数论函数

\(claim\)

• \(* \rightarrow\) 狄利克雷卷积
• \((a, b) \rightarrow gcd(a,b)\)

次方和公式

\(\sum_{i=1}^n i^2 = \frac{n (n + 1) (2 n + 1)}{6}\)

\(\sum_{i=1}^n i^3 = (\frac{n(n+1)}{2}) ^ 2\)

欧拉函数

• \(\varphi(p^k) = p ^ k - p ^ {k - 1}\)

• \(n = \sum_{d|n} \varphi(d)\)

• \(\varphi(n) = n \times \prod(1 - \frac{1}{p_i})\)

• \(\varphi(nm)\varphi((n,m)) = \varphi(n)\varphi(m)(n,m)\)