A096396 - OEIS

A096396

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

0, 2, 1, 1, 2, 2, 2, 5, 2, 6, 3, 6, 2, 6, 5, 7, 8, 8, 3, 10, 4, 6, 6, 14, 4, 20, 9, 9, 6, 14, 6, 21, 8, 10, 10, 14, 12, 18, 12, 18, 8, 20, 8, 21, 10, 12, 13, 28, 8, 42, 11, 18, 12, 26, 10, 29, 12, 18, 15, 32, 8, 30, 19, 19, 32, 24, 14, 32, 16, 22, 14, 42, 12, 36, 23, 22, 18, 30, 14, 50, 16

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OFFSET

0,2

LINKS

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

FORMULA

From Reinhard Zumkeller, Mar 24 2012: (Start)

a(n) = A000010(n) - A096397(n) for n >= 2.

a(n) = A071961(n) + A096397(n). (End)

MAPLE

K := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):

seq(nops(select(k -> K(n, k) = 1, [seq(0..n)])), n = 0..80);

# Peter Luschny, May 15 2024

MATHEMATICA

Table[Count[Table[KroneckerSymbol[n, k], {k, 0, n}], 1], {n, 0, 80}]

(* 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(81)])

# Peter Luschny, May 16 2024

CROSSREFS

Cf. A000010, A051953, A071961.

Cf. this sequence (#K(n,i)=1), A096397 (#K(n,i)=-1), A062830 (#K(n,i)=0).

Sequence in context: A029272 A153904 A128762 * A126307 A320838 A092332

Adjacent sequences: A096393 A096394 A096395 * A096397 A096398 A096399

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Aug 06 2004

EXTENSIONS

Typo in definition fixed by Reinhard Zumkeller, Mar 24 2012

Offset set to 0, a(0) = 0 added, a(1) and name adapted by Peter Luschny, May 15 2024

STATUS

approved