Program for Mobius Function | Set 2

Given an integer N. The task is to find Mobius function of all numbers from 1 to N.

Examples:

Input: N = 5
Output: 1 -1 -1 0 -1

Input: N = 10
Output: 1 -1 -1 0 -1 1 -1 0 0 1

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is to first find the least prime factor of all the numbers from 1 to N using Sieve of Eratosthenes then using these least prime factors the Mobius function can be calculated for all the numbers, depending on a number contains an odd number of distinct primes or even number of distinct primes.

Below is the implementation of the above approach:

C++

 // C++ implementation of the approach #include using namespace std; #define N 100005    int lpf[N];    // Function to calculate least // prime factor of each number void least_prime_factor() {     for (int i = 2; i < N; i++)            // If it is a prime number         if (!lpf[i])                for (int j = i; j < N; j += i)                    // For all multiples which are not                 // visited yet.                 if (!lpf[j])                     lpf[j] = i; }    // Function to find the value of Mobius function // for all the numbers from 1 to n void Mobius(int n) {     // To store the values of Mobius function     int mobius[N];        for (int i = 1; i < N; i++) {            // If number is one         if (i == 1)             mobius[i] = 1;         else {                // If number has a squared prime factor             if (lpf[i / lpf[i]] == lpf[i])                 mobius[i] = 0;                // Multiply -1 with the previous number             else                 mobius[i] = -1 * mobius[i / lpf[i]];         }     }        for (int i = 1; i <= n; i++)         cout << mobius[i] << " "; }    // Driver code int main() {     int n = 5;        // Function to find least prime factor     least_prime_factor();        // Function to find mobius function     Mobius(n); }

Java

 // Java implementation of the approach import java.util.*;    class GFG  {    static int N = 100005;    static int []lpf = new int[N];    // Function to calculate least // prime factor of each number static void least_prime_factor() {     for (int i = 2; i < N; i++)            // If it is a prime number         if (lpf[i] % 2 != 1)                for (int j = i; j < N; j += i)                    // For all multiples which are not                 // visited yet.                 if (lpf[j] % 2 != 0)                     lpf[j] = i; }    // Function to find the value of Mobius function // for all the numbers from 1 to n static void Mobius(int n) {     // To store the values of Mobius function     int []mobius = new int[N];        for (int i = 1; i < N; i++)      {            // If number is one         if (i == 1)             mobius[i] = 1;         else         {                // If number has a squared prime factor             if (lpf[i / lpf[i]] == lpf[i])                 mobius[i] = 0;                // Multiply -1 with the previous number             else                 mobius[i] = -1 * mobius[i / lpf[i]];         }     }        for (int i = 1; i <= n; i++)         System.out.print(mobius[i] + " "); }    // Driver code public static void main(String[] args) {     int n = 5;     Arrays.fill(lpf, -1);            // Function to find least prime factor     least_prime_factor();        // Function to find mobius function     Mobius(n); } }     // This code is contributed by PrinciRaj1992

Python3

 # Python3 implementation of the approach  N = 100005    lpf =  * N;     # Function to calculate least  # prime factor of each number  def least_prime_factor() :        for i in range(2, N) :            # If it is a prime number          if (not lpf[i]) :                for j in range(i, N, i) :                     # For all multiples which are not                  # visited yet.                  if (not lpf[j]) :                     lpf[j] = i;     # Function to find the value of Mobius function  # for all the numbers from 1 to n  def Mobius(n) :        # To store the values of Mobius function      mobius =  * N;         for i in range(1, N) :            # If number is one          if (i == 1) :             mobius[i] = 1;          else :                # If number has a squared prime factor              if (lpf[i // lpf[i]] == lpf[i]) :                 mobius[i] = 0;                 # Multiply -1 with the previous number              else :                 mobius[i] = -1 * mobius[i // lpf[i]];         for i in range(1, n + 1) :         print(mobius[i], end = " ");     # Driver code  if __name__ == "__main__" :         n = 5;         # Function to find least prime factor      least_prime_factor();         # Function to find mobius function      Mobius(n);     # This code is contributed by AnkitRai01

C#

 // C# implementation of the approach using System;    class GFG { static int N = 100005;    static int []lpf = new int[N];    // Function to calculate least // prime factor of each number static void least_prime_factor() {     for (int i = 2; i < N; i++)            // If it is a prime number         if (lpf[i] % 2 != 1)                for (int j = i; j < N; j += i)                    // For all multiples which                  // are not visited yet.                 if (lpf[j] % 2 != 0)                     lpf[j] = i; }    // Function to find the value of  // Mobius function for all the numbers // from 1 to n static void Mobius(int n) {     // To store the values of      // Mobius function     int []mobius = new int[N];        for (int i = 1; i < N; i++)      {            // If number is one         if (i == 1)             mobius[i] = 1;         else         {                // If number has a squared prime factor             if (lpf[i / lpf[i]] == lpf[i])                 mobius[i] = 0;                // Multiply -1 with the              // previous number             else                 mobius[i] = -1 * mobius[i / lpf[i]];         }     }        for (int i = 1; i <= n; i++)         Console.Write(mobius[i] + " "); }    // Driver code static public void Main () {     int n = 5;     Array.Fill(lpf, -1);            // Function to find least prime factor     least_prime_factor();            // Function to find mobius function     Mobius(n); } }     // This code is contributed by ajit.

Output:

1 -1 -1 0 -1

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