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Math Help - number theoretic functions

  1. #1
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    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)
    Last edited by MichaelG; November 30th 2009 at 08:55 AM.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    What is the function? Give enough information when you post a question.
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  3. #3
    Super Member PaulRS's Avatar
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    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}}.
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