login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A138812 a(0)=1, a(n) = sum{k=0 to n-1} floor(n/a(k)). 1

%I

%S 1,1,4,6,9,11,14,16,19,22,24,27,31,33,36,38,42,44,48,51,54,56,60,62,

%T 67,69,71,75,79,81,84,87,91,95,97,99,105,107,111,113,116,118,123,125,

%U 131,134,136,138,145,147,149,152,155,157,163,166,171,174,176,178,183,185

%N a(0)=1, a(n) = sum{k=0 to n-1} floor(n/a(k)).

%F Probably a(n) ~ sqrt(2) n log(n)^(1/2) as n -> oo. - _Robert Israel_, May 02 2008

%F From _Andrew V. Sutherland_, May 02 2008: (Start)

%F This is supported by the following data:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

%F a(131072)= 658761, a(n)/n=5.0259, a(n)/(n*sqrt(log(n)))=1.4641 (End)

%p 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

%t a = {1}; Do[AppendTo[a, Sum[Floor[n/a[[k]]], {k, 1, n}]], {n, 1, 70}]; a (* _Stefan Steinerberger_, Apr 04 2008 *)

%Y Cf. A138813.

%K nonn

%O 0,3

%A _Leroy Quet_, Mar 31 2008

%E More terms from _Stefan Steinerberger_ and _Emeric Deutsch_, Apr 04 2008

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 April 19 11:58 EDT 2021. Contains 343114 sequences. (Running on oeis4.)