Package g1801_1900.s1808_maximize_number_of_nice_divisors

Class Solution

java.lang.Object
g1801_1900.s1808_maximize_number_of_nice_divisors.Solution
public class Solution extends java.lang.Object
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 109 + 7.

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:

  • 1 <= primeFactors <= 109

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    maxNiceDivisors(int pf)
     

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • maxNiceDivisors

      public int maxNiceDivisors(int pf)