%I A058344
%S A058344 0,1,1,1,1,2,1,5,4,4,1,8,1,6,9,13,1,5,1,10,11,10,1,28,6,12,13,12,1,6,1,
%T A058344 29,15,16,13,29,1,18,17,38,1,10,1,16,33,22,1,68,8,19,21,18,1,14,17,48,
%U A058344 23,28,1,60,1,30,41,61,19,18,1,22,27,22,1,97,1,36,49,24,19,22,1,94,40
%V A058344 0,1,1,-1,1,2,1,-5,4,4,1,-8,1,6,9,-13,1,5,1,-10,11,10,1,-28,6,12,13,-12,
               1,6,1,-29,15,
%W A058344 16,13,-29,1,18,17,-38,1,10,1,-16,33,22,1,-68,8,19,21,-18,1,14,17,-48,
               23,28,1,-60,1,30,
%X A058344 41,-61,19,18,1,-22,27,22,1,-97,1,36,49,-24,19,22,1,-94,40
%N A058344 Difference between the sum of the odd aliquot divisors of n and the sum 
               of the even aliquot divisors of n.
%C A058344 The number of terms where the sum of the odd parts is greater than the 
               sum of the even parts up to 10^n: 6, 57, 521, 5070, 50223, 500707, 
               5002236, ...,.
%F A058344 G.f.: Sum_{k>0} -(-1)^k*k*x^(2k)/(1-x^k). (Somos)
%e A058344 a(28) = -12 because the sum of the even divisors of 28 (2, 4 and 14) 
               = 20 and the sum of the odd divisors of 28 (1 and 7) = 8.
%t A058344 f[n_Integer] := Block[{d = Most[Divisors[n]]}, Plus @@ (-d*(-1)^d)]; 
               Table[ f[n], {n, 81}] (* or *)
%t A058344 Rest[ CoefficientList[ Series[ Sum[ -(-1)^k*k*x^(2k)/(1 - x^k), {k, 100}], 
               {x, 0, 81}], x]] (* Robert G. Wilson v, Aug 26 2005 *)
%o A058344 (PARI) a(n) = if(n<1, 0, sumdiv(n,d, (d<n)*d*-(-1)^d)) (Somos)
%o A058344 (PARI) {a(n)=if(n<1, 0, polcoeff( sum(k=1,n\2, -(-1)^k*k*x^(2*k)/(1-x^k),
               x*O(x^n)), n))} (Somos)
%Y A058344 Cf. A002129.
%Y A058344 Sequence in context: A061579 A094064 A159930 this_sequence A010582 A019473 
               A056605
%Y A058344 Adjacent sequences: A058341 A058342 A058343 this_sequence A058345 A058346 
               A058347
%K A058344 sign
%O A058344 1,6
%A A058344 Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 14 2000
%E A058344 Signs added by Michael Somos, Aug 21 2005