一类约数和函数的上界估计

On the upper bound estimation of a class sum of divisors

对于正整数k,设σ(k)是k的不同约数之和.运用初等数论方法,利用等幂和的Bernoulli展开式,得到了关于σ(k)的和式sum σ(kr) from k=1 to n的上界的估计.

For any positive integer k,let σ（k）denote the sum of distinct divisors of k.With some elementary number theory methods,using sum of equal powers of the Bernoulli expansion,the best constant of type of upper bound estimates is determined.