1. ## number theoretic functions

For any integer n greater than or equal to 1 prove the inequality
τ(n) less than or equal to 2sqrt(n)

The function is tau(n) less than or equal to 2sqrt(n)

2. What is the function? Give enough information when you post a question.

3. I suppose you mean the number of divisors function.

Note that for each divisor $d$ (of $n$) $\frac{n}{d}$ is a divisor as well.

And at least one of the following inequalities holds $d\leq{\sqrt{n}}$ or $\frac{n}{d} \leq {\sqrt{n}}$.