%I #15 Aug 14 2020 11:19:58
%S 1,0,1,0,1,0,1,0,-1,0,-1,-2,-1,0,1,0,1,0,1,2,1,0,1,0,1,0,1,2,1,2,1,2,
%T 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,2,1,2,3,2,1,2,3,2,3,2,1,2,1,0,
%U -1,0,-1,0,-1,-2,-3,-2,-3,-2,-3,-4,-3,-4,-3,-2,-1,-2,-1,0
%N Excess of the odd abundant numbers that are congruent to 1 mod 4 over those that are congruent to 3 mod 4.
%C Pollack and Kobayashi ask if a(n) can be arbitrarily large and if 0 can appear infinitely often (see Slide 21 in the links).
%H Paul Pollack and Mits Kobayashi, <a href="http://pollack.uga.edu/INTEGERS2013.pdf">The distribution of abundant numbers</a>, Slides, Integers Conference 2013: Erdős Centennial, University of Georgia, October 24, 2013.
%t Reap[For[nbe = 0; n = 1, n < 10^5, n += 2, If[DivisorSigma[1, n] > 2*n, If[Mod[n, 4] == 1, nbe++, nbe--]; Sow[nbe]]]][[2, 1]] (* _Jean-François Alcover_, Jan 05 2016, adapted from PARI *)
%o (PARI) lista(nn) = {nbe = 0; forstep(n=1, nn, 2, if (sigma(n) > 2*n, if (n % 4 == 1, nbe++, nbe--); print1(nbe, ", ");););}
%Y Cf. A005231.
%K sign
%O 1,12
%A _Michel Marcus_, Jan 05 2016