做P2257的时候这个式子看了快半天了,硬是不知道咋化出来的,看了好多版本都反演写的都不一样,快自闭了,求大佬解答qwq
设 T=kdT=kdT=kd
∑k=1n∑d=1⌊nk⌋μ(d)×⌊nT⌋⌊mT⌋\sum_{k=1}^{n}\sum_{d=1}^{\lfloor \frac{n}{k}\rfloor}\mu(d)\times \lfloor \frac{n}{T}\rfloor\lfloor \frac{m}{T}\rfloor∑k=1n∑d=1⌊kn⌋μ(d)×⌊Tn⌋⌊Tm⌋
=∑T=1n⌊nT⌋×⌊mT⌋∑k∣T,k∈primeμ(Tk)=\sum_{T=1}^{n}\lfloor \frac{n}{T}\rfloor\times \lfloor \frac{m}{T}\rfloor\sum_{k|T,k\in prime}\mu(\frac{T}{k})=∑T=1n⌊Tn⌋×⌊Tm⌋∑k∣T,k∈primeμ(kT)