Question related to sequence A066452

[Diana Mecum]

Joshua,

Thanks a bunch. I would never have been able to find this different spin on
the definition of anti-phi.

I have been able to replicate the original list.

Diana M.

On 6/30/07, Joshua Zucker <joshua.zucker at gmail.com> wrote:
>
> I don't understand it either, but at least I could use the wayback
> machine to track down the URL given, at
>   http://tinyurl.com/2xuvgr
>
> And it says
>   The anti-phi function is defined as the numbers <n that do not have
> any anti-divisor as a factor.
>
> Which may or may not be what they actually mean ... but at least it's
> another possible interpretation to try.
>
> --Joshua Zucker
>
>
> On 6/30/07, Diana Mecum <diana.mecum at gmail.com> wrote:
> > Folks,
> >
> > I am trying to add extension terms for sequence A066452. I have a
> question.
> >
> > This is the internal text describing the sequence:
> >
> > %I A066452
> > %S A066452
> > 1,1,2,1,4,1,4,4,3,2,8,3,7,7,9,2,8,5,10,10,8,6,19,6,12,9,9,8,22,9,12,
> > %T A066452
> > 12,15,10,31,9,11,14,24,13,23,9,24,17,16,10,35,15,23
> > %N A066452 Anti-phi(n).
> > %H A066452 Jon Perry, <a
> > href="
> http://www.users.globalnet.co.uk/~perry/maths/antidivisorother2.htm
> > ">
> >                Anti-phi function</a>
> > %F A066452 anti-phi(n) = number of integers <= n that are coprime to the
> > anti-divisors of n
> > %e A066452 10 has the anti-divisors 3,4,7. Therefore numbers coprime to
> > 3,4,7 and less than
> >                10 are are 1,2,5, therefore anti-phi(10)=3.
> > %Y A066452 Cf. A058838, A066241.
> > %Y A066452 Sequence in context: A024994 A051953 A079277 this_sequence
> > A007104 A102627 A088296
> > %Y A066452 Adjacent sequences: A066449 A066450 A066451 this_sequence
> A066453
> > A066454 A066455
> > %K A066452 nonn,more,easy
> > %O A066452 2,3
> > %A A066452 Jon Perry (perry(AT)globalnet.co.uk), Dec 29 2001
> >
> > I found a definition for "anti-divisor" as follows:
> >
> > "Non-divisor: a number k which does not divide a given number x."
> > "Anti-divisor: a non-divisor k of x with the property that k is an odd
> > divisor of 2x-1 or 2x+1, or an even divisor of 2x."
> >
> > I see how Jon gets 3, 4 and 7 as anti-divisors of 10. However, 2 is not
> > coprime to the anti-divisors of 10. He has 1, 2, and 5 as on the
> anti-phi
> > list.
> >
> > The sequence which I derived for this sequence is:
> >
> > 1, 1, 2, 1, 4, 1, 4, 4, 3, 2, 2, 5, 3, 5, 4, 9, 2, 4, 5, 6, 6, 6, 6, 10,
> 5,
> > 8, 6, 5, 8, 8, 9, 12,
> >  7, 10, 7, 12, 9, 8, 9, 13, 13, 9, 9, 14, 10
> >
> > Can someone tell me if I am misunderstanding the definition of the
> sequence,
> > or if I have found an error?
> >
> > Thanks,
> >
> > Diana M.
> >
> > --
> > "God made the integers, all else is the work of man."
> > L. Kronecker, Jahresber. DMV 2, S. 19.
>



-- 
"God made the integers, all else is the work of man."
L. Kronecker, Jahresber. DMV 2, S. 19.
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