leetcode-problemset/leetcode-cn/originData/number-of-different-subsequences-gcds.json

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        "question": {
            "questionId": "1947",
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            "title": "Number of Different Subsequences GCDs",
            "titleSlug": "number-of-different-subsequences-gcds",
            "content": "<p>You are given an array <code>nums</code> that consists of positive integers.</p>\n\n<p>The <strong>GCD</strong> of a sequence of numbers is defined as the greatest integer that divides <strong>all</strong> the numbers in the sequence evenly.</p>\n\n<ul>\n\t<li>For example, the GCD of the sequence <code>[4,6,16]</code> is <code>2</code>.</li>\n</ul>\n\n<p>A <strong>subsequence</strong> of an array is a sequence that can be formed by removing some elements (possibly none) of the array.</p>\n\n<ul>\n\t<li>For example, <code>[2,5,10]</code> is a subsequence of <code>[1,2,1,<strong><u>2</u></strong>,4,1,<u><strong>5</strong></u>,<u><strong>10</strong></u>]</code>.</li>\n</ul>\n\n<p>Return <em>the <strong>number</strong> of <strong>different</strong> GCDs among all <strong>non-empty</strong> subsequences of</em> <code>nums</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/03/17/image-1.png\" style=\"width: 149px; height: 309px;\" />\n<pre>\n<strong>Input:</strong> nums = [6,10,3]\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The figure shows all the non-empty subsequences and their GCDs.\nThe different GCDs are 6, 10, 3, 2, and 1.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,15,40,5,6]\n<strong>Output:</strong> 7\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 2 * 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "序列中不同最大公约数的数目",
            "translatedContent": "<p>给你一个由正整数组成的数组 <code>nums</code> 。</p>\n\n<p>数字序列的 <strong>最大公约数</strong> 定义为序列中所有整数的共有约数中的最大整数。</p>\n\n<ul>\n\t<li>例如，序列 <code>[4,6,16]</code> 的最大公约数是 <code>2</code> 。</li>\n</ul>\n\n<p>数组的一个 <strong>子序列</strong> 本质是一个序列，可以通过删除数组中的某些元素（或者不删除）得到。</p>\n\n<ul>\n\t<li>例如，<code>[2,5,10]</code> 是 <code>[1,2,1,<strong>2</strong>,4,1,<strong>5</strong>,<strong>10</strong>]</code> 的一个子序列。</li>\n</ul>\n\n<p>计算并返回 <code>nums</code> 的所有 <strong>非空</strong> 子序列中 <strong>不同</strong> 最大公约数的 <strong>数目</strong> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2021/04/03/image-1.png\" />\n<pre>\n<strong>输入：</strong>nums = [6,10,3]\n<strong>输出：</strong>5\n<strong>解释：</strong>上图显示了所有的非空子序列与各自的最大公约数。\n不同的最大公约数为 6 、10 、3 、2 和 1 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [5,15,40,5,6]\n<strong>输出：</strong>7\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= nums[i] <= 2 * 10<sup>5</sup></code></li>\n</ul>\n",
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            "hints": [
                "Think of how to check if a number x is a gcd of a subsequence.",
                "If there is such subsequence, then all of it will be divisible by x. Moreover, if you divide each number in the subsequence by x , then the gcd of the resulting numbers will be 1.",
                "Adding a number to a subsequence cannot increase its gcd. So, if there is a valid subsequence for x , then the subsequence that contains all multiples of x is a valid one too.",
                "Iterate on all possiblex from 1 to 10^5, and check if there is a valid subsequence for x."
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