Moved more problems to Python.

python/lib_prime.py

@@ -1,7 +1,9 @@
 try:
     from lib_misc import get_item_counts
+    from lib_misc import product
 except ModuleNotFoundError:
     from .lib_misc import get_item_counts
+    from .lib_misc import product
 
 
 def prime_factors(n):
@@ -107,3 +109,36 @@ def primes(n_max):
         if b[i - 1]:
             ps.append(i)
     return ps
+
+
+def get_divisors_count(n):
+    """
+    Returns the number of divisors for n.
+    The numbers 1 and n count as a divisor.
+
+    >>> get_divisors_count(1)
+    1
+    >>> get_divisors_count(3)
+    2 # 1, 3
+    >>> get_divisors_count(4)
+    3 # 1, 2, 4
+
+    Getting the number of divisors is a combinatorial
+    problem that can be solved by using the counts
+    for each prime factor. For example, consider
+
+    2 * 2 * 7 = 28
+
+    We have 3 options for 2 (1, 1 * 2, 2 * 2)
+    and 2 options for 7 (1, 1 * 7).
+
+    By multiplying those options we get the number
+    of combinations:
+
+    2 * 3 = 6
+    """
+    if n == 1:
+        return 1
+    factors = prime_factors_count(n)
+    count = product([v + 1 for v in factors.values()])
+    return count