A231589 a(n) = sum_{k=1..(n-1)/2} (k^2 mod n).

0, 0, 1, 1, 5, 5, 7, 6, 12, 20, 22, 19, 39, 35, 35, 28, 68, 60, 76, 65, 91, 99, 92, 74, 125, 156, 144, 147, 203, 175, 186, 152, 242, 272, 245, 201, 333, 323, 286, 270, 410, 392, 430, 363, 420, 437, 423, 340, 490, 550, 578, 585, 689, 639, 605, 546, 760, 812

Offset

1,5

Comments

This expression occurred to S. A. Shirali while demonstrating a result concerning A081115 and A228432. This led him to investigate integers n such that a(n) = n*(n-1)/4, a(n) = floor(n/4), or a(n) = n*(n-1)/4 - n.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

S. A. Shirali, A family portrait of primes-a case study in discrimination, Math. Mag. Vol. 70, No. 4 (Oct., 1997), pp. 263-272.

Mathematica

Table[Sum[PowerMod[k, 2, n], {k, (n-1)/2}], {n, 60}] (* Harvey P. Dale, Jan 30 2016 *)

Prog

(PARI) a(n) = sum(k=1, (n-1)\2, k^2 % n);

Crossrefs

Cf. A048152, A048153.

Sequence in context: A247649 A252655 A021646 * A133888 A244587 A111186

Adjacent sequences: A231586 A231587 A231588 * A231590 A231591 A231592

Keyword

nonn

Author

Michel Marcus, Nov 11 2013

Status

approved