Where records occur in S000868.
2, 4, 6, 40, 106, 314, 1954, 2234, 2794, 11194
1
Observe how different this is from S000872.
T. D. Noe, Plot of 10 terms
(Mma) nn = 2000; s = Table[0, {nn}]; Do[k = DivisorSigma[1, n] - n; If[0 < k <= nn, s[[k]]++], {n, nn^2}]; mx = -1; t1 = {}; Do[If[s[[k]] > mx, mx = s[[k]]; AppendTo[t1, {k, mx}]], {k, 2, nn, 2}]; t1
nonn
T. D. Noe, May 05 2016