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a(n) = Sum_{k = 1..n} floor(2^k / k).
(Formerly M1015 N0381)
2

%I M1015 N0381 #29 Feb 01 2022 02:34:57

%S 2,4,6,10,16,26,44,76,132,234,420,761,1391,2561,4745,8841,16551,31114,

%T 58708,111136,211000,401650,766372,1465422,2807599,5388709,10359735,

%U 19946715,38459505,74250899,143524565,277742293,538043341,1043333611,2025040421

%N a(n) = Sum_{k = 1..n} floor(2^k / k).

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%H T. D. Noe, <a href="/A000801/b000801.txt">Table of n, a(n) for n = 1..500</a>

%p A000801 := proc(n) local k; sum(floor(2^k/k),k=1..n); end;

%t Table[Sum[Floor[2^k/k], {k, n}], {n, 30}] (* _T. D. Noe_, Jun 20 2012 *)

%Y Cf. A000799.

%K nonn

%O 1,1

%A _N. J. A. Sloane_