leetcode-problemset/leetcode/originData/find-the-number-of-subsequences-with-equal-gcd.json

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            "title": "Find the Number of Subsequences With Equal GCD",
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            "content": "<p>You are given an integer array <code>nums</code>.</p>\n\n<p>Your task is to find the number of pairs of <strong>non-empty</strong> <span data-keyword=\"subsequence-array\">subsequences</span> <code>(seq1, seq2)</code> of <code>nums</code> that satisfy the following conditions:</p>\n\n<ul>\n\t<li>The subsequences <code>seq1</code> and <code>seq2</code> are <strong>disjoint</strong>, meaning <strong>no index</strong> of <code>nums</code> is common between them.</li>\n\t<li>The <span data-keyword=\"gcd-function\">GCD</span> of the elements of <code>seq1</code> is equal to the GCD of the elements of <code>seq2</code>.</li>\n</ul>\n\n<p>Return the total number of such pairs.</p>\n\n<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,2,3,4]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">10</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The subsequence pairs which have the GCD of their elements equal to 1 are:</p>\n\n<ul>\n\t<li><code>([<strong><u>1</u></strong>, 2, 3, 4], [1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, 4])</code></li>\n\t<li><code>([<strong><u>1</u></strong>, 2, 3, 4], [1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, <strong><u>4</u></strong>])</code></li>\n\t<li><code>([<strong><u>1</u></strong>, 2, 3, 4], [1, 2, <strong><u>3</u></strong>, <strong><u>4</u></strong>])</code></li>\n\t<li><code>([<strong><u>1</u></strong>, <strong><u>2</u></strong>, 3, 4], [1, 2, <strong><u>3</u></strong>, <strong><u>4</u></strong>])</code></li>\n\t<li><code>([<strong><u>1</u></strong>, 2, 3, <strong><u>4</u></strong>], [1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, 4])</code></li>\n\t<li><code>([1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, 4], [<strong><u>1</u></strong>, 2, 3, 4])</code></li>\n\t<li><code>([1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, 4], [<strong><u>1</u></strong>, 2, 3, <strong><u>4</u></strong>])</code></li>\n\t<li><code>([1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, <strong><u>4</u></strong>], [<strong><u>1</u></strong>, 2, 3, 4])</code></li>\n\t<li><code>([1, 2, <strong><u>3</u></strong>, <strong><u>4</u></strong>], [<strong><u>1</u></strong>, 2, 3, 4])</code></li>\n\t<li><code>([1, 2, <strong><u>3</u></strong>, <strong><u>4</u></strong>], [<strong><u>1</u></strong>, <strong><u>2</u></strong>, 3, 4])</code></li>\n</ul>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [10,20,30]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The subsequence pairs which have the GCD of their elements equal to 10 are:</p>\n\n<ul>\n\t<li><code>([<strong><u>10</u></strong>, 20, 30], [10, <strong><u>20</u></strong>, <strong><u>30</u></strong>])</code></li>\n\t<li><code>([10, <strong><u>20</u></strong>, <strong><u>30</u></strong>], [<strong><u>10</u></strong>, 20, 30])</code></li>\n</ul>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,1,1,1]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">50</span></p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 200</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 200</code></li>\n</ul>\n",
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