PE70: Phi in NlogN, interview

Author: rachitiitr

MyOnlineSubmissions/ProjectEuler/70.py

@@ -0,0 +1,32 @@
+# Interestingly, φ(87109)=79180, and it can be seen that 87109 is a permutation of 79180.
+# Find the value of n, 1 < n < 10^7, for which φ(n) is a permutation of n and the ratio n/φ(n) produces a minimum.
+N = 10**7
+rat = N + 1
+ans = -1
+
+def same(x, y):
+    return sorted(str(x)) == sorted(str(y))
+
+def euler_phi(MAX=N+1):
+    phi = [0 for _ in range(MAX+1)]
+    phi[1] = 1
+    for i in range(2, MAX+1):
+        if not phi[i]:
+            phi[i] = i-1
+            for j in range((i<<1), MAX+1, i):
+                if not phi[j]:
+                    phi[j] = j
+                phi[j] = (phi[j]//i) * (i-1)
+    return phi
+            
+phi = euler_phi()
+
+for n in range(2, N + 1):
+    p = phi[n]
+    if same(p, n):
+        print(n, p)
+        if rat > n/p:
+            rat = n/p
+            ans = n
+
+print(ans)