Data commit

Task/M-bius-function/Python/m-bius-function-1.py

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+# 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)
+# 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)
+
+# 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 (i * i <= n and n % i == 0) :
+            return False
+    return True
+
+def mobius(N) :
+
+    # Base Case
+    if (N == 1) :
+        return 1
+
+    # For a prime factor i
+    # check if i^2 is also
+    # a factor.
+    p = 0
+    for i in range(1, N + 1) :
+        if (N % i == 0 and
+                isPrime(i)) :
+
+            # Check if N is
+            # divisible by i^2
+            if (N % (i * i) == 0) :
+                return 0
+            else :
+
+                # i occurs only once,
+                # increase f
+                p = p + 1
+
+    # All prime factors are
+    # contained only once
+    # Return 1 if p is even
+    # else -1
+    if(p % 2 != 0) :
+        return -1
+    else :
+        return 1
+
+# Driver Code
+print("Mobius numbers from 1..99:")
+
+for i in range(1, 100):
+  print(f"{mobius(i):>4}", end = '')
+
+  if i % 20 == 0: print()
+# This code is contributed by
+# Manish Shaw(manishshaw1)

Task/M-bius-function/Python/m-bius-function-2.py

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+# 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
+    else :
+        return 1
+
+# Driver Code
+print("Mobius numbers from 1..99:")
+
+for i in range(1, 100):
+  print(f"{mobius(i):>4}", end = '')
+# This code is contributed by
+# Manish Shaw(manishshaw1)