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Tau Numbers: A Partial Proof of a Conjecture and Other Results

By Joshua Zelinsky


Abstract. A positive n is called a tau number if τ(n) | n, where τ is the number-ofdivisors function. Colton conjectured that the number of tau numbers ≤ n is at least 1 2 π(n). In this paper I show that Colton’s conjecture is true for all sufficiently large n. I also prove various other results about tau numbers and their generalizations.

Year: 2011
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