Number of divisors of n^2 - 1.

2, 4, 4, 8, 4, 10, 6, 10, 6, 16, 4, 16, 8, 12, 8, 18, 4, 24, 8, 16, 8, 20, 6, 20, 12, 16, 8, 32, 4, 28, 8, 14, 16, 24, 8, 24, 8, 20, 8, 40, 4, 32, 12, 16, 12, 24, 6, 36, 12, 24, 8, 32, 8, 40, 16, 20, 8, 32, 4, 32, 12, 16, 24, 32, 8, 32, 8, 32, 8, 60, 4, 30, 12

2

Dudek shows that the sum is (6/Pi^2) N (Log N)^2 as N goes to infinity.

T. D. Noe, Plot of terms 2..1000

T. D. Noe, Table of terms 2..1000

Adrian Dudek, On the number of divisors of n^2 - 1, arxiv 1507.08893 (Jul 30 2015)

(Mma) Table[DivisorSigma[0, n^2 - 1], {n, 2, 100}]

Cf. S000695, S000696, S000697.

nonn

T. D. Noe, Aug 04 2015