A096061 a(n) = floor((Sum of the first n natural numbers)/(Sum of the first n terms of the harmonic series)).

1, 2, 3, 4, 6, 8, 10, 13, 15, 18, 21, 25, 28, 32, 36, 40, 44, 48, 53, 58, 63, 68, 73, 79, 85, 91, 97, 103, 109, 116, 123, 130, 137, 144, 151, 159, 167, 175, 183, 191, 200, 208, 217, 226, 235, 244, 254, 263, 273, 283, 293, 303, 314, 324, 335, 346, 357, 368, 379

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

The sequence has the asymptotic behavior n^2/log(n). - Stefan Steinerberger, Mar 18 2006

(n*(n+1))/(2*log(n)) >= a(n) >= (n*(n+1))/(2*log(n)+2). - Stefan Steinerberger, Mar 18 2006

Example

a(5) = floor((1 + 2 + 3 + 4 + 5)/(1 + 1/2 + 1/3 + 1/4 + 1/5)) = floor(15/(137/60)) = floor(900/137) = 6.

Maple

a:= n-> floor(sum(i, i=1..n)/sum(1/i, i=1..n)):
seq(a(n), n=1..60);  # Alois P. Heinz, Aug 26 2015

Mathematica

Table[Floor[(n*(n + 1))/(2*Sum[1/i, {i, 1, n}])], {n, 1, 55}] (* Stefan Steinerberger, Mar 18 2006 *)

Crossrefs

Sequence in context: A083006 A352929 A392896 * A100919 A184109 A214780

Adjacent sequences: A096058 A096059 A096060 * A096062 A096063 A096064

Keyword

nonn

Author

Amarnath Murthy, Jun 18 2004

Extensions

More terms from Stefan Steinerberger, Mar 18 2006

Offset corrected by Jon E. Schoenfield, Aug 26 2015

Status

approved