Where records occur in S000867.
3, 13, 21, 31, 49, 73, 91, 115, 121, 169, 211, 301, 331, 361, 391, 421, 511, 631, 721, 781, 841, 1051, 1261, 1471, 1561, 1681, 1891, 2101, 2311, 2521, 2731, 3151, 3361, 3571, 3991, 4201, 4411, 4621, 5251, 5461, 6091, 6511, 6721, 6931, 7771, 7981, 8191, 9031
1
Observe how different this is from S000871.
T. D. Noe, Plot of 60 terms
T. D. Noe, Table of 60 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; t2 = {}; Do[If[s[[k]] > mx, mx = s[[k]]; AppendTo[t2, {k, mx}]], {k, 3, nn, 2}]; t2
nonn
T. D. Noe, May 05 2016