# 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 ``=` `[``0``] ``*` `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 ``=` `[``0``] ``*` `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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