关于广义位数码和的一个注记

A Note on the Sum of General Digit

给定非负实数b1<b2<b3<…<bk,称它们是B-数码.设n=bi1bi2…bij,1≤ij≤k,j=1,2,3,…,称s(n)=bi1+bi2+…+bij是n的B-数码和.对于给定的x=bi0bi1…bik,b1≤bij≤bk,j=0,1,2,…,n,给出了∑s(n)和∑s2(n)的一个估计.

The non-negative real numbers b1,b2,b3,…bk, which are arrayed from small to large, are called B-digit. Denote the sum of B-digit of n by s（n）= bi1＋bi2＋…＋bij, where n=bi1bi2…bij,1≤ij≤k,j=1,2,3,…. To the digit x=bi0bi1…bil b1≤bij≤bk,j=0,1,2,…,n, the estimations about ∑n≤x s（n） and ∑n≤x s^2（n） were given.