Geodesic
Tau numbers: a partial proof of a conjecture and other results
Journal of integer sequences, Tome 5 (2002) no. 2
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 .
Classification : 11B05, 11A25
Keywords: tau number, number-of-divisors function 16 (Concerned with sequence 
@article{JIS_2002__5_2_a0,
     author = {Zelinsky,  Joshua},
     title = {Tau numbers: a partial proof of a conjecture and other results},
     journal = {Journal of integer sequences},
     year = {2002},
     volume = {5},
     number = {2},
     zbl = {1064.11004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2002__5_2_a0/}
}
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Zelinsky,  Joshua. Tau numbers: a partial proof of a conjecture and other results. Journal of integer sequences, Tome 5 (2002) no. 2. http://geodesic.mathdoc.fr/item/JIS_2002__5_2_a0/