tata_d2的博客

杜教筛 求积性函数f(x)f(x)f(x)的前缀和S(n)=∑ni=1f(i)S(n)=∑i=1nf(i)S(n) = \sum_{i=1}^n f(i) 狄利克雷卷积： (g∗f)(x)=∑d|xg(d)f(xd)(g∗f)(x)=∑d|xg(d)f(xd)(g*f)(x) = \sum_{d|x} g(d) f(\dfrac{x}{d}) ∑x=1n(g∗f)(x)=∑x=1n∑d|x...

求 ∑i=1n∑j=1nij gcd(i,j)∑i=1n∑j=1nij gcd(i,j)\sum_{i=1}^n \sum_{j=1}^n ij \ gcd(i, j) n≤1010n≤1010n \leq 10^{10} ans=∑d=1nd∑i=1n∑j=1nij [gcd(i,j)=d]ans=∑d=1nd∑i=1n∑j=1nij [gcd...