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A multiplicative function is an arithmetic function f with f(mn) = f(m)f(n) whenever gcd(m, n) = 1.
Euler's Totient Function φ(n) counts how many integers from 1 to n are coprime with n.
The linear sieve builds all primes up to n in O(n) time by ensuring each composite is marked exactly once by its smallest prime factor (SPF).