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

The Hopkins School

New Haven, CT 06515

USA

`Lord_Bern@hotmail.com`

**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 .

**
Full version: pdf,
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latex
**

(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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