{VERSION 3 0 "DEC ALPHA UNIX" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "
Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 
0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" 
-1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 
0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "x:=100;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"xG\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "F:=add(z^(k^2),k=0..isqrt(x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"FG,8\"\"\"F&%\"zGF&*$)F'\"\"%\"\"\"F&*$)F'\"\"*F+F&
*$)F'\"#;F+F&*$)F'\"#DF+F&*$)F'\"#OF+F&*$)F'\"#\\F+F&*$)F'\"#kF+F&*$)F
'\"#\")F+F&*$)F'\"$+\"F+F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "series(F^2,z,x+1);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#+gp%\"zG\"\"
\"\"\"!\"\"#\"\"\"F%\"\"#F'\"\"%F'\"\"&F%\"\")F'\"\"*F'\"#5F'\"#8F'\"#
;F'\"#<F%\"#=F'\"#?\"\"%\"#DF'\"#EF'\"#HF%\"#KF'\"#MF'\"#OF'\"#PF'\"#S
F'\"#TF'\"#XF'\"#\\\"\"$\"#]F'\"#_F'\"#`F'\"#eF'\"#hF'\"#kF4\"#lF'\"#o
F%\"#sF'\"#tF'\"#uF'\"#!)F'\"#\")F'\"##)F4\"#&)F'\"#*)F'\"#!*F'\"#(*F%
\"#)*F4\"$+\"-%\"OG6#F%\"$,\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 308 "N:=proc(x::\{numeric,name\})\n  local xx,F,z,S,P,counter,i,k;\n
  if type(x,name) then RETURN('N'(x)) fi;\n  xx:=floor(x);\n  F:=add(z
^(k^2),k=0..isqrt(xx));\n  S:=series(F^2,z,xx+1);\n  P:=convert(S,poly
nom);\n  counter:=0;\n  for i from 0 to xx do\n    if coeff(P,z,i)>0 t
hen counter:=counter+1 fi\n  od;\n  counter\nend:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 9 "N(100.5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"#W" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(N(t),t=0..100,
scaling=constrained);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7jx7
$\"\"!$\"\"\"F(7$$\"+;arz@!\"*$\"\"$F(7$$\"+XTFwSF.$\"\"%F(7$$\"+\"z_
\"4iF.$\"\"&F(7$$\"+zp!fu'F.F97$$\"+m6m#G(F.F97$$\"+g#Q5b(F.F97$$\"+``
T>yF.F97$$\"+G'4l)yF.F97$$\"+,Rg`zF.F97$$\"+v\")p?!)F.$\"\"'F(7$$\"+ZC
z(3)F.FP7$$\"+%*4)>A)F.FP7$$\"+S&phN)F.FP7$$\"+:ddC%*F.$\"\"(F(7$$\"+*
=)H\\5!\")$\"\")F(7$$\"+>JN[6F]oF^o7$$\"+[!3uC\"F]oF^o7$$\"+f%\\IF\"F]
oF^o7$$\"+p3p)H\"F]oF^o7$$\"+A7508F]o$\"\"*F(7$$\"+v:^68F]oF_p7$$\"+G>
#zJ\"F]oF_p7$$\"+!GKVK\"F]oF_p7$$\"+&)H:P8F]oF_p7$$\"+!pt*\\8F]oF_p7$$
\"+6lD,9F]oF_p7$$\"+J$RDX\"F]oF_p7$$\"+)R'ok;F]o$\"#5F(7$$\"+_(>/x\"F]
o$\"#6F(7$$\"+1J:w=F]o$\"#7F(7$$\"+#)H`I>F]oFcr7$$\"+dG\"\\)>F]oFcr7$$
\"+U.r\"*>F]oFcr7$$\"+Fy])*>F]oFcr7$$\"+7`I0?F]o$\"#8F(7$$\"+'z-@,#F]o
Fds7$$\"+lxpD?F]oFds7$$\"+LFHR?F]oFds7$$\"+rE[m?F]oFds7$$\"+3En$4#F]oF
ds7$$\"+c#o%*=#F]oFds7$$\"+/RE&G#F]oFds7$$\"+5b=RBF]oFds7$$\"+:r5$R#F]
oFds7$$\"+>z1?CF]oFds7$$\"+@(GqW#F]oFds7$$\"+B\"40Y#F]oFds7$$\"+C&*)RZ
#F]oFds7$$\"+D(H2[#F]oFds7$$\"+D*pu[#F]oFds7$$\"+E,@%\\#F]oFds7$$\"+D.
&4]#F]o$\"#9F(7$$\"+vB_<FF]o$\"#:F(7$$\"+,#*ppFF]oF^w7$$\"+Eg(=#GF]oF^
w7$$\"+RW'z%GF]oF^w7$$\"+^G0uGF]oF^w7$$\"+b\\d!)GF]oF^w7$$\"+eq4()GF]o
F^w7$$\"+h\">O*GF]oF^w7$$\"+k79+HF]o$\"#;F(7$$\"+qa=8HF]oFhx7$$\"+v'Hi
#HF]oFhx7$$\"+(y#*4-$F]oFhx7$$\"+(*ev:JF]oFhx7$$\"+Dl#R9$F]oFhx7$$\"+^
r4sJF]oFhx7$$\"+4)R\"zJF]oFhx7$$\"+lC='=$F]oFhx7$$\"+A^A$>$F]oFhx7$$\"
+yxE+KF]o$\"#<F(7$$\"+\"4`V@$F]oFhz7$$\"+.%Q%GKF]oFhz7$$\"+c'zZG$F]oFh
z7$$\"+347TLF]oFhz7$$\"+LY.KNF]o$\"#=F(7$$\"+eO2VOF]o$\"#>F(7$$\"+\"o7
Tv$F]o$\"#?F(7$$\"+L5S_QF]oFc\\l7$$\"+$Q*o]RF]oFc\\l7$$\"+$GF&eSF]o$\"
#@F(7$$\"+\"=lj;%F]o$\"#AF(7$$\"+jB0pUF]oFc]l7$$\"+V&R<P%F]oFc]l7$$\"+
&>6`U%F]oFc]l7$$\"+XG))yWF]oFc]l7$$\"+.$zb[%F]oFc]l7$$\"+fdF#\\%F]oFc]
l7$$\"+;A(*)\\%F]oFc]l7$$\"+r'oc]%F]o$\"#BF(7$$\"+%eh!>XF]oF]_l7$$\"+'
\\aC`%F]oF]_l7$$\"+@.CfXF]oF]_l7$$\"+Xh-'e%F]oF]_l7$$\"+VrT%o%F]oF]_l7
$$\"+R\"3Gy%F]oF]_l7$$\"+J@(e$[F]oF]_l7$$\"+Ah$*))[F]oF]_l7$$\"+@\"pb*
[F]oF]_l7$$\"+?@?-\\F]o$\"#CF(7$$\"+>^$)3\\F]oF]al7$$\"+=\"oa\"\\F]oF]
al7$$\"+;TtG\\F]oF]al7$$\"+8,+U\\F]oF]al7$$\"+4@`o\\F]oF]al7$$\"+.T1&*
\\F]oF]al7$$\"+(RQb@&F]o$\"#EF(7$$\"+Q)G&R_F]oFdbl7$$\"+y#>NE&F]oFdbl7
$$\"+)\\9bF&F]oFdbl7$$\"+=(4vG&F]oFdbl7$$\"+Gt]$H&F]oFdbl7$$\"+Q\\]*H&
F]oFdbl7$$\"+[D]0`F]o$\"#FF(7$$\"+e,]6`F]oF[dl7$$\"+Q5[f`F]oF[dl7$$\"+
=>Y2aF]oF[dl7$$\"+[K56bF]oF[dl7$$\"+yXu9cF]oF[dl7$$\"+'R!GocF]oF[dl7$$
\"+9i\"=s&F]oF[dl7$$\"+BTe[dF]oF[dl7$$\"+K?NvdF]oF[dl7$$\"+5S/#y&F]oF[
dl7$$\"+()ft)y&F]oF[dl7$$\"+lzU&z&F]oF[dl7$$\"+T*>@!eF]o$\"#GF(7$$\"+'
*Q]:eF]oFdfl7$$\"+\\y))GeF]oFdfl7$$\"+cljLfF]oFdfl7$$\"+i_QQgF]oFdfl7$
$\"+-FsjgF]oFdfl7$$\"+U,1*3'F]oFdfl7$$\"+-XR&4'F]oFdfl7$$\"+i)G<5'F]o$
\"#HF(7$$\"+AK13hF]oF^hl7$$\"+#e(R9hF]oF^hl7$$\"+-j1FhF]oF^hl7$$\"+@]t
RhF]oF^hl7$$\"+,*4/>'F]oF^hl7$$\"+!y%3TiF]oF^hl7$$\"+O![hY'F]o$\"#IF(7
$$\"+#Qx$omF]o$\"#JF(7$$\"+I\"eBs'F]oFjil7$$\"+y)Qjx'F]oFjil7$$\"+sk3$
y'F]oFjil7$$\"+lS$)*y'F]oFjil7$$\"+f;e'z'F]oFjil7$$\"+_#HL!oF]o$\"#KF(
7$$\"+RW#o\"oF]oF^[m7$$\"+E'>.$oF]oF^[m7$$\"+++JdoF]oF^[m7$$\"+u.I%)oF
]oF^[m7$$\"+O&H@)pF]oF^[m7$$\"+(pe*zqF]oF^[m7$$\"+b_VLrF]oF^[m7$$\"+6=
\"p=(F]oF^[m7$$\"+#Q'f$>(F]oF^[m7$$\"+^4G+sF]o$\"#LF(7$$\"+@b'p?(F]oF^
]m7$$\"+!4]O@(F]oF^]m7$$\"+H#>qA(F]oF^]m7$$\"+o$)QSsF]oF^]m7$$\"+Ym7ns
F]oF^]m7$$\"+C\\'QH(F]oF^]m7$$\"+p%*\\%R(F]o$\"#MF(7$$\"+8S8&\\(F]o$\"
#NF(7$$\"+5hK+wF]oFj^m7$$\"+0#=bq(F]oFj^m7$$\"+2FO3yF]oFj^m7$$\"+2s?6z
F]oFj^m7$$\"+pe()=!)F]o$\"#OF(7$$\"+IXaE\")F]o$\"#PF(7$$\"+l*RRL)F]o$
\"#QF(7$$\"+8H'pQ)F]oFe`m7$$\"+ge)*R%)F]oFe`m7$$\"+Mt\\m%)F]oFe`m7$$\"
+2)3I\\)F]oFe`m7$$\"+xmj*\\)F]oFe`m7$$\"+XXE1&)F]o$\"#RF(7$$\"+9C*G^)F
]oFiam7$$\"+\"G?&>&)F]oFiam7$$\"+=gxK&)F]oFiam7$$\"+`<.Y&)F]oFiam7$$\"
+M&*>^')F]oFiam7$$\"+8tOc()F]oFiam7$$\"+[ko/))F]oFiam7$$\"+#e0I&))F]oF
iam7$$\"+m`3l))F]oFiam7$$\"+\\^;x))F]oFiam7$$\"+U]?$)))F]oFiam7$$\"+L
\\C*)))F]oFiam7$$\"+D[G&*))F]oFiam7$$\"+;ZK,*)F]o$\"#SF(7$$\"+$G%[D*)F
]oFedm7$$\"+\\Qk\\*)F]oFedm7$$\"+X')[j*)F]oFedm7$$\"+SMLx*)F]oFedm7$$
\"+QeD%)*)F]oFedm7$$\"+N#y6**)F]oFedm7$$\"+L15)**)F]oFedm7$$\"+II-0!*F
]o$\"#TF(7$$\"+?ErK!*F]oF_fm7$$\"+5ASg!*F]oF_fm7$$\"+!R\"y:\"*F]oF_fm7
$$\"+p0;r\"*F]oF_fm7$$\"+oTAq#*F]oF_fm7$$\"+lxGp$*F]oF_fm7$$\"+B-\"\\Z
*F]oF_fm7$$\"+!oK0e*F]oF_fm7$$\"+l(z5j*F]oF_fm7$$\"+\\oi\"o*F]oF_fm7$$
\"+O_%zo*F]oF_fm7$$\"+@OE%p*F]oF_fm7$$\"+2?e+(*F]o$\"#UF(7$$\"+#R+pq*F
]oFhhm7$$\"+jr`>(*F]oFhhm7$$\"+MR<K(*F]oFhhm7$$\"+wuWd(*F]oFhhm7$$\"+<
5s#y*F]oFhhm7$$\"$+\"F($\"#WF(-%'COLOURG6&%$RGBG$Fjq!\"\"F(F(-%+AXESLA
BELSG6$Q\"t6\"%!G-%(SCALINGG6#%,CONSTRAINEDG-%%VIEWG6$;F(Fjim%(DEFAULT
G" 2 299 299 299 2 0 1 0 2 9 0 4 1 1.000000 45.000000 45.000000 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 59 "for k to 10 do\n  x:=2^k; \n  evalf(N(x)/
(x/ln(x)^(1/2)))\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG\"\"#" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+<>$)[7!\"*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"xG\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+A+Tx
6!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG\"\")" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#$\"+l,_\"3\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"xG\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+kKpS5!\"*" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"xG\"#K" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#$\"+^(3+*)*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG\"#k" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+J!y$f&*!#5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"xG\"$G\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+8g'
[Y*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG\"$c#" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#$\"+&[XX,*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"xG\"$7&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+5>jH))!#5" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"xG\"%C5" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#$\"+\\S>!p)!#5" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "u^2*v;" "6
#*&)%\"uG\"\"#\"\"\"%\"vGF'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "
u;" "6#%\"uG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "v;" "6#%\"vG" }
}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "N[k](x);" "6#-&%\"NG6#%\"kG6#%
\"xG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "x;" "6#%\"xG" }}}
{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "k;" "6#%\"kG" }}}{EXCHG {PARA 0 
"" 0 "" {XPPEDIT 18 0 "k-1;" "6#,&%\"kG\"\"\"\"\"\"!\"\"" }}}{EXCHG 
{PARA 0 "" 0 "" {XPPEDIT 18 0 "N[1](x);" "6#-&%\"NG6#\"\"\"6#%\"xG" }}
}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "N[2](x);" "6#-&%\"NG6#\"\"#6#%
\"xG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "N[3](x);" "6#-&%\"NG6#
\"\"$6#%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "N[4](x);" "6#-&
%\"NG6#\"\"%6#%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "sqrt(x);
" "6#-%%sqrtG6#%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "b*x/sqr
t(ln(x));" "6#*&*&%\"bG\"\"\"%\"xGF&F&-%%sqrtG6#-%#lnG6#F'!\"\"" }}}
{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "b = sqrt(PI)/sqrt(2);" "6#/%\"bG
*&-%%sqrtG6#%#PIG\"\"\"-F'6#\"\"#!\"\"" }}}{EXCHG {PARA 0 "" 0 "" 
{XPPEDIT 18 0 "PI;" "6#%#PIG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 
"PI = Product(1/(1-1/(p^2)),p);" "6#/%#PIG-%(ProductG6$*&\"\"\"\"\"\",
&\"\"\"F**&\"\"\"F**$)%\"pG\"\"#F*!\"\"F3F3F1" }}}{EXCHG {PARA 0 "" 0 
"" {XPPEDIT 18 0 "p;" "6#%\"pG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 
0 "x/6;" "6#*&%\"xG\"\"\"\"\"'!\"\"" }}}{EXCHG {PARA 0 "" 0 "" 
{XPPEDIT 18 0 "5*x/6;" "6#*&*&\"\"&\"\"\"%\"xGF&F&\"\"'!\"\"" }}}
{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "b;" "6#%\"bG" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 105 "pi:=1:\np:=2:\nto 100 do\n  p:=nextprime(p
);\n  if irem(p,4)=3 then pi:=pi*(1-1/p^2) fi\nod:\nb:=1/sqrt(2.*pi);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG$\"+m$e<k(!#5" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "26 0 0" 0 }{VIEWOPTS 1 
1 0 1 1 1803 }