Package g1801_1900.s1808_maximize_number_of_nice_divisors

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    1808 - Maximize Number of Nice Divisors\.

    Hard

    You are given a positive integer primeFactors. You are asked to construct a positive integer n that satisfies the following conditions:

    • The number of prime factors of n (not necessarily distinct) is at most primeFactors.

    • The number of nice divisors of n is maximized. Note that a divisor of n is nice if it is divisible by every prime factor of n. For example, if n = 12, then its prime factors are [2,2,3], then 6 and 12 are nice divisors, while 3 and 4 are not.

    Return the number of nice divisors of n. Since that number can be too large, return it modulo <code>10<sup>9</sup> + 7</code>.

    Note that a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. The prime factors of a number n is a list of prime numbers such that their product equals n.

    Example 1:

    Input: primeFactors = 5

    Output: 6

    Explanation: 200 is a valid value of n. It has 5 prime factors: 2,2,2,5,5, and it has 6 nice divisors: 10,20,40,50,100,200. There is not other value of n that has at most 5 prime factors and more nice divisors.

    Example 2:

    Input: primeFactors = 8

    Output: 18

    Constraints:

    • <code>1 <= primeFactors <= 10<sup>9</sup></code>

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Integer maxNiceDivisors(Integer pf)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait