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a(n) = Sum_{i=0..n-1} K(i,n)*i, where K(,) is Kronecker symbol.
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%I #15 Nov 03 2024 16:38:58

%S 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 250,106,-9,0,0,68,-93,0,0,44,-70,216,0,82,-156,0,0,60,-43,-88,0,148,

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

%C For prime n==1 (mod 4), a(n) = 0.

%C For prime n==3 (mod 4) and n>3, i.e., n=A002145(m) for m>1, a(n) = -n*A002143(m).

%H G. C. Greubel, <a href="/A228131/b228131.txt">Table of n, a(n) for n = 1..5000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Kronecker_symbol">Kronecker symbol</a>

%t Table[Sum[KroneckerSymbol[k, n]*k, {k, 0, n - 1}], {n, 0, 50}] (* _G. C. Greubel_, Apr 23 2018 *)

%o (PARI) a(n) = sum(i=1,n-1, kronecker(i,n)*i)

%Y Cf. A255643, A255644

%K sign

%O 1,4

%A _Max Alekseyev_, Aug 11 2013