Two numbers are coprime if their greatest common divisor equals 1. Euler's totient function f(x) is defined as the number of positive integers less than x which are coprime to x. The special case f(1) equals 1. Write a function which calculates Euler's totient function.

(ns live.test
  (:require [cljs.test :refer-macros [deftest is testing run-tests]]))

(defn totient [n]
  (let [gcd (fn [a b]
              (let [[q r] ((juxt quot rem) b a)]
                (if (zero? r) a (recur r a))))]
    (if (= n 1) 1
      (count (filter #(= 1 (gcd % n)) (range 1 n))))))

(deftest test-75
  (is (= (totient 1) 1))
  (is (= (totient 10) (count '(1 3 7 9)) 4))
  (is (= (totient 40) 16))
  (is (= (totient 99) 60)))

(run-tests)