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leetcode/problem/maximize-number-of-nice-divisors.html

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+<p>You are given a positive integer <code>primeFactors</code>. You are asked to construct a positive integer <code>n</code> that satisfies the following conditions:</p>
+
+
+
+<ul>
+
+  <li>The number of prime factors of <code>n</code> (not necessarily distinct) is <strong>at most</strong> <code>primeFactors</code>.</li>
+
+  <li>The number of nice divisors of <code>n</code> is maximized. Note that a divisor of <code>n</code> is <strong>nice</strong> if it is divisible by every prime factor of <code>n</code>. For example, if <code>n = 12</code>, then its prime factors are <code>[2,2,3]</code>, then <code>6</code> and <code>12</code> are nice divisors, while <code>3</code> and <code>4</code> are not.</li>
+
+</ul>
+
+
+
+<p>Return <em>the number of nice divisors of</em> <code>n</code>. Since that number can be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>
+
+
+
+<p>Note that a prime number is a natural number greater than <code>1</code> that is not a product of two smaller natural numbers. The prime factors of a number <code>n</code> is a list of prime numbers such that their product equals <code>n</code>.</p>
+
+
+
+<p>&nbsp;</p>
+
+<p><strong>Example 1:</strong></p>
+
+
+
+<pre>
+
+<strong>Input:</strong> primeFactors = 5
+
+<strong>Output:</strong> 6
+
+<strong>Explanation:</strong> 200 is a valid value of n.