Find the sum of numbers from 1 to n excluding those which are powers of K

Given two integer **N** and **K**, the task is to find the sum of all the numbers from the range **[1, N]** excluding those which are powers of **K**.

**Examples:**

Input:N = 10, K = 3

Output:42

2 + 4 + 5 + 6 + 7 + 8 + 10 = 42

1, 3 and 9 are excluded as they are powers of 3.

Input:N = 200, K = 30

Output:20069

**Approach:** Find the sum of the following series:

**pwrK:**The sum of all the powers of**K**from**[1, N]**i.e.**K**such that^{0}+ K^{1}+ K^{2}+ … + K^{r}**K**^{r}≤ N**sumAll:**The sum of all the integers from the range**[1, N]**i.e.**(N * (N + 1)) / 2**.

The result will be **sumAll – pwrK**

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` `#define ll long long int ` ` ` `// Function to return the sum of all the ` `// powers of k from the range [1, n] ` `ll sumPowersK(ll n, ll k) ` `{ ` ` ` ` ` `// To store the sum of the series ` ` ` `ll sum = 0, num = 1; ` ` ` ` ` `// While current power of k <= n ` ` ` `while` `(num <= n) { ` ` ` ` ` `// Add current power to the sum ` ` ` `sum += num; ` ` ` ` ` `// Next power of k ` ` ` `num *= k; ` ` ` `} ` ` ` ` ` `// Return the sum of the series ` ` ` `return` `sum; ` `} ` ` ` `// Find to return the sum of the ` `// elements from the range [1, n] ` `// excluding those which are powers of k ` `ll getSum(ll n, ll k) ` `{ ` ` ` `// Sum of all the powers of k from [1, n] ` ` ` `ll pwrK = sumPowersK(n, k); ` ` ` ` ` `// Sum of all the elements from [1, n] ` ` ` `ll sumAll = (n * (n + 1)) / 2; ` ` ` ` ` `// Return the required sum ` ` ` `return` `(sumAll - pwrK); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `ll n = 10, k = 3; ` ` ` ` ` `cout << getSum(n, k); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java implementation of the approach ` `import` `java.io.*; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to return the sum of all the ` `// powers of k from the range [1, n] ` `static` `long` `sumPowersK(` `long` `n, ` `long` `k) ` `{ ` ` ` ` ` `// To store the sum of the series ` ` ` `long` `sum = ` `0` `, num = ` `1` `; ` ` ` ` ` `// While current power of k <= n ` ` ` `while` `(num <= n) ` ` ` `{ ` ` ` ` ` `// Add current power to the sum ` ` ` `sum += num; ` ` ` ` ` `// Next power of k ` ` ` `num *= k; ` ` ` `} ` ` ` ` ` `// Return the sum of the series ` ` ` `return` `sum; ` `} ` ` ` `// Find to return the sum of the ` `// elements from the range [1, n] ` `// excluding those which are powers of k ` `static` `long` `getSum(` `long` `n, ` `long` `k) ` `{ ` ` ` `// Sum of all the powers of k from [1, n] ` ` ` `long` `pwrK = sumPowersK(n, k); ` ` ` ` ` `// Sum of all the elements from [1, n] ` ` ` `long` `sumAll = (n * (n + ` `1` `)) / ` `2` `; ` ` ` ` ` `// Return the required sum ` ` ` `return` `(sumAll - pwrK); ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{ ` ` ` `long` `n = ` `10` `, k = ` `3` `; ` ` ` `System.out.println( getSum(n, k)); ` ` ` ` ` `} ` `} ` ` ` `// This code is contributed by anuj_67.. ` |

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## Python3

`# Python3 implementation of the approach ` ` ` `# Function to return the sum of all the ` `# powers of k from the range [1, n] ` `def` `sumPowersK(n, k) : ` ` ` ` ` `# To store the sum of the series ` ` ` `sum` `=` `0` `; num ` `=` `1` `; ` ` ` ` ` `# While current power of k <= n ` ` ` `while` `(num <` `=` `n) : ` ` ` ` ` `# Add current power to the sum ` ` ` `sum` `+` `=` `num; ` ` ` ` ` `# Next power of k ` ` ` `num ` `*` `=` `k; ` ` ` ` ` `# Return the sum of the series ` ` ` `return` `sum` `; ` ` ` ` ` `# Find to return the sum of the ` `# elements from the range [1, n] ` `# excluding those which are powers of k ` `def` `getSum(n, k) : ` ` ` ` ` `# Sum of all the powers of k from [1, n] ` ` ` `pwrK ` `=` `sumPowersK(n, k); ` ` ` ` ` `# Sum of all the elements from [1, n] ` ` ` `sumAll ` `=` `(n ` `*` `(n ` `+` `1` `)) ` `/` `2` `; ` ` ` ` ` `# Return the required sum ` ` ` `return` `(sumAll ` `-` `pwrK); ` ` ` ` ` `# Driver code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `n ` `=` `10` `; k ` `=` `3` `; ` ` ` ` ` `print` `(getSum(n, k)); ` ` ` `# This code is contributed by AnkitRai01 ` |

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## C#

`// C# implementation of the approach ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to return the sum of all the ` `// powers of k from the range [1, n] ` `static` `long` `sumPowersK(` `long` `n, ` `long` `k) ` `{ ` ` ` ` ` `// To store the sum of the series ` ` ` `long` `sum = 0, num = 1; ` ` ` ` ` `// While current power of k <= n ` ` ` `while` `(num <= n) ` ` ` `{ ` ` ` ` ` `// Add current power to the sum ` ` ` `sum += num; ` ` ` ` ` `// Next power of k ` ` ` `num *= k; ` ` ` `} ` ` ` ` ` `// Return the sum of the series ` ` ` `return` `sum; ` `} ` ` ` `// Find to return the sum of the ` `// elements from the range [1, n] ` `// excluding those which are powers of k ` `static` `long` `getSum(` `long` `n, ` `long` `k) ` `{ ` ` ` `// Sum of all the powers of k from [1, n] ` ` ` `long` `pwrK = sumPowersK(n, k); ` ` ` ` ` `// Sum of all the elements from [1, n] ` ` ` `long` `sumAll = (n * (n + 1)) / 2; ` ` ` ` ` `// Return the required sum ` ` ` `return` `(sumAll - pwrK); ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main () ` `{ ` ` ` `long` `n = 10, k = 3; ` ` ` `Console.WriteLine( getSum(n, k)); ` ` ` `} ` `} ` ` ` `// This code is contributed by anuj_67.. ` |

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**Output:**

42