A049760 a(n) = Sum_{k=1..n} T(n,k), array T as in A049759.

0, 0, 1, 1, 3, 1, 8, 10, 11, 12, 13, 13, 31, 37, 31, 41, 42, 47, 58, 60, 82, 86, 95, 76, 125, 123, 140, 103, 115, 134, 188, 229, 235, 213, 186, 239, 264, 283, 244, 243, 263, 342, 369, 430, 387, 407, 473, 413, 446, 489, 522, 492, 558, 570, 569, 547, 692

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Row sums of A049759.

Programs

GAP

List([1..60], n-> Sum([1..n], k-> PowerMod(n,2,k)) ); # G. C. Greubel, Dec 14 2019

Magma

[&+[n^2 mod i: i in [1..n]]: n in [1..60]]; // Vincenzo Librandi, Sep 18 2017

Maple

seq( add( `mod`(n^2, k), k = 1..n), n = 1..60); # G. C. Greubel, Dec 14 2019

Mathematica

Table[Sum[Mod[n^2, i], {i, n}], {n, 60}] (* Vincenzo Librandi, Sep 18 2017 *)
Table[Sum[PowerMod[n,2,k],{k,n}],{n,60}] (* Harvey P. Dale, Mar 29 2018 *)

PARI

a(n)=my(N=n^2);sum(k=2,n-1,N%k) \\ Charles R Greathouse IV, Mar 27 2014

Sage

[sum(power_mod(n,2,k) for k in (1..n)) for n in (1..60)] # G. C. Greubel, Dec 14 2019

Formula

a(n) = Sum_{i=1..n} (n^2 mod i). - Wesley Ivan Hurt, Sep 15 2017