Merge pull request #156 from VincentVanTaro/main

Added Totient function

Python/Euler's Toteint Function.py

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+# This is a program to operate euler's toteint function.
+
+import math
+
+"""
+What is a euler's toteint function??
+Th function is represented as the greek letter Phi with a given parameter n where n is any real integer.
+The totient function gives the number of all the numbers smaller than and coprime to n.
+
+example: phi(2) = 1 {only 1}, phi(13) = 12 { 1 to 12 since 13 is a prime number}, phi(6) = 2 {1 and 5 only}, etc.  
+
+for more info visit, https://brilliant.org/wiki/eulers-totient-function/
+"""
+
+
+# recieving the number n from user end
+# n = int(input('Give a whole number:     '))
+
+# the euler's function
+def φ(number):
+    """
+    Function used to find the euler's totient function of the given number
+
+    returns:
+    tuple ===> (0: prime factors of the given number, 1: euler'stotient function answer)
+    """
+
+    # this is the function to find all the uniqe prime factors of the given number
+    def primes(n=number):
+        # now time to find all the prime factors of n
+        primeFactors = [n]
+
+        if n % 2 == 0:
+            primeFactors.append(2)
+        while n % 2 == 0:
+            n = n / 2
+
+        for i in range(3, math.floor(math.sqrt(n)) + 1):
+            if n % i == 0:
+                while n % i == 0:
+                    n = n / i
+                primeFactors.append(i)
+
+        return primeFactors
+
+    # this is the function to calculate the euler's multiplication method
+    def eulerMult(answer=number, primes=primes(number)):
+        # now we will us ethe euler's multiplication method to find the phi function
+        for i in primes:
+            answer = answer * (1 - 1 / (int(i)))
+        return int(math.ceil(answer))
+
+    # this function returns a tuple
+    return primes(), eulerMult()
+
+
+# this function will show you the formula used
+def eulFunc(primes):
+    string = ""
+    for i in primes:
+        string += f"(1 - 1/{i})"
+    return string
+
+
+# printing a table of the numbers, their euler's function and their formula/prime factors
+for i in range(2, 100 + 1):
+
+    # table with prime factors
+    print(f"number: {i},    φ({i}) = {φ(i)[1]},    Prime Factors: {φ(i)[0] + [1]}")
+
+    # table with the formula
+    # print(f"number: {i},    φ({i}) = {φ(i)[1]},    formula: {str(i) + eulFunc(φ(i)[0])}")