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<DIV>This suggests a couple of other sequences to me:</DIV>
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<DIV>Smallest m such that n can be represented as the sum of distinct divisors of m in more than one way (offset 3):</DIV>
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<DIV class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">6,12,12,6,12,12,6,12,12,12,12,12,24,24,24,18,18,18,18,20</SPAN><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"><?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p></SPAN></DIV>
<DIV class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"><o:p></o:p></SPAN></DIV>
<DIV class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"></SPAN> </DIV>
<DIV class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana">Same, except the divisor sets must be disjoint (also offset 3):<o:p></o:p></SPAN></DIV></DIV>
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<DIV><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">6,12,12,6,12,12,18,20,20,12,12,12,24,24,24,18,36,20,20,36</SPAN></DIV>
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<DIV>These are related to A070172.</DIV>
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<DIV>Obviously, each of these can only take on values in Emeric's sequence.</DIV>
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<DIV>Franklin T. Adams-Watters<BR> </DIV> <BR>-----Original Message-----<BR>From: Emeric Deutsch <A href="mailto:deutsch@duke.poly.edu">deutsch@duke.poly.edu</A><BR><BR>
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<DIV class=AOLPlainTextBody> <BR>Values of n such that the number of distinct sums of <BR>distinct divisors of n is less than 2^tau(n) - 1 (clearly, <BR>the latter is the largest number of possible distinct sums). <BR> <BR>...<BR> <BR>6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 45, 48, 54, 56, 60, <BR>63, 66, 70, 72, 78, 80, 84, 88, 90, 96, 99, 100, 102, 104, <BR>105, 108, 110, 112, 114, 117, 120, 126, 130, 132, 135, 138, <BR>140, 144, 150, 154, 156, 160, 162, 165, 168, 170, 174, 176, <BR>180, <BR></DIV><!-- end of AOLMsgPart_0_bcb1f476-aee3-451c-b3ab-734e5972eea8 --></DIV></DIV>
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