# [seqfan] Re: tau(n) vs d(n). Was: Is This Sequence Ever Negative?

zak seidov zakseidov at yahoo.com
Mon Mar 8 16:34:08 CET 2010

```See:
A000005 d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.

AUTHOR  N. J. A. Sloane

--- On Sun, 3/7/10, Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:

> From: Leroy Quet <q1qq2qqq3qqqq at yahoo.com>
> Subject: [seqfan]  tau(n) vs d(n). Was: Is This Sequence Ever Negative?
> To: seqfan at seqfan.eu, "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Date: Sunday, March 7, 2010, 11:39 AM
>
> [ ( [ ([( [ ( ([[o0Oo0Ooo0Oo(0)oO0ooO0oO0o]]) ) ] )]) ] )
> ]
>
> Richard Mathar wrote in part:
> >...
> > On a side note, I prefer to write tau(.), never d(.),
> for
> > the number of divisors
> > of an argument. It is a good idea to stick to
> sigma(.),
> > tau(.),
> > phi(.), prime(.), Fibonacci(.), rad(.), mu(.), pi(.),
> > binomial(.,.) for the basic
> > number-theoretical functions. If one needs to use *a*
> > divisor
> > or *a* prime, one would likely use d, like in
> sum_{d|n}, or
> > p, q, r etc for
> > individual primes.
> >...
>
> The reason I use d(n) is because tau(n) is used in other
> mathematical contexts, such as the Ramanujan tau function.
>
> But, as you point out, d(n) is used in other contexts too.
>
> In either case, I always make sure to include a note
> whenever I use d(.) in my contributions to the OEIS to say
> that d(.) is the number of divisors of ..
>
> Maybe sigma_0(.) is less ambiguous? But this might be a
> much less obvious notation than even tau to people who
> prefer d, or d to people who prefer tau.
>
> My opinion: Use either, but be sure to state somewhere
> exactly what you mean, since there is some controversy
> regarding the notation.
>
> Thanks,
> Leroy Quet
>
>
>
>
>
>
>
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>

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