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<DIV><FONT face="MS UI Gothic" size=2> Neil</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> I submit two Sigma
sequences.</FONT></DIV>
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<DIV><FONT face="MS UI Gothic" size=2> %I
A000001<BR> %S A000001 1, 2, 2, 4, 3, 4, 3, 6, 5, 6, 4,
8<BR> %N A000001 SquareRootSigma(n) : Integerization of sum of
square root of divisors of n
<BR>
If n = Product p_i^r_i then SRSigma(n) = Product
Floor[(p_i^(r_i/2+1/2)-1)/(p_i^(1/2)-1) ]. <BR> %O
A000001 1.2 <BR> %Y
A000001 A033635<BR> %K
A000001 nonn, mult<BR> %A
A000001 Yasutoshi Kohmoto (<A
href="mailto:zbi74583@boat.zero.ad.jp">zbi74583@boat.zero.ad.jp</A>)</FONT></DIV>
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<DIV><FONT face="MS UI Gothic" size=2> %I
A000002<BR> %S A000002 1, 1, 2, 5, 4, 2, 6, 13, 11, 4, 10, 10,
12, 6, 8, 29, 16, 11, 19, 20 <BR> %N A000002 (-1)Sigma(n) : a
difference of divisors of n
<BR>
If x=Product p_i^r_i, then (-1)Sigma(x)=Product (-1+Sum p_i^s_i, s_i=1 to r_i) =
Product ((p_i^(r_i+1)-1)/(p_i-1)-2)
<BR>
(-1)Sigma(1)=1<BR> %e A000002
<BR>
(-1)sigma(24)=(-1+2+4+8)*(-1+3)=1-2-4-8-3+6+12+24
<BR> all
terms are divisors of 24, but it is not the sum of divisors.
<BR> It is
a difference of divisors. <BR> %O
A000002 1.3 <BR> %Y
A000002 A0<BR> %K A000002
nonn, mult<BR> %A A000002 Yasutoshi Kohmoto
(<A
href="mailto:zbi74583@boat.zero.ad.jp">zbi74583@boat.zero.ad.jp</A>)<BR></FONT></DIV>
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<DIV><FONT face="MS UI Gothic" size=2> Yasutsohi</FONT></DIV>
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