[seqfan] Experimental Number Theory, Part I : Tower Arithmetic

[Jonathan Post]

Through a(48) the below seq seems to agree with A165412  Divisors of 2520.

What's the reason, and is the arXiv paper and its Mathematica cited a
basis for submitting the seq from page 3:
g(x) = 1 + x + x^x + x^x^x + x^x^x^x + · · ·

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35,
36, 40, 42, 45, 56, 60, 63, 64, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180,
192, 210, 252, 280, 315, 320, 360, 420, 448, 504, 576, 630, 840
, 960, 1260, 1344, 2240, 2520, 2880, 4032, 6720, 20160}

Page 9 of the following is the source for the above values

arXiv:1101.3026 [pdf, ps, other]
    Title: Experimental Number Theory, Part I : Tower Arithmetic
    Authors: Edinah K. Gnang
    Subjects: Number Theory (math.NT); Combinatorics (math.CO)

    We introduce in this section an Algebraic and Combinatorial
approach to the theory of Numbers. The approach rests on the
observation that numbers can be identified with familiar combinatorial
objects namely rooted trees, which we shall here refer to as towers.
The bijection between numbers and towers provides some insights into
unexpected connexions between Number theory, combinatorics and
discrete probability theory.