A071961 a(n) = Sum_{i=0..n} K(n, i) where K(x, y) is the Kronecker symbol (x / y).

0, 2, 1, 0, 2, 0, 2, 4, 0, 6, 2, 2, 0, 0, 4, 6, 8, 0, 0, 2, 0, 0, 2, 6, 0, 20, 6, 0, 0, 0, 4, 12, 0, 0, 4, 4, 12, 0, 6, 12, 0, 0, 4, 0, 0, 0, 4, 10, 0, 42, 2, 4, 0, 0, 2, 18, 0, 0, 2, 6, 0, 0, 8, 2, 32, 0, 8, -2, 0, 0, 4, 14, 0, 0, 10, 4, 0, 0, 4, 22, 0, 54

Offset: 0

Author

Benoit Cloitre, Jun 16 2002

Keywords

• easy
• sign
• look

Comments

a(n) = A096396(n) - A096397(n). - Reinhard Zumkeller, Mar 24 2012

a(n) < 0 for n in A071958. - Robert G. Wilson v, Mar 21 2015

Links

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

Crossrefs

Row sums of A372728.

Records and their positions: A372933, A372934, A372935, A372936.

Programs

Mathematica

f[n_] := Sum[KroneckerSymbol[n, k], {k, 0, n}];
Table[f[n], {n, 0, 81}]  (* Robert G. Wilson v, Mar 21 2015 *)

PARI

for(n=0, 100, print1(sum(i=1, n, kronecker(n,i)), ","))

SageMath

print([sum(kronecker(n, k) for k in range(n + 1)) for n in range(82)])
# Peter Luschny, May 16 2024

Extensions

Offset set to 0, a(0) = 0 added, a(1) and name adapted by Peter Luschny, May 16 2024