

A014819


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


2



1, 8, 32, 88, 195, 377, 666, 1096, 1701, 2530, 3630, 5056, 6863, 9115, 11884, 15240, 19249, 24012, 29606, 36126, 43665, 52327, 62220, 73452, 86137, 100398, 116364, 134158, 153915, 175789, 199908, 226432, 255501, 287288, 321958, 359672, 400599, 444927, 492842
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


REFERENCES

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


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000


MAPLE

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


MATHEMATICA

Table[Sum[Floor[k^4/n], {k, 1, n}], {n, 1, 40}] (* G. C. Greubel, Nov 21 2018 *)


PROG

(PARI) vector(40, n, sum(k=1, n, floor(k^4/n))) \\ G. C. Greubel, Nov 21 2018
(Magma) [(&+[Floor(k^4/n): k in [1..n]]): n in [1..40]]; // G. C. Greubel, Nov 21 2018
(Sage) [sum(floor(k^4/n) for k in (1..n)) for n in (1..40)] # G. C. Greubel, Nov 21 2018


CROSSREFS

Cf. A014817, A014818.
Sequence in context: A333174 A018839 A008412 * A033155 A132117 A159941
Adjacent sequences: A014816 A014817 A014818 * A014820 A014821 A014822


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Title improved by Sean A. Irvine, Nov 21 2018


STATUS

approved



