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A096061 a(n) = floor((Sum of the first n natural numbers)/(Sum of the first n terms of the harmonic series)). 1

%I

%S 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,

%T 91,97,103,109,116,123,130,137,144,151,159,167,175,183,191,200,208,

%U 217,226,235,244,254,263,273,283,293,303,314,324,335,346,357,368,379

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

%H Alois P. Heinz, <a href="/A096061/b096061.txt">Table of n, a(n) for n = 1..10000</a>

%F The sequence has the asymptotic behavior n^2/log(n). - _Stefan Steinerberger_, Mar 18 2006

%F (n*(n+1))/(2*log(n)) >= a(n) >= (n*(n+1))/(2*log(n)+2). - _Stefan Steinerberger_, Mar 18 2006

%e 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.

%p a:= n-> floor(sum(i, i=1..n)/sum(1/i, i=1..n)):

%p seq(a(n), n=1..60); # _Alois P. Heinz_, Aug 26 2015

%t Table[Floor[(n*(n + 1))/(2*Sum[1/i, {i, 1, n}])], {n, 1, 55}] (* _Stefan Steinerberger_, Mar 18 2006 *)

%K nonn

%O 1,2

%A _Amarnath Murthy_, Jun 18 2004

%E More terms from _Stefan Steinerberger_, Mar 18 2006

%E Offset corrected by _Jon E. Schoenfield_, Aug 26 2015

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Last modified March 21 12:12 EDT 2019. Contains 321369 sequences. (Running on oeis4.)