{ "data": { "question": { "questionId": "2105", "questionFrontendId": "1994", "categoryTitle": "Algorithms", "boundTopicId": 973040, "title": "The Number of Good Subsets", "titleSlug": "the-number-of-good-subsets", "content": "

You are given an integer array nums. We call a subset of nums good if its product can be represented as a product of one or more distinct prime numbers.

\n\n\n\n

Return the number of different good subsets in nums modulo 109 + 7.

\n\n

A subset of nums is any array that can be obtained by deleting some (possibly none or all) elements from nums. Two subsets are different if and only if the chosen indices to delete are different.

\n\n

 

\n

Example 1:

\n\n
\nInput: nums = [1,2,3,4]\nOutput: 6\nExplanation: The good subsets are:\n- [1,2]: product is 2, which is the product of distinct prime 2.\n- [1,2,3]: product is 6, which is the product of distinct primes 2 and 3.\n- [1,3]: product is 3, which is the product of distinct prime 3.\n- [2]: product is 2, which is the product of distinct prime 2.\n- [2,3]: product is 6, which is the product of distinct primes 2 and 3.\n- [3]: product is 3, which is the product of distinct prime 3.\n
\n\n

Example 2:

\n\n
\nInput: nums = [4,2,3,15]\nOutput: 5\nExplanation: The good subsets are:\n- [2]: product is 2, which is the product of distinct prime 2.\n- [2,3]: product is 6, which is the product of distinct primes 2 and 3.\n- [2,15]: product is 30, which is the product of distinct primes 2, 3, and 5.\n- [3]: product is 3, which is the product of distinct prime 3.\n- [15]: product is 15, which is the product of distinct primes 3 and 5.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "好子集的数目", "translatedContent": "

给你一个整数数组 nums 。如果 nums 的一个子集中，所有元素的乘积可以表示为一个或多个 互不相同的质数 的乘积，那么我们称它为 好子集 。

\n\n\n\n

请你返回 nums 中不同的 好 子集的数目对 109 + 7 取余 的结果。

\n\n

nums 中的 子集 是通过删除 nums 中一些（可能一个都不删除，也可能全部都删除）元素后剩余元素组成的数组。如果两个子集删除的下标不同，那么它们被视为不同的子集。

\n\n

 

\n\n

示例 1：

\n\n
\n输入：nums = [1,2,3,4]\n输出：6\n解释：好子集为：\n- [1,2]：乘积为 2 ，可以表示为质数 2 的乘积。\n- [1,2,3]：乘积为 6 ，可以表示为互不相同的质数 2 和 3 的乘积。\n- [1,3]：乘积为 3 ，可以表示为质数 3 的乘积。\n- [2]：乘积为 2 ，可以表示为质数 2 的乘积。\n- [2,3]：乘积为 6 ，可以表示为互不相同的质数 2 和 3 的乘积。\n- [3]：乘积为 3 ，可以表示为质数 3 的乘积。\n
\n\n

示例 2：

\n\n
\n输入：nums = [4,2,3,15]\n输出：5\n解释：好子集为：\n- [2]：乘积为 2 ，可以表示为质数 2 的乘积。\n- [2,3]：乘积为 6 ，可以表示为互不相同质数 2 和 3 的乘积。\n- [2,15]：乘积为 30 ，可以表示为互不相同质数 2，3 和 5 的乘积。\n- [3]：乘积为 3 ，可以表示为质数 3 的乘积。\n- [15]：乘积为 15 ，可以表示为互不相同质数 3 和 5 的乘积。\n
\n\n

 

\n\n

提示：

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