Euler's Totient Function

Pick a number n. Among 1, 2, 3, …, n, how many share no common factor with n beyond 1? For a prime p, it's every number up to p except p itself — so p − 1. For 12, it's just four numbers: 1, 5, 7, 11. This count is Euler's totient function φ(n), and though it sounds like a curiosity, it is the exact quantity that makes RSA encryption reversible.