k,p,nk,p,nk,p,n 均为正整数，记 f(n)=∑ip∣n1f(n)=\sum_{i^p|n}1f(n)=∑ip∣n1。证明当 n→∞n\to \inftyn→∞ 时：
∑i=1ni⋅fk(i)∑i=1nfk(i)→n2\frac{\sum_{i=1}^n i\cdot f^k(i)}{\sum_{i=1}^n f^k(i)}\to\frac n 2∑i=1nfk(i)∑i=1ni⋅fk(i)→2n
