; } ```