[seqfan] Re: Intermediate result for ordering problem: 2-D \phi()

Philippe LALLOUET philip.lallouet at orange.fr
Mon Dec 1 06:58:22 CET 2008







> Message du 30/11/08 14:25
> De : "Hugo van der Sanden" 
> A : "Sequence Fanatics Discussion list" 
> Copie à : 
> Objet : [seqfan] Re: Intermediate result for ordering problem: 2-D \phi()
> 
> 
> Yes, but only to zero, and the extension a(0, n) = a(n, 0) = 0 falls
> naturally out of the definition.
> 
> Hugo
> 
> 2008/11/30 David Wilson 
> 
> > Yes, your sum is prettier.
> >
> > Does it actually define the same function though?
> >
> > Doesn't it force you to extend the function to non-positive arguments?
> >
> > ----- Original Message -----
> > From: 
> > To: "Sequence Fanatics Discussion list" 
> > Cc: 
> > Sent: Sunday, November 30, 2008 3:13 AM
> > Subject: [seqfan] Re: Intermediate result for ordering problem: 2-D \phi()
> >
> >
> > > That's very nice. Though it makes the computation less obvious, I'd
> > rather
> > > express it as:
> > >
> > > mn = sum_{k=1}^\inf { a([m/k], [n/k]) }
> > >
> > > .. in which each component of the sum counts the pairs with gcd equal to
> > k
> > > (and analogously for higher dimension).
> > >
> > > Hugo
> >
> >
> >
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> >
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> >
> 
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