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 3Input: 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; } |
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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.. |
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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 = 2print(find_sum(n, k)) # This code is contributed # by Shrikant13 |
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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.. |
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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.. ?> |
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Output:
52
