KURSCHAK 1999 Problem 1

For any positive integer $m$ , denote by $d_i(m)$ the number of positive divisors of $m$ that are congruent to $i$ modulo $2$ . Prove that if $n$ is a positive integer, then $$\left|\sum_{k=1}^n \left(d_0(k)-d_1(k)\right)\right|\le n.$$