Moved 20 to 26 to Python.

python/lib_misc.py

@@ -134,4 +134,46 @@ def collatz_sequence_length(n):
     return length + collatz_sequence_length(n // 2)
 
 
+@lru_cache(maxsize=10000)
+def factorial(n):
+    if n == 1:
+        return 1
+    return n * factorial(n - 1)
 
+
+def proper_divisors(n):
+    """
+    Returns the list of divisors for n excluding n.
+    """
+    if n < 2:
+        return []
+    divisors = [1, ]
+    d = 2
+    while d * d <= n:
+        if n % d == 0:
+            divisors.append(d)
+        d += 1
+    # Ignore first element and iterate list backwards.
+    for d in divisors[1:][::-1]:
+        q = n // d
+        if q != d:
+            divisors.append(q)
+    return divisors
+
+
+def sum_proper_divisors(n):
+    """
+    Returns the sum of proper divisors of a number.
+    """
+    if n < 2:
+        return 0
+    s = 1
+    d = 2
+    while d * d <= n:
+        if n % d == 0:
+            s += d
+            q = n // d
+            if q != d:
+                s += q
+        d += 1
+    return s