Sum of first N natural numbers which are not powers of K

Given two integers n and k, the task is to find the sum of all the numbers within the range [1, n] excluding the numbers which are positive powers of k i.e. the numbers k, k2, k3 and so on.

Examples:

Input: n = 10, k = 3
Output: 43
1 + 2 + 4 + 5 + 6 + 7 + 8 + 10 = 43
3 and 9 are excluded as they are powers of 3

Input: n = 11, k = 2
Output: 52

Approach:



  • Store the sum of first n natural numbers in a variable sum i.e. sum = (n * (n + 1)) / 2.
  • Now for every positive power of k which is less than n, subtract it from the sum.
  • Print the value of the variable sum in the end.

Below is the implementation of the above approach:

C++

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// C++ program to find the sum of
// first n natural numbers which are
// not positive powers of k
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the sum of
// first n natural numbers which are
// not positive powers of k
int find_sum(int n, int k)
{
    // sum of first n natural numbers
    int total_sum = (n * (n + 1)) / 2;
  
    int power = k;
    while (power <= n) {
  
        // subtract all positive powers
        // of k which are less than n
        total_sum -= power;
  
        // next power of k
        power *= k;
    }
  
    return total_sum;
}
  
// Driver code
int main()
{
    int n = 11, k = 2;
  
    cout << find_sum(n, k);
  
    return 0;
}

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Java














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// Java program to find the sum of 


// first n natural numbers which are 


// not positive powers of k 


import java.io.*; 


  


class GFG { 


    


  


  


// Function to return the sum of 


// first n natural numbers which are 


// not positive powers of k 


static int find_sum(int n, int k) 


{ 


    // sum of first n natural numbers 


    int total_sum = (n * (n + 1)) / 2; 


  


    int power = k; 


    while (power <= n) { 


  


        // subtract all positive powers 


        // of k which are less than n 


        total_sum -= power; 


  


        // next power of k 


        power *= k; 


    } 


  


    return total_sum; 


} 


  


// Driver code 


  


    public static void main (String[] args) { 


        int n = 11, k = 2; 


  


    System.out.println(find_sum(n, k)); 


    } 


} 


// This code is contributed by inder_verma.. 



















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Python3














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# Python 3 program to find the sum of  


# first n natural numbers which are  


# not positive powers of k  


  


# Function to return the sum of  


# first n natural numbers which are  


# not positive powers of k  


def find_sum(n, k): 


  


    # sum of first n natural numbers  


    total_sum = (n * (n + 1)) // 2


    power = k 


    while power <= n: 


  


        # subtract all positive powers  


        # of k which are less than n  


        total_sum -= power 


  


        # next power of k  


        power *= k 


    return total_sum 


  


# Driver code 


n = 11; k = 2


print(find_sum(n, k)) 


  


# This code is contributed  


# by Shrikant13 



















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C#














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// C# program to find the sum of 


// first n natural numbers which are 


// not positive powers of k 


using System; 


  


class GFG { 


  


  


  


// Function to return the sum of 


// first n natural numbers which are 


// not positive powers of k 


static int find_sum(int n, int k) 


{ 


    // sum of first n natural numbers 


    int total_sum = (n * (n + 1)) / 2; 


  


    int power = k; 


    while (power <= n) { 


  


        // subtract all positive powers 


        // of k which are less than n 


        total_sum -= power; 


  


        // next power of k 


        power *= k; 


    } 


  


    return total_sum; 


} 


  


// Driver code 


  


    public static void Main () { 


        int n = 11, k = 2; 


  


    Console.WriteLine(find_sum(n, k)); 


    } 


} 


// This code is contributed by inder_verma.. 



















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PHP














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<?php 


// PHP program to find the sum of 


// first n natural numbers which are 


// not positive powers of k 


  


// Function to return the sum of 


// first n natural numbers which are 


// not positive powers of k 


function find_sum($n, $k) 


{ 


    // sum of first n natural numbers 


    $total_sum = ($n * ($n + 1)) / 2; 


  


    $power = $k; 


    while ($power <= $n) 


    { 


  


        // subtract all positive powers 


        // of k which are less than n 


        $total_sum -= $power; 


  


        // next power of k 


        $power *= $k; 


    } 


  


    return $total_sum; 


} 


  


// Driver code 


$n = 11; $k = 2; 


  


echo find_sum($n, $k); 


  


// This code is contributed by inder_verma.. 


?> 



















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Output:


52





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Improved By :  inderDuMCA, shrikanth13