From b44d5bfd41aae78eaf3a838fc3e71da78d65d326 Mon Sep 17 00:00:00 2001
From: utkarsh <ucponia@gmail.com>
Date: Fri, 2 Oct 2020 00:28:19 +0530
Subject: [PATCH] Added EulersTotient

---
 Maths/EulersTotient.js | 40 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 40 insertions(+)
 create mode 100644 Maths/EulersTotient.js

diff --git a/Maths/EulersTotient.js b/Maths/EulersTotient.js
new file mode 100644
index 000000000..eaf64d904
--- /dev/null
+++ b/Maths/EulersTotient.js
@@ -0,0 +1,40 @@
+/*
+  Source:
+    https://en.wikipedia.org/wiki/Euler%27s_totient_function
+
+  EulersTotient(n) = n * product(1 - 1/p for all prime p dividing n)
+
+  Complexity:
+    O(sqrt(n))
+*/
+
+const EulersTotient = (n) => {
+  // input: n: int
+  // output: phi(n): count of numbers b/w 1 and n that are coprime to n
+  let res = n
+  for (let i = 2; i * i <= n; i++) {
+    if (n % i === 0) {
+      while (n % i === 0) {
+        n = Math.floor(n / i)
+      }
+      // i is a prime diving n, multiply res by 1 - 1/i
+      // res = res * (1 - 1/i) = res - (res / i)
+      res = res - Math.floor(res / i)
+    }
+  }
+  if (n > 1) {
+    res = res - Math.floor(res / n)
+  }
+  return res
+}
+
+const main = () => {
+  // EulersTotient(9) = 6 as 1, 2, 4, 5, 7, and 8 are coprime to 9
+  // > 6
+  console.log(EulersTotient(9))
+  // EulersTotient(10) = 4 as 1, 3, 7, 9 are coprime to 10
+  // > 4
+  console.log(EulersTotient(10))
+}
+
+main()