[Tutor] List comprehension question

[Richard D. Moores]

On Tue, Nov 9, 2010 at 18:29, C or L Smith <smiles at worksmail.net> wrote:

> >From sympy you simply do:
>
>>>> from sympy import divisors
>>>> list(divisors(256))
> [1, 2, 4, 8, 16, 32, 64, 128, 256]
>
> So your proper divisors would just be sum(divisors(n)) - n.
> The divisors function there is in the ntheory/factor_.py file.

Thanks for letting me know about this.

def proper_divisors_sum(n):
    return sum(list(divisors(n))) - n

Using Steven's suggested speed test
this gets 6.2404818210135886

My up-to-now fastest version,

def proper_divisors_sum(n):
    pd = set((1,))
    for x in range(2, int(n**.5)+1):
        if n % x == 0:
            pd.update((x, n//x))
    return sum(list(pd))

gets 6.1753780857622473

So they're about even.

Dick