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

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, 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, 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

Offset

0,6

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

From Reinhard Zumkeller, Mar 24 2012: (Start)

a(A096398(n)) = 0;

a(n) = A000010(n) - A096396(n) for n >= 2.

a(n) = A096396(n) - A071961(n). (End)

Maple

K := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):
seq(nops(select(k -> K(n, k) = -1, [seq(0..n)])), n = 0..85);
# Peter Luschny, May 15 2024

Mathematica

Table[Count[Table[KroneckerSymbol[n, k], {k, 0, n}], -1], {n, 0, 70}]
(* Peter Luschny, May 15 2024 *)

Prog

(PARI) a(n) = sum(i=0, n, if(kronecker(n, i) + 1, 0, 1))
(SageMath)
print([sum(kronecker(n, k) == -1 for k in range(n + 1)) for n in range(86)])
# Peter Luschny, May 16 2024

Crossrefs

Cf. A000010, A051953, A096398, A071961, A372728.

Cf. A096396 (#K(n,i)=1), this sequence (#K(n,i)=-1), A062830 (#K(n,i)=0).

Sequence in context: A058685 A351637 A029300 * A337547 A291969 A321434

Adjacent sequences: A096394 A096395 A096396 * A096398 A096399 A096400

Keyword

nonn

Author

Benoit Cloitre, Aug 06 2004

Extensions

Offset set to 0, a(0) = 0 added, and name adapted by Peter Luschny, May 15 2024

Status

approved