S000695


Sum of the number of divisors of i^2 - 1 for i = 2..n.

2, 6, 10, 18, 22, 32, 38, 48, 54, 70, 74, 90, 98, 110, 118, 136, 140, 164, 172, 188, 196, 216, 222, 242, 254, 270, 278, 310, 314, 342, 350, 364, 380, 404, 412, 436, 444, 464, 472, 512, 516, 548, 560, 576, 588, 612, 618, 654, 666, 690, 698, 730, 738, 778

2

S000695

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

Cf. S000694, S000696, S000697.

nonn

T. D. Noe, Aug 04 2015

© Tony D Noe 2014-2015