Implementation of Hardy Ramanujan Algorithm in /maths (#1355)

* Implementation of Hardy Ramanujan Algorithm

* added docstrings

* added doctests

* Run Python black on the code

* Travis CI: Upgrade to Python 3.8

* Revert to Python 3.7

.travis.yml

@@ -1,5 +1,4 @@
 language: python
-dist: xenial  # required for Python >= 3.7
 python: 3.7
 cache: pip
 before_install: pip install --upgrade pip setuptools

maths/hardy_ramanujanalgo.py

@@ -0,0 +1,45 @@
+# This theorem states that the number of prime factors of n
+# will be approximately log(log(n)) for most natural numbers n
+
+import math
+
+
+def exactPrimeFactorCount(n):
+    """
+    >>> exactPrimeFactorCount(51242183)
+    3
+    """
+    count = 0
+    if n % 2 == 0:
+        count += 1
+        while n % 2 == 0:
+            n = int(n / 2)
+    # the n input value must be odd so that
+    # we can skip one element (ie i += 2)
+
+    i = 3
+
+    while i <= int(math.sqrt(n)):
+        if n % i == 0:
+            count += 1
+            while n % i == 0:
+                n = int(n / i)
+        i = i + 2
+
+    # this condition checks the prime
+    # number n is greater than 2
+
+    if n > 2:
+        count += 1
+    return count
+
+
+if __name__ == "__main__":
+    n = 51242183
+    print(f"The number of distinct prime factors is/are {exactPrimeFactorCount(n)}")
+    print("The value of log(log(n)) is {0:.4f}".format(math.log(math.log(n))))
+
+    """
+    The number of distinct prime factors is/are 3
+    The value of log(log(n)) is 2.8765
+    """