A228432 -id:A228432 - cp's OEIS frontend

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

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Michel Marcus, Nov 11 2013

nonn

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.

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.

Cf. A048152, A048153.

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

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

cp's OEIS Frontend

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

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