[seqfan] Re: Question regarding submitting potentially duplicated sequence

Ami Eldar amiram.eldar at gmail.com
Thu Oct 5 09:21:35 CEST 2017


The sequences that I am trying to calculate are analogous to
  A065218: Consider the subsets of proper divisors of a number that sum to
the number. These are numbers that set a record number of such subsets.
  1, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520,
5040, 7560, 10080, 15120, 20160, 25200, 27720, 45360, 50400, 55440, 83160,
110880, 166320, 221760, 277200, 332640, 498960, 554400, 665280, 720720,
831600, 1081080, 1441440
and
  A065219: Number of subsets of proper divisors of numbers in A065218
summing to the number.
  1, 2, 5, 7, 10, 34, 278, 751, 2157, 22208, 676327, 2225346, 23259536,
265050967,
with unitary and bi-unitary divisors.

Starting from 6,  A065218 has 35 common terms with highly composite numbers
(A002182) and 16 common terms with superabundant numbers (A004394).

With unitary divisors I get: 6, 30, 210, 2310, 30030
and the corresponding records are 1, 3, 151, 974412, 304020558577529
The sequence begins as the primorials (A002110) which are also the unitary
version of highly composite numbers and superabundant numbers.

With bi-unitary divisors I get: 6, 24, 96, 120, 480, 840
and the corresponding records are  1, 5, 21, 278, 17049, 2225346
The sequence begins as bi-unitary superabundant numbers (A292984) and
bi-unitary highly composite numbers (A293185, still a draft), except for 1
and 2.

I am calculating the terms with
udiv[n_] := Block[{d = Divisors[n]}, Select[d, GCD[#, n/#] == 1 &]];
a = {}; n = 0; cm = 0; While[Length[a] < 10, n++; d = Most[udiv[n]];
c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0,
n}], n]; If[c > cm, cm = c; AppendTo[a, n]]]; a

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] :=
Select[Divisors[m], Last at Intersection[f@#, f[m/#]] == 1 &];
a={}; cm = 0; n=0; While[Length[a] < 10, n++; d = Most[bdiv[n]];
c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0,
n}], n];  If[c > cm, cm = c; AppendTo[a,n]]]; a


On Thu, Oct 5, 2017 at 5:16 AM, Alonso Del Arte <alonso.delarte at gmail.com>
wrote:

> Then I suggest you post the formula here on this mailing list. Even I might
> be able to wring out one or two more terms for you.
>
> Al
>
> On Wed, Oct 4, 2017 at 1:41 PM, Ami Eldar <amiram.eldar at gmail.com> wrote:
>
> > Only computational, otherwise I would generate more terms that may help
> me
> > decide.
> >
> > On Wed, Oct 4, 2017 at 8:03 PM, Alonso Del Arte <
> alonso.delarte at gmail.com>
> > wrote:
> >
> > > > In each sequence I can calculate only 5-6 terms due to its high
> > > complexity.
> > >
> > > This "complexity," is it theoretical or computational? In other words,
> is
> > > it something that could be helped by someone with more number crunching
> > > power, or does it require some kind of inspiration to overcome?
> > >
> > > Al
> > >
> > > On Wed, Oct 4, 2017 at 11:12 AM, Ami Eldar <amiram.eldar at gmail.com>
> > wrote:
> > >
> > > > Hello,
> > > >
> > > > I have a general question, but I may be more specific if needed. It
> > > regards
> > > > to a couple of sequences that I want to submit.
> > > >
> > > > In each sequence I can calculate only 5-6 terms due to its high
> > > complexity.
> > > > By searching the terms in OEIS I find a related sequence, but it is
> not
> > > > clear that the sequences are the same. In fact, I believe that
> > ultimately
> > > > the sequences may differ. But still, I may be wrong.
> > > >
> > > > It is like highly composite numbers (A002182) and superabundant
> numbers
> > > > (A166981) that have the first 19 terms common.
> > > >
> > > > What is the OEIS policy with such an issue?
> > > >
> > > > Thanks.
> > > >
> > > > --
> > > > Seqfan Mailing list - http://list.seqfan.eu/
> > > >
> > >
> > >
> > >
> > > --
> > > Alonso del Arte
> > > Author at SmashWords.com
> > > <https://www.smashwords.com/profile/view/AlonsoDelarte>
> > > Musician at ReverbNation.com <http://www.reverbnation.com/
> alonsodelarte>
> > >
> > > --
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
>
>
> --
> Alonso del Arte
> Author at SmashWords.com
> <https://www.smashwords.com/profile/view/AlonsoDelarte>
> Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>


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