MathNet 2017-part-04 — 176 problems (EN–VI) Question 158

Let $n$ be a positive integer. For each of the numbers $1, 2, \dots, n$ we compute the difference between the number of its odd positive divisors and its even positive divisors. Prove that the sum of these differences is at least $0$ and at most $n$.
Kürschák Competition, 1999