login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A138813 a(0) = 1; thereafter, a(n) = Sum_{k=0..n-1} ceiling(n/a(k)). 1
1, 1, 4, 7, 10, 14, 17, 20, 24, 28, 31, 35, 38, 42, 45, 50, 53, 57, 61, 64, 67, 73, 77, 80, 83, 88, 91, 94, 97, 104, 107, 111, 115, 119, 122, 126, 131, 135, 138, 142, 145, 151, 154, 160, 163, 167, 171, 174, 177, 182, 186, 191, 195, 199, 203, 206, 209, 216, 220, 223 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..59.

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)= 10, a(n)/n=2.5000, a(n)/(n*sqrt(log(n)))=2.1233

a( 8)= 24, a(n)/n=3.0000, a(n)/(n*sqrt(log(n)))=2.0804

a( 16)= 53, a(n)/n=3.3125, a(n)/(n*sqrt(log(n)))=1.9894

a( 32)= 115, a(n)/n=3.5938, a(n)/(n*sqrt(log(n)))=1.9304

a( 64)= 244, a(n)/n=3.8125, a(n)/(n*sqrt(log(n)))=1.8695

a( 128)= 514, a(n)/n=4.0156, a(n)/(n*sqrt(log(n)))=1.8230

a( 256)= 1075, a(n)/n=4.1992, a(n)/(n*sqrt(log(n)))=1.7832

a( 512)= 2237, a(n)/n=4.3691, a(n)/(n*sqrt(log(n)))=1.7493

a( 1024)= 4642, a(n)/n=4.5332, a(n)/(n*sqrt(log(n)))=1.7218

a( 2048)= 9608, a(n)/n=4.6914, a(n)/(n*sqrt(log(n)))=1.6990

a( 4096)= 19843, a(n)/n=4.8445, a(n)/(n*sqrt(log(n)))=1.6797

a( 8192)= 40895, a(n)/n=4.9921, a(n)/(n*sqrt(log(n)))=1.6630

a( 16384)= 84129, a(n)/n=5.1348, a(n)/(n*sqrt(log(n)))=1.6483

a( 32768)= 172797, a(n)/n=5.2733, a(n)/(n*sqrt(log(n)))=1.6354

a( 65536)= 354437, a(n)/n=5.4083, a(n)/(n*sqrt(log(n)))=1.6240

a(131072)= 726143, a(n)/n=5.5400, a(n)/(n*sqrt(log(n)))=1.6139 (End)

MATHEMATICA

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

CROSSREFS

Cf. A138812.

Sequence in context: A198266 A067497 A123384 * A310689 A184625 A184118

Adjacent sequences:  A138810 A138811 A138812 * A138814 A138815 A138816

KEYWORD

nonn

AUTHOR

Leroy Quet, Mar 31 2008

EXTENSIONS

More terms from Stefan Steinerberger, Apr 04 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 17 03:06 EST 2019. Contains 329216 sequences. (Running on oeis4.)