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

Leroy Quet qq-quet at
Fri Dec 5 00:10:40 CET 2003

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 

...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.)

Leroy Quet

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