Mobius transform question

[franktaw at netscape.net]

 No.  Consider S(a) = 2 if 4|a or 6|a, otherwise 1.  This meets your conditions, but T(12)=1/2.
 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645
 
 
-----Original Message-----
From: Don Reble <djr at nk.ca>
To: Seqfan <seqfan at ext.jussieu.fr>
Sent: Fri, 04 Nov 2005 06:27:03 -0700
Subject: Mobius transform question


Seqfans:

    Given an integer sequence S, define a transformed sequence T:
    T(k) = S(k) / [ product(d divides k and d<k) T(d) ]
    (So log T is the Mobius transform of log S. Or maybe vice-versa.)

    T might be an integer sequence or not. Suppose
    S(a) divides S(ab)
    and
    (c coprime d) implies (S(c) coprime S(d)).
    Is that enough to imply that T is integers?

-- 
Don Reble  djr at nk.ca

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