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A138812
a(0)=1; for n > 0, a(n) = Sum_{k=0..n-1} floor(n/a(k)).
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
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 31 2008
EXTENSIONS
More terms from Stefan Steinerberger and Emeric Deutsch, Apr 04 2008
STATUS
approved