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a(n) = Sum_{k=1..n} k - floor(sqrt(k)+1/2) * floor(sqrt(k-1)).
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%I #4 Sep 18 2021 21:55:02

%S 1,2,3,5,6,8,9,11,14,15,17,20,21,23,26,30,31,33,36,40,41,43,46,50,55,

%T 56,58,61,65,70,71,73,76,80,85,91,92,94,97,101,106,112,113,115,118,

%U 122,127,133,140,141,143,146,150,155,161,168,169,171,174,178,183,189,196,204

%N a(n) = Sum_{k=1..n} k - floor(sqrt(k)+1/2) * floor(sqrt(k-1)).

%C Partial sums of A122197.

%t Table[Sum[k - Floor[Sqrt[k] + 1/2]*Floor[Sqrt[k - 1]], {k, n}], {n, 100}]

%Y Cf. A122197.

%K nonn,easy

%O 1,2

%A _Wesley Ivan Hurt_, Sep 18 2021