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a(n) = Sum_{i=0..n} K(n, i) where K(x, y) is the Kronecker symbol (x / y).
10

%I #38 May 19 2024 02:16:41

%S 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,

%T 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,

%U 32,0,8,-2,0,0,4,14,0,0,10,4,0,0,4,22,0,54

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

%C a(n) = A096396(n) - A096397(n). - _Reinhard Zumkeller_, Mar 24 2012

%C a(n) < 0 for n in A071958. - _Robert G. Wilson v_, Mar 21 2015

%H Reinhard Zumkeller, <a href="/A071961/b071961.txt">Table of n, a(n) for n = 0..10000</a>

%t f[n_] := Sum[KroneckerSymbol[n, k], {k, 0, n}];

%t Table[f[n], {n, 0, 81}] (* _Robert G. Wilson v_, Mar 21 2015 *)

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

%o (SageMath)

%o print([sum(kronecker(n, k) for k in range(n + 1)) for n in range(82)])

%o # _Peter Luschny_, May 16 2024

%Y Row sums of A372728.

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

%K easy,sign,look

%O 0,2

%A _Benoit Cloitre_, Jun 16 2002

%E Offset set to 0, a(0) = 0 added, a(1) and name adapted by _Peter Luschny_, May 16 2024