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a(1) = 1; a(n) = Sum_{k=1..n} a(ceiling((n-1)/k)).
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%I #4 Aug 15 2017 20:37:40

%S 1,2,4,8,14,24,36,56,78,110,148,200,254,334,416,522,644,798,954,1162,

%T 1372,1640,1934,2284,2636,3090,3556,4106,4694,5394,6096,6972,7850,

%U 8882,9972,11220,12500,14048,15598,17360,19208,21346,23486,26016,28548,31436,34478,37874,41272,45246

%N a(1) = 1; a(n) = Sum_{k=1..n} a(ceiling((n-1)/k)).

%F a(n) = 2*A003318(n-1) for n > 1.

%e a(1) = 1;

%e a(2) = a(ceiling(1/1)) + a(ceiling(1/2)) = a(1) + a(1) = 2;

%e a(3) = a(ceiling(2/1)) + a(ceiling(2/2)) + a(ceiling(2/3)) = a(2) + a(1) + a(1) = 4, etc.

%t a[1] = 1; a[n_] := a[n] = Sum[a[Ceiling[(n - 1)/k]], {k, 1, n}]; Table[a[n], {n, 50}]

%Y Cf. A003318, A025523, A068336 (first differences), A078346.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Aug 12 2017