%I A117001
%S A117001 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,
%T A117001 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,
%U A117001 48,8,40,30,60,22,62,30,46,1,56,24,68,16,44,38,70,11,72,38,28,20,96,28
%V A117001 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,
%W A117001 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,
%X A117001 48,-8,40,-30,-60,22,-62,30,46,-1,56,24,-68,16,-44,-38,70,11,72,-38,-28,
               -20,-96,28
%N A117001 Sum_{d|n, sqrt(n) < d <= n} Jacobi(2,d)*d - Sum_{d|n, 1 <= d < sqrt(n)} 
               Jacobi(2,d)*d..
%D A117001 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.
%p A117001 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;
%Y A117001 Cf. A117000.
%Y A117001 Sequence in context: A050307 A021710 A127555 this_sequence A098986 A000593 
               A115607
%Y A117001 Adjacent sequences: A116998 A116999 A117000 this_sequence A117002 A117003 
               A117004
%K A117001 sign
%O A117001 1,3
%A A117001 N. J. A. Sloane (njas(AT)research.att.com), Apr 15 2006