A230366 a(n) = Sum_{k=1..floor(n/2)} (k^2 mod n).

0, 1, 1, 1, 5, 8, 7, 6, 12, 25, 22, 19, 39, 42, 35, 28, 68, 69, 76, 65, 91, 110, 92, 74, 125, 169, 144, 147, 203, 190, 186, 152, 242, 289, 245, 201, 333, 342, 286, 270, 410, 413, 430, 363, 420, 460, 423, 340, 490, 575, 578, 585, 689, 666, 605, 546, 760, 841

Offset

1,5

Comments

a(26) and a(27) are both squares. Conjecture: the number of n such that a(n) and a(n+1) are both squares is infinite.

a(p = prime) == 0 (mod p) for p > 3.

Links

Table of n, a(n) for n=1..58.

Mathematica

Table[Sum[Mod[k^2, n], {k, Floor[n/2]}], {n, 100}] (* T. D. Noe, Oct 22 2013 *)
Table[Sum[PowerMod[k, 2, n], {k, Floor[n/2]}], {n, 100}] (* Harvey P. Dale, Jul 03 2022 *)

Prog

(JavaScript)
for (i=1; i<50; i++) {
c=0;
for (j=1; j<=i/2; j++) c+=(j*j)%i;
document.write(c+", ");
}
(PARI) a(n)=sum(i=1, floor(n/2), (i*i)%n) \\ Ralf Stephan, Oct 19 2013
(Python)
def A230366(n): return sum(k**2%n for k in range(1, (n>>1)+1)) # Chai Wah Wu, Jun 02 2024

Crossrefs

Cf. A048153.

Sequence in context: A165909 A334482 A243598 * A358361 A197415 A019845

Adjacent sequences: A230363 A230364 A230365 * A230367 A230368 A230369

Keyword

nonn

Author

Jon Perry, Oct 17 2013

Status

approved