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Count the numbers < N which have equal number of divisors as K in C++
We are given two numbers N and K. The goal is to find the count of numbers between 1 and N that have divisors equal to the divisors of K in range [1,N].
We will first count the divisors of K in range [1,N] and store in variable count.
Now we will start from i=1 to i=N. Now for each number num=i (such that i!=K), count divisors of num in range[1,N]. And store their occurrences in variable divisors.
If divisors=count means num has the same divisors as K in range [1,N]. increment count of such numbers.
Let’s understand with examples.
Input − N=5, K=2
Output − Count of numbers <N which have equal divisors as K − 1
Explanation −
Between 1 and 5, 2 has divisors 1,2 only. count=2 1 has only 1 divisor which is 1 3 has divisors 1,3 → 2 4 has divisors 1,2,4 → 3 1 number 3 has 2 divisors like K=2.
Input − N=15, K=10
Output − Count of numbers <N which have equal divisors as K − 3
Explanation −
Between 1 and 15, 10 has divisors 1,10 only. count=2 Similarly 6, 8, 14 have only 2 divisors.
Approach used in the below program is as follows
We take N and K as integers.
Function countDivisibles(int n, int k,) takes N and K as parameters and returns the count of numbers between < N that have equal divisors as K.
Take the initial count as 0. For the number of divisors<n of k.
Take the initial numcount as 0. For the numbers that have the same divisors as k.
Using for loop, start from i=1 to i<n. If k%i==0 then increment count.
Now count has number of divisors of k that are <n
Again using for loop, start from i=1 to i<n. For each num=i (such that it is not equal to k ) take initial count of divisors as variable divisors which is 0.
Now between i=1 and i<n find if num%i==0 if yes increment divisors. At the end divsors will have a number of divisors of num that are <n.
Check if divisors=count. If true increment variable numcount which stores count of numbers <n which have equal divisors as k.
Return numcount as result in the end of both loops.
Example
#include <bits/stdc++.h>
using namespace std;
int countDivisibles(int n, int k){
int count = 0;
int numcount=0;
for (int i = 1; i < n;i++ ){
if (k % i == 0)
{ count++; }
}
//now count has number of divisors of k
// cout<<count<<endl;
for(int i=1;i<n;i++){
int num;
if(i!=k){
num=i;
int divisors=0;
for(int j=1;j<n;j++){
if(num%j==0)
{ divisors++; }
}
//cout<<endl<<num<<" "<<divisors;
if(divisors==count)
{ numcount++; }
}
}
return numcount;
}
int main(){
int N = 50, K = 6;
cout<<endl<<"Numbers < N which have equal divisors as K:"<<countDivisibles(N,K);
return 0;
}Output
If we run the above code it will generate the following output −
Numbers < N which have equal divisors as K:14
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