Number of Ordered Factorizations
A resource page relating to the number of ordered factorizations of natural numbers. Pete Brown Falls Creek, Southern Autumn of 2004
Web Publication by Mountain Man Graphics, Australia

Introduction to this resource

This reference index has been created in order to gather together in one place any and all work associated with the investigation of a very specific factorization of natural numbers known as the ordered factorizations. Essentially this represents the number of ways a natural number can be factored into an ordered product of integers (not necessarily prime factors) greater than one.

In particular, this reference index presents information related to the number of ordered factrizations.

"Ordered Factorization" - Mathworld - For a background to this subject matter this page is a good place to start. It provides a definitive outline of the area in general, including the series numbers (Sloan's Sequence Number A074206), the series generating function, and a number of recurrence equations.

Integer Sequence Research - Integer "core" sequence number A074206.

Constructive Bounds on Ordered Factorizations - The number of ways to factor a natural number into an ordered product of integers, each factor greater than one, is called the ordered factorization of n and is denoted H(n). We show upper and lower bounds on H(n) with explicit constructions .... [2004] Don Coppersmith, Moshe Lewenstein

Theory of Harmonics - Ray Tomes definitive exploration of the large and small structures of scale in the cosmos. Special mention should be made here that Ray's work relates to a specific subset of the series of the number of ordered factorizations - those with the greatest number of factors when compared to their local range. Ray Tomes, through the Harmonics Theory, examines the Himalayan form of the huge and mountainous peaks he has called the mainline harmonic numbers. These have been investigated to approximately 10^49 as at April 2004.

Ancient Analysis of Abundance - Pete Brown. This article presents an interesting (computational) analysis of the number of ordered factorizations in terms of ancient concepts, including Abundance, such terms previously restricted to summation of the divisors. Surprising results are listed, and conclusions are drawn.

Domains of Scales in the Cosmos: This article examines the theoretical classification of all things in the universe according to their scale of operation. Again, this article was inspired by the work of Ray Tomes.

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QuoteForTheDay:

  "Consciousness is never experienced in the plural, only in
   the singular. How does the idea of plurality (emphatically
   opposed by the Upanishad writers arise at all? .... the
   only possible alternative is simply to keep the immediate
   experience that consciousness is a singular of which the
   plural is unkown; that there *is* only one thing and that
   what seems to be a plurality is merely a series of different
   aspects of this one thing produced by deception (the Indian
   maya) - in much the same way Gaurisankar and Mt Everest turn
   out to be the same peak seen from different valleys."

    -  E. Schrodinger, "What is Life"