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A138812 a(0)=1, a(n) = sum{k=0 to n-1} floor(n/a(k)). 1
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; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..61.

FORMULA

Probably a(n) ~ sqrt(2) n log(n)^(1/2) as n -> oo. - Robert Israel, May 02 2008

From Andrew V. Sutherland, May 02 2008: (Start)

This is supported by the following data:

a( 2) = 4, a(n)/n=2.0000, a(n)/(n*sqrt(log(n)))=2.4022

a( 4)= 9, a(n)/n=2.2500, a(n)/(n*sqrt(log(n)))=1.9110

a( 8)= 19, a(n)/n=2.3750, a(n)/(n*sqrt(log(n)))=1.6470

a( 16)= 42, a(n)/n=2.6250, a(n)/(n*sqrt(log(n)))=1.5765

a( 32)= 91, a(n)/n=2.8438, a(n)/(n*sqrt(log(n)))=1.5275

a( 64)= 196, a(n)/n=3.0625, a(n)/(n*sqrt(log(n)))=1.5017

a( 128)= 421, a(n)/n=3.2891, a(n)/(n*sqrt(log(n)))=1.4932

a( 256)= 896, a(n)/n=3.5000, a(n)/(n*sqrt(log(n)))=1.4863

a( 512)= 1892, a(n)/n=3.6953, a(n)/(n*sqrt(log(n)))=1.4795

a( 1024)= 3979, a(n)/n=3.8857, a(n)/(n*sqrt(log(n)))=1.4759

a( 2048)= 8335, a(n)/n=4.0698, a(n)/(n*sqrt(log(n)))=1.4739

a( 4096)= 17386, a(n)/n=4.2446, a(n)/(n*sqrt(log(n)))=1.4718

a( 8192)= 36146, a(n)/n=4.4124, a(n)/(n*sqrt(log(n)))=1.4699

a( 16384)= 74931, a(n)/n=4.5734, a(n)/(n*sqrt(log(n)))=1.4681

a( 32768)= 154964, a(n)/n=4.7291, a(n)/(n*sqrt(log(n)))=1.4666

a( 65536)= 319818, a(n)/n=4.8800, a(n)/(n*sqrt(log(n)))=1.4654

a(131072)= 658761, a(n)/n=5.0259, a(n)/(n*sqrt(log(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, Apr 04 2008

MATHEMATICA

a = {1}; Do[AppendTo[a, Sum[Floor[n/a[[k]]], {k, 1, n}]], {n, 1, 70}]; a (* Stefan Steinerberger, Apr 04 2008 *)

CROSSREFS

Cf. A138813.

Sequence in context: A010387 A010411 A047209 * A003259 A020935 A267149

Adjacent sequences:  A138809 A138810 A138811 * A138813 A138814 A138815

KEYWORD

nonn

AUTHOR

Leroy Quet, Mar 31 2008

EXTENSIONS

More terms from Stefan Steinerberger and Emeric Deutsch, Apr 04 2008

STATUS

approved

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Last modified April 18 11:10 EDT 2019. Contains 322209 sequences. (Running on oeis4.)