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HMMT 二月 2009 · 冲刺赛 · 第 14 题

HMMT February 2009 — Guts Round — Problem 14

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 8 ] Compute
    (⌊ ⌋ ⌊ ⌋)
    2009
    ∑
    2009 2008
    k − .
    k kk =1
    Here b x c denotes the largest integer that is less than or equal to x .
解析

英文解析

  1. [ 8 ] Compute
    (⌊ ⌋ ⌊ ⌋)
    2009
    ∑
    2009 2008
    k − .
    k kk =1
    Answer: 2394
    Solution: The summand is equal to k if k divides 2009 and 0 otherwise. Thus the sum is equal tothe sum of the divisors of 2009, or 2394.