|
Search: id:A138812
|
|
|
| A138812 |
|
a(0)=1. a(n) = sum{k=0 to n-1} floor(n/a(k)). |
|
+0
2
|
|
| 1, 1, 4, 6, 9, 11, 14, 16, 19, 22, 24, 27, 31, 33, 36, 38, 42, 44, 48, 51, 54, 56, 60, 62, 67, 69, 71, 75, 79, 81, 84, 87, 91, 95, 97, 99, 105, 107, 111, 113, 116, 118, 123, 125, 131, 134, 136, 138, 145, 147, 149, 152, 155, 157, 163, 166, 171, 174, 176, 178, 183, 185
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
Leroy Quet, Home Page (listed in lieu of email address)
|
|
FORMULA
|
Probably a(n) ~ sqrt(2) n ln(n)^(1/2) as n -> oo. - Robert Israel (israel(AT)math.ubc.ca), May 02 2008
Comment from Andrew V. Sutherland (drew(AT)math.mit.edu), May 02 2008 (Start): This is supported by the following data:
a( 2) = 4, a(n)/n=2.0000, a(n)/(n*sqrt(ln(n)))=2.4022
a( 4)= 9, a(n)/n=2.2500, a(n)/(n*sqrt(ln(n)))=1.9110
a( 8)= 19, a(n)/n=2.3750, a(n)/(n*sqrt(ln(n)))=1.6470
a( 16)= 42, a(n)/n=2.6250, a(n)/(n*sqrt(ln(n)))=1.5765
a( 32)= 91, a(n)/n=2.8438, a(n)/(n*sqrt(ln(n)))=1.5275
a( 64)= 196, a(n)/n=3.0625, a(n)/(n*sqrt(ln(n)))=1.5017
a( 128)= 421, a(n)/n=3.2891, a(n)/(n*sqrt(ln(n)))=1.4932
a( 256)= 896, a(n)/n=3.5000, a(n)/(n*sqrt(ln(n)))=1.4863
a( 512)= 1892, a(n)/n=3.6953, a(n)/(n*sqrt(ln(n)))=1.4795
a( 1024)= 3979, a(n)/n=3.8857, a(n)/(n*sqrt(ln(n)))=1.4759
a( 2048)= 8335, a(n)/n=4.0698, a(n)/(n*sqrt(ln(n)))=1.4739
a( 4096)= 17386, a(n)/n=4.2446, a(n)/(n*sqrt(ln(n)))=1.4718
a( 8192)= 36146, a(n)/n=4.4124, a(n)/(n*sqrt(ln(n)))=1.4699
a( 16384)= 74931, a(n)/n=4.5734, a(n)/(n*sqrt(ln(n)))=1.4681
a( 32768)= 154964, a(n)/n=4.7291, a(n)/(n*sqrt(ln(n)))=1.4666
a( 65536)= 319818, a(n)/n=4.8800, a(n)/(n*sqrt(ln(n)))=1.4654
a(131072)= 658761, a(n)/n=5.0259, a(n)/(n*sqrt(ln(n)))=1.4641 (End)
|
|
MAPLE
|
a[0]:=1: for n to 65 do a[n]:=sum(floor(n/a[k]), k=0..n-1) end do: seq(a[n], n =0..65); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2008
|
|
MATHEMATICA
|
a = {1}; Do[AppendTo[a, Sum[Floor[n/a[[k]]], {k, 1, n}]], {n, 1, 70}]; a - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 04 2008
|
|
CROSSREFS
|
Cf. A138813.
Sequence in context: A010387 A010411 A047209 this_sequence A003259 A020935 A066095
Adjacent sequences: A138809 A138810 A138811 this_sequence A138813 A138814 A138815
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Leroy Quet Mar 31 2008
|
|
EXTENSIONS
|
More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2008
|
|
|
Search completed in 0.002 seconds
|
