Sort on the basis of number of factors using STL

Given an array of positive integers. Sort the given array in decreasing order of a number of factors of each element, i.e., an element having the highest number of factors should be the first to be displayed and the number having the least number of factors should be the last one. Two elements with an equal number of factors should be in the same order as in the original array. 

Examples:

Input : {5, 11, 10, 20, 9, 16, 23}
Output : 20 16 10 9 5 11 23
Number of distinct factors:
For 20 = 6, 16 = 5, 10 = 4, 9 = 3
and for 5, 11, 23 = 2 (same number of factors
therefore sorted in increasing order of index)

Input : {104, 210, 315, 166, 441, 180}
Output : 180 210 315 441 104 166

We have already discussed a structure-based solution to sort according to a number of factors. The following steps sort numbers in decreasing order of count of factors.

1. Count a distinct number of factors of each element. Refer this.
2. Create a vector of pairs that stores elements and their factor counts.
3. Sort this array based on the problem statement using any sorting algorithm.

Implementation:

20 16 10 9 5 11 23

Time Complexity: O(n*log(n)) 
Auxiliary Complexity: O(n)