The number of ways a prime p can participate in a list of divisors is 1+e
where e is its exponent in the prime factorization of x . __ q: x gives
you the primes and the corresponding exponents. Therefore:
# div 24
8
*/ 1 + {: __ q: 24
8
# div 64e8
135
*/ 1 + {: __ q: 64e8
135
On Fri, Apr 24, 2020 at 1:13 PM 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
> >>> ----------------------------------------------------------------------
> >>> For information about J forums see http://www.jsoftware.com/forums.htm
> >>>
> >> ----------------------------------------------------------------------
> >> For information about J forums see http://www.jsoftware.com/forums.htm
> >>
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
> >
>
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