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## Remarks
## https://www.geeksforgeeks.org/program-mobius-function/
## Python program to evaluate
## Mobius def M(N) = 1 if N = 1
## M(N) = 0 if any prime factor of N is contained twice
## M(N) = (-1) ^ (no of distinct prime factors)
import math
## def to check if n is prime or not
def isPrime(n) :
if (n < 2) :
return False
for i in range(2, n + 1) :
if (n % i == 0) :
return False
i = i * i
return True
def mobius(n) :
p = 0
## Handling 2 separately
if (n % 2 == 0) :
n = int(n / 2)
p = p + 1
## If 2^2 also divides N
if (n % 2 == 0) :
return 0
## Check for all other prime factors
for i in range(3, int(math.sqrt(n)) + 1) :
## If i divides n
if (n % i == 0) :
n = int(n / i)
p = p + 1
## If i ^ 2 also divides N
if (n % i == 0) :
return 0
i = i + 2
if(p % 2 == 0) :
return -1
return 1
## Driver Code
## N = 5 ## Example: 1
## N = 10 ## Example: 2
N = 20 ## Example: 3
print ("Mobius defs M(N) at N = {} is: {}\n" . format(N, mobius(N)));
## This code is contributed by Manish Shaw (manishshaw1)
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