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<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><FONT
face="MS UI Gothic"> Neil wrote on comment line of
A038260. </FONT></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><FONT
face="MS UI Gothic" size=2><FONT size=3> ><TT>Surely there
are smaller members! njas, Nov 07 2006 </TT></FONT></P>
<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left></FONT></SPAN><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"></SPAN> </P>
<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
Why do you<SPAN style="mso-spacerun: yes"> think</SPAN></SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><SPAN
style="mso-spacerun: yes"> </SPAN>that?</SPAN></P>
<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><SPAN
style="mso-spacerun: yes"> </SPAN>I searched<SPAN
style="mso-spacerun: yes"> the </SPAN>“seeds” for “regular” Rational
Amicable Number again.</SPAN></P>
<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"> <SPAN
style="mso-spacerun: yes"> </SPAN>.<?xml:namespace
prefix = o ns = "urn:schemas-microsoft-com:office:office"
/><o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><SPAN
style="mso-spacerun: yes"> </SPAN>And {11*19,<SPAN
style="mso-spacerun: yes"> 239 </SPAN>} is the<SPAN
style="mso-spacerun: yes"> smallest
one.
</SPAN>.<o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><SPAN
style="mso-spacerun: yes"> So, I<SPAN
style="mso-spacerun: yes"> think </SPAN>that at least it is the first terms
of regular<SPAN style="mso-spacerun: yes"> Rational Amicable
Pair.</SPAN></P>
<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></SPAN></SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><SPAN
style="mso-spacerun: yes">
</SPAN>.<o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><SPAN
style="mso-spacerun: yes"> </SPAN>Such a Diophantine<SPAN
style="mso-spacerun: yes"> equation </SPAN>which is high degree and
is involved<SPAN style="mso-spacerun: yes"> </SPAN>with Sigma<SPAN
style="mso-spacerun: yes"> function </SPAN>has many conditions<SPAN
style="mso-spacerun: yes"> </SPAN>, so the<SPAN
style="mso-spacerun: yes"> solution </SPAN>must have<SPAN
style="mso-spacerun: yes"> many </SPAN>prime factors for having good<SPAN
style="mso-spacerun: yes"> property,</SPAN><SPAN style="mso-spacerun: yes">
hence </SPAN>it becomes to<SPAN style="mso-spacerun: yes"> have many
</SPAN>digits.<o:p></o:p></SPAN></P>
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style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><SPAN
style="mso-spacerun: yes"></SPAN></SPAN> </P>
<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><SPAN
style="mso-spacerun: yes"> </SPAN>I guess<SPAN
style="mso-spacerun: yes"> </SPAN>that 2^2*7*<FONT
face="ＭＳ ゴシック">3*5^2*13*31*139*277*3877*11*19 </FONT>is the smallest<SPAN
style="mso-spacerun: yes"> </SPAN>and if an irregular example<SPAN
style="mso-spacerun: yes"> </SPAN>exists then it has around 16
digits.</SPAN></P>
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style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN> <SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan"
align=left><SPAN lang=EN-US
style="FONT-SIZE: 12pt; FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt"><SPAN
style="mso-spacerun: yes"> Yasutoshi</SPAN></SPAN></P>
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style="mso-spacerun: yes">
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