Initial commit

src/task69 - Totient maximum.py

@@ -0,0 +1,57 @@
+import math
+
+def is_prime(n):
+    if n == 2 or n == 3: return True
+    if n < 2 or n%2 == 0: return False
+    if n < 9: return True
+    if n%3 == 0: return False
+    r = int(n**0.5)
+    f = 5
+    while f <= r:
+        if n%f == 0: return False
+        if n%(f+2) == 0: return False
+        f +=6
+    return True
+
+def tot(n):
+    if is_prime(n):
+        return n-1
+    else:
+        return len([i for i in range(1,n) if math.gcd(i,n)==1])
+
+def phi(n) : 
+  
+    result = n   # Initialize result as n 
+       
+    # Consider all prime factors 
+    # of n and for every prime 
+    # factor p, multiply result with (1 - 1 / p) 
+    p = 2
+    while(p * p<= n) : 
+  
+        # Check if p is a prime factor. 
+        if (n % p == 0) : 
+  
+            # If yes, then update n and result 
+            while (n % p == 0) : 
+                n = n // p 
+            result = result * (1.0 - (1.0 / (float) (p))) 
+        p = p + 1
+          
+          
+    # If n has a prime factor 
+    # greater than sqrt(n) 
+    # (There can be at-most one 
+    # such prime factor) 
+    if (n > 1) : 
+        result = result * (1.0 - (1.0 / (float)(n))) 
+   
+    return (int)(result)
+
+max = [0,0]
+for n in range(2,1000001):
+    totn = phi(n)
+    if n/totn > max[1]:
+        max = [n, n/totn]
+
+print(max)