A049764 a(n) = Sum_{k=1..n} T(n,k), array T as in A049763.

0, 0, 1, 1, 3, 1, 5, 7, 9, 10, 18, 10, 18, 25, 28, 40, 44, 26, 52, 79, 60, 78, 73, 101, 117, 133, 114, 136, 91, 90, 158, 188, 220, 244, 218, 220, 208, 283, 280, 303, 220, 319, 287, 393, 398, 446, 391, 459, 435, 534, 481, 471, 428, 499

Offset

1,5

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{i=1..n} (n^4 mod i). - Wesley Ivan Hurt, Sep 15 2017

Maple

seq( add( `mod`(n^4, k), k = 1..n), n = 1..60); # G. C. Greubel, Dec 13 2019

Mathematica

Table[Sum[Mod[n^4, i], {i, n}], {n, 60}] (* Vincenzo Librandi, Sep 18 2017 *)
Table[Sum[PowerMod[n, 4, i], {i, n}], {n, 60}] (* Harvey P. Dale, Aug 29 2021 *)

Prog

(Magma) [&+[n^4 mod i: i in [1..n]]: n in [1..60]]; // Vincenzo Librandi, Sep 18 2017
(PARI) a(n) = sum(i=1, n, lift(Mod(n, i)^4)); \\ Michel Marcus, Sep 18 2017
(Sage) [sum(power_mod(n, 4, k) for k in (1..n)) for n in (1..60)] # G. C. Greubel, Dec 13 2019
(GAP) List([1..60], n-> Sum([1..n], k-> PowerMod(n, 4, k)) ); # G. C. Greubel, Dec 13 2019

Crossrefs

Row sums of A049763.

Sequence in context: A159285 A021080 A354576 * A136437 A137328 A140991

Adjacent sequences: A049761 A049762 A049763 * A049765 A049766 A049767

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved