Maximize Number of Nice Divisors - Practice Coding | SlaveCode
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1808. Maximize Number of Nice Divisors
Hard
50 Points
Math
Recursion
Number Theory
You are given a positive integer primeFactors. You are asked to construct a positive integer n that satisfies the following conditions:
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.
Examples
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
1808. Maximize Number of Nice Divisors
Hard
50 Points
Math
Recursion
Number Theory
You are given a positive integer primeFactors. You are asked to construct a positive integer n that satisfies the following conditions:
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.
Examples
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.