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%I M2434 #16 Feb 08 2022 17:06:59
%S 1,3,5,8,11,14,17,22,24,28,33,36,40,45,48,53,57,62,66,71,74,79,86,89,
%T 93,99,102,109,114,117,122,129,133,138,143,148,152,159,164,169,175,
%U 178,185,190,193,202,207,212,215,223,227,232,241,244,249,256,259,266,273
%N a(n) = Sum_{k=1..n} nearest integer to n/k (if n/k is midway between two numbers take the smaller).
%C Number of ways the numbers from 1..n divide the numbers from n..2n-1, n>=2. - _Wesley Ivan Hurt_, Feb 08 2022
%D _Marc LeBrun_, personal communication.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H M. Le Brun, <a href="/A006577/a006577.pdf">Email to N. J. A. Sloane, Jul 1991</a>
%F a(n) = n^2 - Sum_{k=1..n} Sum_{i=n..2n-1} sign(i mod k). - _Wesley Ivan Hurt_, Feb 08 2022
%e a(3) = 3 + 1 + 1 = 5. a(7) = 17 = 7 + 3 + 2 + 2 + 1 + 1 + 1.
%t rnd[n_] := If[Mod[n, 1] > .5, Ceiling[n], Floor[n]]; Table[ Sum[ rnd[ n/k], {k, 1, n} ], {n, 1, 70} ]
%Y Cf. A006218.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_.
%E More terms from _Robert G. Wilson v_, Oct 22 2001
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