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

Author

Jon Perry, Oct 17 2013

Keywords

• nonn

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.

Crossrefs

Cf. A048153.

Programs

JavaScript

for (i=1;i<50;i++) {
c=0;
for (j=1;j<=i/2;j++) c+=(j*j)%i;
document.write(c+", ");
}

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 *)

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