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

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Sun Mar 7 17:39:55 CET 2010

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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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