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MathGroup Archive 2000

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Re: Divisors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24295] Re: [mg24272] Divisors
  • From: Arnold <arnoldk at gauss.cam.wits.ac.za>
  • Date: Fri, 7 Jul 2000 00:11:35 -0400 (EDT)
  • References: <200007060310.XAA26697@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
here's one approach to getting divisors from the known factorization list:


divisors[lst_] :=
  Times @@@ Flatten[
      Outer[List, Sequence @@ (#[[1]]^Range[0, #[[2]]] & /@ lst)],
      Length[lst] - 1]

lst = FactorInteger[7!]
Out[1]=
{{2, 4}, {3, 2}, {5, 1}, {7, 1}}

divisors[lst]
Out[2]=
{1, 7, 5, 35, 3, 21, 15, 105, 9, 63, 45, 315, 2, 14, 10, 70, 6, 42, 30,
210, \
18, 126, 90, 630, 4, 28, 20, 140, 12, 84, 60, 420, 36, 252, 180, 1260, 8,
56, \
40, 280, 24, 168, 120, 840, 72, 504, 360, 2520, 16, 112, 80, 560, 48, 336,
\
240, 1680, 144, 1008, 720, 5040}

Sort[%] == Divisors[7!]
Out[3]=
True

Cheers,

Arnold Knopfmacher
University of the Witwatersrand
South Africa

Hans Havermann wrote:

> I need a re-formulated "divisors" function that works, *not* on
> Integers, but on the *list of factors* that one gets when one applies
> FactorInteger to a number. That way I can still get the divisors of a
> number whose factorization is difficult, but nonetheless known.
>
> I have a rough working model of such a function but it relies on the
> function Subsets found in DiscreteMath`Combinatorica` (see below) and I
> don't have enough RAM to apply Subsets to lists larger than 20 elements.
> Unfortunately, I need to find the divisors of numbers whose
> factorization comprises as many as 40 elements.
>
> Can anyone provide a programming solution?
>
> --
> << DiscreteMath`Combinatorica`
>
> fac = First[Transpose[FactorInteger[2*3*3*11*11*11*13]]];
> pow = Last[Transpose[FactorInteger[2*3*3*11*11*11*13]]];
> expfac = {}; Do[
>   Do[expfac = Append[expfac, fac[[i]]], {j, 1, pow[[i]]}], {i, 1,
>     Length[pow]}]; expfac
>
> {2, 3, 3, 11, 11, 11, 13}
>
> div = ReplacePart[Union[Subsets[expfac]], {1}, 1]
>
> {{1}, {2}, {3}, {11}, {13}, {2, 3}, {2, 11}, {2, 13}, {3, 3}, {3, 11},
> {3, 13}, {11, 11}, {11, 13}, {2, 3, 3}, {2, 3, 11}, {2, 3, 13}, {2, 11,
> 11}, {2, 11, 13}, {3, 3, 11}, {3, 3, 13}, {3, 11, 11}, {3, 11, 13}, {11,
> 11, 11}, {11, 11, 13}, {2, 3, 3, 11}, {2, 3, 3, 13}, {2, 3, 11, 11}, {2,
> 3, 11, 13}, {2, 11, 11, 11}, {2, 11, 11, 13}, {3, 3, 11, 11}, {3, 3, 11,
> 13}, {3, 11, 11, 11}, {3, 11, 11, 13}, {11, 11, 11, 13}, {2, 3, 3, 11,
> 11}, {2, 3, 3, 11, 13}, {2, 3, 11, 11, 11}, {2, 3, 11, 11, 13}, {2, 11,
> 11, 11, 13}, {3, 3, 11, 11, 11}, {3, 3, 11, 11, 13}, {3, 11, 11, 11,
> 13}, {2, 3, 3, 11, 11, 11}, {2, 3, 3, 11, 11, 13}, {2, 3, 11, 11, 11,
> 13}, {3, 3, 11, 11, 11, 13}, {2, 3, 3, 11, 11, 11, 13}}
>
> Sort[Table[Apply[Times, div[[i]]], {i, 1, Length[div]}]]
>
> {1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 33, 39, 66, 78, 99, 117, 121, 143,
> 198, 234, 242, 286, 363, 429, 726, 858, 1089, 1287, 1331, 1573, 2178,
> 2574, 2662, 3146, 3993, 4719, 7986, 9438, 11979, 14157, 17303, 23958,
> 28314, 34606, 51909, 103818, 155727, 311454}
>
> Divisors[2*3*3*11*11*11*13] - %
>
> {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}



  • References:
    • Divisors
      • From: hahaj@home.com (Hans Havermann)
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