Code for Eulers Totient function (#1229)

* Create eulersTotient.py

* Rename eulersTotient.py to eulers_totient.py

* Update eulers_totient.py

maths/eulers_totient.py

@@ -0,0 +1,45 @@
+# Eulers Totient function finds the number of relative primes of a number n from 1 to n
+def totient(n: int) -> list:
+    is_prime = [True for i in range(n + 1)]
+    totients = [i - 1 for i in range(n + 1)]
+    primes = []
+    for i in range(2, n + 1):
+        if is_prime[i]:
+            primes.append(i)
+        for j in range(0, len(primes)):
+            if i * primes[j] >= n:
+                break
+            is_prime[i * primes[j]] = False
+
+            if i % primes[j] == 0:
+                totients[i * primes[j]] = totients[i] * primes[j]
+                break
+
+            totients[i * primes[j]] = totients[i] * (primes[j] - 1)
+
+    return totients
+
+
+def test_totient() -> None:
+    """
+    >>> n = 10
+    >>> totient_calculation = totient(n)
+    >>> for i in range(1, n):
+    ...     print(f"{i} has {totient_calculation[i]} relative primes.")
+    1 has 0 relative primes.
+    2 has 1 relative primes.
+    3 has 2 relative primes.
+    4 has 2 relative primes.
+    5 has 4 relative primes.
+    6 has 2 relative primes.
+    7 has 6 relative primes.
+    8 has 4 relative primes.
+    9 has 6 relative primes.
+    """
+    pass
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()