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<DIV> No. Consider S(a) = 2 if 4|a or 6|a, otherwise 1. This meets your conditions, but T(12)=1/2.</DIV>
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<DIV>Franklin T. Adams-Watters<BR>16 W. Michigan Ave.<BR>Palatine, IL 60067<BR>847-776-7645</DIV>
<DIV> </DIV> <BR>-----Original Message-----<BR>From: Don Reble <djr@nk.ca><BR>To: Seqfan <seqfan@ext.jussieu.fr><BR>Sent: Fri, 04 Nov 2005 06:27:03 -0700<BR>Subject: Mobius transform question<BR><BR>
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<DIV class=AOLPlainTextBody id=AOLMsgPart_0_8a8f83e4-b125-4a3d-abce-c986980b5abe><PRE><TT>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 <A href="mailto:djr%40nk.ca">djr@nk.ca</A>
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