Merge branch 'manwar:master' into master

2 files changed, 62 insertions, 0 deletions

diff --git a/challenge-169/michael-dicicco/python/ch-1.py b/challenge-169/michael-dicicco/python/ch-1.py
new file mode 100644
index 0000000000..102d3eaeb5
--- /dev/null
+++ b/challenge-169/michael-dicicco/python/ch-1.py
@@ -0,0 +1,24 @@
+def is_brilliant(factors):
+    """a brilliant number has only two prime factors of the same length"""
+    return len(factors) == 2 and len(str(int(factors[0]))) == len(str(int(factors[1])))
+
+
+def prime_factors(n):
+    output = []
+
+    while n % 2 == 0:
+        output.append(2)
+        n /= 2
+
+    for i in range(3, int(n ** 1 / 2 + 1), 2):
+        while n % i == 0:
+            output.append(i)
+            n /= i
+
+    if n > 2:
+        output.append(int(n))
+    return output
+
+
+if __name__ == '__main__':
+    print(", ".join([str(i) for i in range(4, 300) if is_brilliant(prime_factors(i))]))
diff --git a/challenge-169/michael-dicicco/python/ch-2.py b/challenge-169/michael-dicicco/python/ch-2.py
new file mode 100644
index 0000000000..8052d94e24
--- /dev/null
+++ b/challenge-169/michael-dicicco/python/ch-2.py
@@ -0,0 +1,38 @@
+def is_achilles(factors, given):
+    """Achilles was powerful but imperfect"""
+    for factor in factors:
+        """a powerful number is divisible by the squares of its prime factors"""
+        if not given % factor ** 2 == 0:
+            return False
+    for i in range(2, 10):
+        """a number is a perfect power if it has any integer roots"""
+        if nth_root(given, i) % 1 == 0:
+            return False
+    """the number is powerful and imperfect, like Achilles"""
+    return True
+
+
+def nth_root(some_number, n):
+    """raising a number to a fractional power of 1/n is the same as taking the nth root"""
+    return some_number ** (1 / n)
+
+
+def prime_factors(n):
+    output = []
+
+    while n % 2 == 0:
+        output.append(2)
+        n /= 2
+
+    for i in range(3, int(n ** 1 / 2 + 1), 2):
+        while n % i == 0:
+            output.append(i)
+            n /= i
+
+    if n > 2:
+        output.append(int(n))
+    return output
+
+
+if __name__ == '__main__':
+    print(", ".join([str(i) for i in range(72, 1801) if is_achilles(prime_factors(i), i)]))