Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.8

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

Joshua Zelinsky
The Hopkins School
New Haven, CT 06515

Abstract: A positive n is called a tau number if tau(n) divides n, where tau is the number-of-divisors function. Colton conjectured that the number of tau numbers <= n is at least 1/2 pi(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 .

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(Concerned with sequence A033950 .)

Received August 1, 2002; revised version received December 15, 2002. Published in Journal of Integer Sequences December 16, 2002. Corrections, February 17, 2003.

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