A117001 Sum_{d|n, sqrt(n) < d <= n} Jacobi(2,d)*d - Sum_{d|n, 1 <= d < sqrt(n)} Jacobi(2,d)*d..

0, -1, -4, -1, -6, -4, 6, -1, 8, -6, -12, 2, -14, 6, 12, -1, 16, 11, -20, -6, -12, -12, 22, 2, 24, -14, -16, 6, -30, 22, 30, -1, 24, 16, -24, 11, -38, -20, 28, 4, 40, -12, -44, -12, -14, 22, 46, 2, 48, 29, -32, -14, -54, -16, 48, -8, 40, -30, -60, 22, -62, 30, 46, -1, 56, 24, -68, 16, -44, -38, 70, 11, 72, -38, -28, -20, -96, 28

Offset

1,3

References

H. J. S. Smith, Report on the Theory of Numbers, reprinted in Vol. 1 of his Collected Math. Papers, Chelsea, NY, 1979, see p. 323.

Links

Table of n, a(n) for n=1..78.

Maple

with(numtheory); A117001:=proc(n) local d, t1, t2; t1:=0; t2:=0; for d from 1 to n do if n mod d = 0 then if d^2>n then t1:=t1+jacobi(2, d)*d; fi; if d^2<n then t2:=t2+jacobi(2, d)*d; fi; fi; od: t1-t2; end;

Mathematica

a[n_] := Sum[Which[Sqrt[n]<d<=n, 1, 1<=d<Sqrt[n], -1, True, 0]*JacobiSymbol[2, d]*d, {d, Divisors[n]}];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 17 2023 *)

Crossrefs

Cf. A117000.

Sequence in context: A021710 A127555 A192085 * A206787 A327419 A192066

Adjacent sequences: A116998 A116999 A117000 * A117002 A117003 A117004

Keyword

sign

Author

N. J. A. Sloane, Apr 15 2006

Status

approved