NetNews Usenet Archive 1992 #26/NN_1992_26.iso/spool/sci/math/14770

Text File | 1992-11-11 | 1.5 KB | 41 lines

Newsgroups: sci.math
Path: sparky!uunet!sun-barr!ames!agate!stanford.edu!rock!concert!sas!mozart.unx.sas.com!sasrdt
From: [e-mail] (Randall D. Tobias)
Subject: Re: An Interesting Function
Originator: [e-mail]
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Date: Wed, 11 Nov 1992 18:37:05 GMT
References:  <[e-mail]>
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In article <[e-mail]>, [e-mail] (Frank Adams) writes:
|> Consider the function W(n) = sum(0<i<n,mod(n,i)).  The problem is to find an
|> asymptotic expression for W(n).
|>
|> It is pretty clear that W(n) = O(n^2).  In fact, we can write
|> W(n)=c n^2 + o(n^2).  The question is, what is c?  I know the answer, and
|> will post it later if no one gets it.
|>
|> I think in fact W(n) = c n^2 + O(n), but I can't prove it.  It seems that
|> W(n) /= c n^2 + d n + o(n); the O(n) stuff "wanders around".

Well?  I got as far as empirically verifying the

   W(n) /= c n^2 + d n + o(n)

for n up to 100000 or so.  But i haven't got the number theory know-how
to go much further.  Pretty function, though.

--

Randy Tobias          SAS Institute Inc.     [e-mail]
[phone] x7933  SAS Campus Dr.         [e-mail]
[phone] (Fax)  Cary, NC   27512-8000  [e-mail]

 ... just my $(-exp(2*sqrt(-1)*arcos(0))/(((2**(2 + 1)) - 1)**2 + 1)).