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A014819 a(n) = Sum_{k=1..n} floor(k^4/n). 2

%I

%S 1,8,32,88,195,377,666,1096,1701,2530,3630,5056,6863,9115,11884,15240,

%T 19249,24012,29606,36126,43665,52327,62220,73452,86137,100398,116364,

%U 134158,153915,175789,199908,226432,255501,287288,321958,359672,400599,444927,492842

%N a(n) = Sum_{k=1..n} floor(k^4/n).

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

%H G. C. Greubel, <a href="/A014819/b014819.txt">Table of n, a(n) for n = 1..1000</a>

%p f := m-> add( floor((nu)^4/m), nu=0..m): seq(f(n), n=1..40);

%t Table[Sum[Floor[k^4/n], {k, 1, n}], {n, 1, 40}] (* _G. C. Greubel_, Nov 21 2018 *)

%o (PARI) vector(40, n, sum(k=1,n, floor(k^4/n))) \\ _G. C. Greubel_, Nov 21 2018

%o (MAGMA) [(&+[Floor(k^4/n): k in [1..n]]): n in [1..40]]; // _G. C. Greubel_, Nov 21 2018

%o (Sage) [sum(floor(k^4/n) for k in (1..n)) for n in (1..40)] # _G. C. Greubel_, Nov 21 2018

%Y Cf. A014817, A014818.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

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

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Last modified August 3 17:04 EDT 2021. Contains 346439 sequences. (Running on oeis4.)