f\mathbf ff 是积性函数:f(1)=1,f(pk)=pk+1,p∈prime,k∈N∗\mathbf f(1)=1,\mathbf f(p^k)=p^k+1,p\in prime,k\in \mathbf N^*f(1)=1,f(pk)=pk+1,p∈prime,k∈N∗
∑i=1nf(i)\sum\limits_{i=1}^{n}\mathbf f(i)i=1∑nf(i)
=∑ii∑ij≤n[gcd(i,j)=1]=\sum\limits_i i\sum\limits_{ij\le n}[\gcd(i,j)=1]=i∑iij≤n∑[gcd(i,j)=1]
这一步怎么做的?(等号左边是要求的)