A138812 a(0)=1; for n > 0, a(n) = Sum_{k=0..n-1} floor(n/a(k)).

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

Offset

0,3

Links

Robin Visser, Table of n, a(n) for n = 0..10000

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:

.

n a(n) a(n)/n a(n)/(n*sqrt(log(n)))

------ ------ ------ ---------------------

2 4 2.0000 2.4022

4 9 2.2500 1.9110

8 19 2.3750 1.6470

16 42 2.6250 1.5765

32 91 2.8438 1.5275

64 196 3.0625 1.5017

128 421 3.2891 1.4932

256 896 3.5000 1.4863

512 1892 3.6953 1.4795

1024 3979 3.8857 1.4759

2048 8335 4.0698 1.4739

4096 17386 4.2446 1.4718

8192 36146 4.4124 1.4699

16384 74931 4.5734 1.4681

32768 154964 4.7291 1.4666

65536 319818 4.8800 1.4654

131072 658761 5.0259 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 * A332587 A003259 A020935

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