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 A006591 Sum_{k = 1..n } nearest integer to n/k (if n/k is midway between two numbers take the smaller). (Formerly M2434) 0

%I M2434

%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 Sum_{k = 1..n } nearest integer to n/k (if n/k is midway between two numbers take the smaller).

%D _Marc LeBrun_, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%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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