jzoj6150
题意
给定\(n\)个不同的\(a_i\),对于\(i=1\sim n\),求\(F(a_{1...i})\)
\(f(n)=\sum\limits_{i=1}^n \sum\limits_{j=1}^n \mu(ij)\)
\(g(n)=\sum\limits_{i=1}^n \sum\limits_{j=1}^n ij[(i,j)=1]\)
\(F(S)=\sum\limits_{T\subseteq S}f(gcd_{a\in T}(a))\prod\limits_{a\in T}g(a)\)
做法
\(f(n)=\sum\limits_{i=1}^n i^2\phi(i)\)
\(g(n)=\sum\limits_{i=1}^n \mu(i)(\sum\limits_{j=1}^{\frac{n}{i}}\mu(ij))^2\)
令\(f(n)=\sum\limits_{d|n}h(d)\)
则\(F(S)=\sum\limits_{T\subseteq S}(\sum\limits_{d|gcd_{a\in T}(a)}h(d))\prod\limits_{a\in T}g(a)=\sum h(d)((\prod\limits_{d|a}g(a)+1)-1)\)
由于\(a\)均不同,插入的时候考虑约数的贡献即可