MathDB
2015-2016 Fall OMO #18

Source:

November 18, 2015
Online Math Open

Problem Statement

Given an integer nn, an integer 1≤a≤n1 \le a \le n is called nn-well if ⌊n⌊n/a⌋⌋=a. \left\lfloor\frac{n}{\left\lfloor n/a \right\rfloor}\right\rfloor = a. Let f(n)f(n) be the number of nn-well numbers, for each integer n≥1n \ge 1. Compute f(1)+f(2)+…+f(9999)f(1) + f(2) + \ldots + f(9999).
Proposed by Ashwin Sah
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