Number-Divisors Almost = ln(m) + 2c-1

[Leroy Quet]

Hans Havermann wrote:

>Earlier, I opined:
>
>> Mathematica's DivisorSigma does sum of (powers of) divisors. For 
>> number-of-divisors, I use Length[Divisors].
>
>D'oh. The sum of the *zero* powers of the divisors *is* the number of 
>divisors. Turns out this is actually a bit faster than 
>Length[Divisors].


...but using Length[Divisors] would be better in this case, where 
precision is essential, if Mathematica evaluated 
sum-of-powers-of-divisors numerically. (I bet it does this symbolically, 
anyway, but am uncertain.)

thanks,
Leroy Quet