Jordan函数r次方J_k^r(n)的均值估计

MEAN VALUE ESTIMATE OF THE R-TH POWER OF THE JORDAN TOTIENT FUNCTION

给出了和式sum from n≤x to J_k^r(n)的渐近公式,此处J_k(n)=n^k multiply form p|n (1—1/p^k),k是正整数,r是非零整数.结果包含并推广了关于φ(n)的一系列已有结果。

An asymptotic formula for the sum sum from n≤x J^T_k(n) is proved by means of the complex integal methed, where J_k(n)=n^k multiply from pln=1 (1-1/p^k), k.r are positive and nonzero integers respectively. Our result contains and generilizes those about φ~r(n) hitherto known.