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%I #7 Jan 30 2016 09:21:27
%S 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,
%T 156,144,147,203,175,186,152,242,272,245,201,333,323,286,270,410,392,
%U 430,363,420,437,423,340,490,550,578,585,689,639,605,546,760,812
%N a(n) = sum_{k=1..(n-1)/2} (k^2 mod n).
%C 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.
%H Harvey P. Dale, <a href="/A231589/b231589.txt">Table of n, a(n) for n = 1..1000</a>
%H S. A. Shirali, <a href="http://www.jstor.org/stable/2690862">A family portrait of primes-a case study in discrimination</a>, Math. Mag. Vol. 70, No. 4 (Oct., 1997), pp. 263-272.
%t Table[Sum[PowerMod[k,2,n],{k,(n-1)/2}],{n,60}] (* _Harvey P. Dale_, Jan 30 2016 *)
%o (PARI) a(n) = sum(k=1, (n-1)\2, k^2 % n);
%Y Cf. A048152, A048153.
%K nonn
%O 1,5
%A _Michel Marcus_, Nov 11 2013