phi9162

Phi9162 is a compact notation sometimes used to denote Euler's totient function evaluated at 9162, i.e., φ(9162). The totient function φ(n) counts the positive integers up to n that are relatively prime to n. For 9162, prime factorization is 9162 = 2 × 3^2 × 509. Using multiplicativity, φ(9162) = 9162 × (1 − 1/2) × (1 − 1/3) × (1 − 1/509) = 9162 × 1/2 × 2/3 × 508/509 = 3048. Thus there are 3048 integers in the range 1 to 9162 that are coprime to 9162. This illustrates how φ(n) depends on the prime structure of n, decreasing when n contains small repeated primes or large prime factors. The Euler totient function is a key concept in number theory and is used in areas such as modular arithmetic, primitive roots, and RSA cryptography. In practice, φ(n) is multiplicative for coprime factors, meaning φ(ab) = φ(a)φ(b) when gcd(a,b)=1. The value φ(9162) is part of tables of totients and can be used to determine the order of units modulo 9162 and to study the distribution of totatives. See also Euler’s totient function, multiplicative arithmetic functions, and RSA cryptography.