I found this one in my bag of tricks:
allFactors=: */&>@{@((^ i.@>:)&.>/)@q:~&__
#,allFactors */p:i.10
1024
On Fri, Apr 24, 2020 at 7:15 PM 'Mike Day' via Programming <
[email protected]> wrote:
> Numbers of divisors below, not the divisors themselves... the thread had
> split! I was attempting to comment on Hauke Rehr’s post.
> M
>
> Sent from my iPad
>
> > On 24 Apr 2020, at 23:52, 'Jon' via Programming <
> [email protected]> wrote:
> >
> > This is missing a few divisors. It seems Skip's original method would be
> difficult to beat. It's O(n) in time and space. You could improve space
> complexity by doing a simple loop, but as far as I can see there are no
> shortcuts, and the best way is to just "brute force" it.
> >
> > Sent from BlueMail
> >
> >> On Apr 25, 2020, 5:35 AM, at 5:35 AM, 'Mike Day' via Programming <
> [email protected]> wrote:
> >> I think this is near to the approved way:
> >>
> >> (*/"1@:>:@(_& q:))24 360 4711
> >> 8 24 4
> >>
> >> Mike
> >>
> >> Sent from my iPad
> >>
> >>> On 24 Apr 2020, at 21:13, Hauke Rehr <[email protected]> wrote:
> >>>
> >>> I now have an answer for the number of results:
> >>>
> >>> */ >: +/"1 (=/~ ~.) q: 4711
> >>> 4
> >>> */ >: +/"1 (=/~ ~.) q: 42
> >>> 8
> >>>
> >>> I hesitate using =/~ (it’s actually deprecated)
> >>> but I wouldn’t know a better way in this case
> >>>
> >>>
> >>>> Am 24.04.20 um 21:09 schrieb Skip Cave:
> >>>> I have used the wrong terminology. I want to find all the positive
> >> integer
> >>>> *divisors* of an integer n (not just primes) which includes 1 and
> >> the
> >>>> integer.
> >>>> Here's a brute force verb I wrote:
> >>>> div=:3 : 'a#~0=(a=.1+i.y)|y'
> >>>> Test it:
> >>>> div each 40+i.5
> >>>> │1 2 4 5 8 10 20 40│1 41│1 2 3 6 7 14 21 42│1 43│1 2 4 11 22 44│
> >>>> However my div verb is inefficient, slow, and runs out of memory
> >> quickly on
> >>>> larger integers. Is there a way to take advantage of J's prime
> >> factoring
> >>>> verb q: to more efficiently find and/or count *all* positive
> >> divisors (not
> >>>> just primes) of a large (>1e7) integers?
> >>>> Skip
> >>>> Skip Cave
> >>>> Cave Consulting LLC
> >>>> Skip Cave
> >>>> Cave Consulting LLC
> >>>>> On Fri, Apr 24, 2020 at 1:31 PM Roger Hui
> >> <[email protected]> wrote:
> >>>>> See https://code.jsoftware.com/wiki/Essays/Factorings
> >>>>>
> >>>>>
> >>>>>
> >>>>> On Fri, Apr 24, 2020 at 11:29 AM Skip Cave
> >> <[email protected]>
> >>>>> wrote:
> >>>>>
> >>>>>> I want to find all the integer factors of a positive integer,
> >>>>>> which includes 1 and the integer.
> >>>>>> Here's a brute force verb I wrote:
> >>>>>> fac=:3 : 'a#~0=(a=.1+i.y)|y'
> >>>>>>
> >>>>>> Test it:
> >>>>>>
> >>>>>> fac each 40+i.5
> >>>>>>
> >>>>>> │1 2 4 5 8 10 20 40│1 41│1 2 3 6 7 14 21 42│1 43│1 2 4 11 22 44│
> >>>>>>
> >>>>>>
> >>>>>> However my fac verb is inefficient, slow, and runs out of memory
> >> quickly
> >>>>> on
> >>>>>> larger integers. Is there a way to take advantage of J's prime
> >> factoring
> >>>>>> verb q: to more efficiently find and/or count *all* positive
> >> factors (not
> >>>>>> just primes) of a large (>1e7) integers?
> >>>>>>
> >>>>>>
> >>>>>> Skip
> >>>>>>
> >>>>>>
> >>>>>> Skip Cave
> >>>>>> Cave Consulting LLC
> >>>>>>
> >> ----------------------------------------------------------------------
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> >>>>>>
> >>>>>
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> >> http://www.jsoftware.com/forums.htm
> >>>>>
> >>>>
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> >>>
> >>> --
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Devon McCormick, CFA
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