range() vs xrange() Python2|3 issues for performance

[Steven D'Aprano]

Chris Angelico wrote:

> On Thu, Aug 4, 2011 at 4:01 AM, Steven D'Aprano
> <steve+comp.lang.python at pearwood.info> wrote:
>> a, b = divmod(n, i)
>> if b == 0:
>> total += a+i
>>
> 
> Wouldn't this fail on squares? It happens to give correct results as
> far as I've checked; no square up to 10,000 is called perfect, and
> there are no perfect squares in that range, but I think it's
> technically using an incorrect intermediate result.

Yes, you're correct -- it counts sqrt(n) twice as a factor if n is a perfect
square. The obvious fix is to change the increment to:

total += a if a==i else a+i

I don't believe it actually makes a difference for perfect numbers, but it's
worth getting right.


-- 
Steven