The Optimized Sequence

The Optimized (Superior Highly Composite Number) Sequence

This table, “The Optimized Sequence”, shows the argam numerals for superior highly composite numbers (SHCNs), expressed in bases that are themselves SHCNs. The table developed around 24 May 2007, tayya 7970, (Salcyra Karlmelal, “Life Phase of Karl Michael, Son”), St. Louis. The table below, “My Reference for Mixed Radixes Which Represent Higher Integer Radixes in the Optimized Sequence”, summarizes the argam numerals for pure and coded number bases that are SHCNs. The table developed around 27 December 2007, tayya 7b11, (Salcyra Lectajinal, “Life Phase of the Virtual Solid Order”), St. Louis.

In spring 2018 (tayya a140), I revisited the subject of highly composite and superabundant numbers, resulting in several sequences in the OEIS (A301414, A304234, A304235) that derive from the chart below. This chart derives from plotting highly composite (blue) or superabundant (red) m at (x, y) where the ordered pair represents the largest primorial that divides m, A002110(y) × A301414(x) = m. (The chart has y increasing downward, x increasing rightward).

Writ large, this sort of plot illustrates the differences between the highly composite and superabundant numbers:

Read more about further examinations of the highly composite and superabundant numbers here.

This page last modified Tuesday 15 May 2018.