[seqfan] Re: Upper bound for A091895 and A091896
Hugo Pfoertner
yae9911 at gmail.com
Sun Apr 3 18:05:41 CEST 2022
A bound of k <= 2*n^2 should be sufficient. This covers the extreme cases
n=2 with d(8)/8 = 4/8 = 1/2 and n=6 with d(72)/72 = 12/72 = 1/6. The factor
f=2 in the required bound for k to exclude d(k)/k=n decreases for larger n.
E.g, f=5/3 at n=12, f=6/5 at n=20, f=20/21 at n=42, f=24/35 at n=70, f=8/15
at n=90, f=24/55 at n=110, ....
On Sun, Apr 3, 2022 at 8:45 AM Michel Marcus <michel.marcus183 at gmail.com>
wrote:
> Maybe use d(n) <= 2 sqrt(n) [see Mitrinovich, p. 39, also A046522].
> from A000005.
>
> MM
>
> Le dim. 3 avr. 2022 à 07:43, Neil Sloane <njasloane at gmail.com> a écrit :
>
> > What about sequence A091896? These are supposed to be the n for which
> no k
> > exists, and there is a program.
> > Which seems to use the bound 25000000. So is this just a guess? Would
> > this be called a "program based on a conjecture"?
> > Or is there some mathematics behind it? Bob?
> >
> > Is there a proof that 18 is in A091896?
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, Chairman, OEIS Foundation.
> > Also Visiting Scientist, Math. Dept., Rutgers University,
> > Email: njasloane at gmail.com
> >
> >
> >
> > On Sun, Apr 3, 2022 at 12:44 AM Michel Marcus <
> michel.marcus183 at gmail.com>
> > wrote:
> >
> > > Dear Seqfans,
> > >
> > > What would be a good upper bound when looking for terms of A091895 and
> > > A091896 ?
> > > Thanks.
> > >
> > > MM
> > >
> > > --
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> > >
> >
> > --
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> >
>
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