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a(n) = Sum_{k=0..n} ceiling(k^3/n).
0

%I #15 Sep 08 2022 08:44:39

%S 1,5,13,26,47,76,115,164,228,307,401,512,643,794,967,1162,1385,1632,

%T 1909,2214,2551,2920,3323,3760,4235,4751,5301,5900,6539,7222,7951,

%U 8724,9553,10429,11357,12336,13375,14468,15619,16828,18101,19435,20833,22296,23826

%N a(n) = Sum_{k=0..n} ceiling(k^3/n).

%D M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhauser, 1985, p. 103.

%p f := m->add( ceil(nu^3/m), nu=0..m): seq(f(m), m=1..45);

%t Table[Sum[Ceiling[k^3/n],{k,0,n}],{n,50}] (* _Harvey P. Dale_, May 05 2019 *)

%o (Magma) [&+[Ceiling(k^3/n): k in [0..n]]: n in [1..60]]; // _Vincenzo Librandi_, May 31 2019

%K nonn

%O 1,2

%A _N. J. A. Sloane_.

%E Title improved by _Sean A. Irvine_, Nov 21 2018