%I A083344
%S A083344 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,
               0,0,2,0,0,0,0,0,
%T A083344 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,
               0,0,0,0,0,0,0,
%U A083344 0,0,0,0,0,0,0,0,0,0,6,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,0,0,30,0,
               0,0,0,0,0,4,0,0
%V A083344 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,
               0,0,2,0,0,0,0,0,
%W A083344 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,
               0,0,0,0,0,0,0,0,
%X A083344 0,0,0,0,0,0,0,0,0,0,6,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,0,0,30,0,
               0,0,0,0,0,4,0,0
%N A083344 a(n)=A082457(n)-A066715(n)= GCD[2n+1, A057643(2n+1)]-GCD[2n+1, A000203(2n+1)].
%F A083344 a(n)=GCD[2n+1, LCM[1+D(2n+1)]]-GCD[2n+1, sigma(2n+1)], GCD[2n+1, A057643(2n+1)]-GCD[2n+1, 
               A000203(2n+1)], where D(x)=divisor-set of x
%e A083344 n=22: 2n+1=45, A057643(45)=5520, a(22)=GCD[45,5520]=15 while A066715[45]=3; 
               a(22)=15-3=12; sites where nonzero terms appear see in A082452.
%t A083344 di[x_] := Apply[LCM, Divisors[x]+1] (*A066715=*)t1=Table[GCD[2*n+1, DivisorSigma[1, 
               2*n+1]], {n, 1, 2048}]; (*A082457=*)t2=Table[GCD[2*w+1, di[1+2*w]], 
               {w, 1, 2048}]; (*A083344=*)t2-t1;
%Y A083344 Cf. A057643, A066715, A000203, A082457, A082452.
%Y A083344 Sequence in context: A046844 A066953 A004022 this_sequence A063863 A101364 
               A104203
%Y A083344 Adjacent sequences: A083341 A083342 A083343 this_sequence A083345 A083346 
               A083347
%K A083344 sign
%O A083344 1,22
%A A083344 Labos E. (labos(AT)ana.sote.hu), Apr 25 2003