S000696


Numbers n at which the number of divisors of n^2 -1 reaches a new record.

2, 3, 5, 7, 11, 17, 19, 29, 41, 71, 109, 161, 169, 181, 379, 449, 649, 701, 881, 1079, 1189, 1871, 2449, 3079, 4159, 5851, 11969, 19601, 23561, 23869, 24751, 43471, 82081, 94249, 157249, 222641, 252449, 313039, 627199, 677249, 790399, 1276001, 2308879, 4058209, 4406401, 5395391, 9843679, 10285001, 14579839, 14632001

1

S000696

Note that many, but not all, of these numbers are prime.

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][[1]]

Cf. S000694, S000695, S000697.

nonn,hard

T. D. Noe, Aug 04 2015

© Tony D Noe 2014-2015