Moved solutions till 35 to Python.

python/lib_misc.py

@@ -136,9 +136,10 @@ def collatz_sequence_length(n):
 
 @lru_cache(maxsize=10000)
 def factorial(n):
-    if n == 1:
-        return 1
-    return n * factorial(n - 1)
+    p = 1
+    for i in range(1, n + 1):
+        p *= i
+    return p
 
 
 def proper_divisors(n):
@@ -177,3 +178,25 @@ def sum_proper_divisors(n):
                 s += q
         d += 1
     return s
+
+
+def permutations(iterable):
+    """
+    Generator that returns all permutations for the iterable.
+
+    Generates equivalent result to itertools.permutations.
+    """
+    if not iterable:
+        yield iterable
+    for i in range(len(iterable)):
+        elem = iterable[i:i + 1]
+        rest = iterable[:i] + iterable[i + 1:]
+        for ps in permutations(rest):
+            yield elem + ps
+
+
+def gcd(a, b):
+    """ Returns the greatest commond divisor of a and b. """
+    if b == 0:
+        return a
+    return gcd(b, a % b)