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A096397 a(n) = #{ 0 <= i <= n : K(n, i) = -1 } where K(n, i) is the Kronecker symbol.

%I A096397 #30 May 17 2024 09:47:57
%S A096397 0,0,0,1,0,2,0,1,2,0,1,4,2,6,1,1,0,8,3,8,4,6,4,8,4,0,3,9,6,14,2,9,8,
%T A096397 10,6,10,0,18,6,6,8,20,4,21,10,12,9,18,8,0,9,14,12,26,8,11,12,18,13,
%U A096397 26,8,30,11,17,0,24,6,34,16,22,10,28,12,36,13,18,18,30,10,28,16,0,18,39,12,32
%N A096397 a(n) = #{ 0 <= i <= n : K(n, i) = -1 } where K(n, i) is the Kronecker symbol.
%H A096397 Reinhard Zumkeller, <a href="/A096397/b096397.txt">Table of n, a(n) for n = 0..10000</a>
%F A096397 From _Reinhard Zumkeller_, Mar 24 2012: (Start)
%F A096397 a(A096398(n)) = 0;
%F A096397 a(n) = A000010(n) - A096396(n) for n >= 2.
%F A096397 a(n) = A096396(n) - A071961(n). (End)
%p A096397 K := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):
%p A096397 seq(nops(select(k -> K(n, k) = -1, [seq(0..n)])), n = 0..85);
%p A096397 # _Peter Luschny_, May 15 2024
%t A096397 Table[Count[Table[KroneckerSymbol[n, k], {k, 0, n}], -1], {n, 0, 70}]
%t A096397 (* _Peter Luschny_, May 15 2024 *)
%o A096397 (PARI) a(n) = sum(i=0, n, if(kronecker(n, i) + 1, 0, 1))
%o A096397 (SageMath)
%o A096397 print([sum(kronecker(n, k) == -1 for k in range(n + 1)) for n in range(86)])
%o A096397 # _Peter Luschny_, May 16 2024
%Y A096397 Cf. A000010, A051953, A096398, A071961, A372728.
%Y A096397 Cf. A096396 (#K(n,i)=1), this sequence (#K(n,i)=-1), A062830 (#K(n,i)=0).
%K A096397 nonn
%O A096397 0,6
%A A096397 _Benoit Cloitre_, Aug 06 2004
%E A096397 Offset set to 0, a(0) = 0 added, and name adapted by _Peter Luschny_, May 15 2024