返回题库

HMMT 二月 2009 · 冲刺赛 · 第 14 题

HMMT February 2009 — Guts Round — Problem 14

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 8 ] Compute (⌊ ⌋ ⌊ ⌋) 2009 ∑ 2009 2008 k − . k k k =1 Here b x c denotes the largest integer that is less than or equal to x .
解析
  1. [ 8 ] Compute (⌊ ⌋ ⌊ ⌋) 2009 ∑ 2009 2008 k − . k k k =1 Answer: 2394 Solution: The summand is equal to k if k divides 2009 and 0 otherwise. Thus the sum is equal to the sum of the divisors of 2009, or 2394.