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A228131 a(n) = Sum_{i=0..n-1} K(i,n)*i, where K(,) is Kronecker symbol.

%I A228131 #15 Nov 03 2024 16:38:58
%S A228131 0,1,-1,4,0,6,-7,0,27,6,-11,-8,0,20,-30,64,0,-4,-19,0,0,46,-69,-48,
%T A228131 250,106,-9,0,0,68,-93,0,0,44,-70,216,0,82,-156,0,0,60,-43,-88,0,148,
%U A228131 -235,-32,1029,94,-102,0,0,6,-220,-224,0,-82,-177,0,0,168,-126,1024,0,304,-67,0,0,268,-497,0,0,494,-50,-152,0,276,-395,0,2187,4,-249,0,0,310,-522,-176,0,388,-182,0,0,424,-760,-192,0,202,0,2000
%N A228131 a(n) = Sum_{i=0..n-1} K(i,n)*i, where K(,) is Kronecker symbol.
%C A228131 For prime n==1 (mod 4), a(n) = 0.
%C A228131 For prime n==3 (mod 4) and n>3, i.e., n=A002145(m) for m>1, a(n) = -n*A002143(m).
%H A228131 G. C. Greubel, <a href="/A228131/b228131.txt">Table of n, a(n) for n = 1..5000</a>
%H A228131 Wikipedia, <a href="http://en.wikipedia.org/wiki/Kronecker_symbol">Kronecker symbol</a>
%t A228131 Table[Sum[KroneckerSymbol[k, n]*k, {k, 0, n - 1}], {n, 0, 50}] (* _G. C. Greubel_, Apr 23 2018 *)
%o A228131 (PARI) a(n) = sum(i=1,n-1, kronecker(i,n)*i)
%Y A228131 Cf. A255643, A255644
%K A228131 sign
%O A228131 1,4
%A A228131 _Max Alekseyev_, Aug 11 2013