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

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

Below is the implementation of the above approach: 

C++

// 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;
}

Java

// 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..

Python3

# 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

C#

// 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..

PHP

<?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..
?>

Javascript

<script>

// Javascript 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
    let total_sum = (n * (n + 1)) / 2;

    let 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
    let n = 11, k = 2;

    document.write(find_sum(n, k));

// This code is contributed by Mayank Tyagi

</script>

Output:

52

Time Complexity: O(log_kn), where n and k represents the value of the given integers.
Auxiliary Space: O(1), no extra space is required, so it is a constant.