For the numbers n in S000696, the number of divisors of n^2 - 1.
2, 4, 8, 10, 16, 18, 24, 32, 40, 60, 64, 70, 80, 96, 128, 144, 150, 192, 216, 240, 256, 288, 324, 400, 512, 576, 768, 810, 960, 1024, 1152, 1536, 1792, 1920, 2048, 2304, 2688, 3072, 3168, 3456, 4320, 5376, 6912, 7168, 8640, 9216, 10752, 10800, 11520, 12288
1
T. D. Noe, Plot of 50 terms
Adrian Dudek, On the number of divisors of n^2 - 1, arxiv 1507.08893 (Jul 30 2015)
(Mma) mx = 0; t = {}; Do[s = DivisorSigma[0, n^2 - 1]; If[s > mx, mx = s; AppendTo[t, {n, mx}]], {n, 2, 1000000}]; Transpose[t][[2]]
Cf. S000694, S000695, S000696.
nonn
T. D. Noe, Aug 04 2015