Kinoctoval Geometric Progressions and SHCN Totatives

The table at the top left, “Kinoctoval Geometric Progressions”, shows powers of the six smallest primes in base 360. The table below it, “Cycles Exhibited in Kinoctoval Geometric Progressions”, the power residues of the five smallest primes (mod 360). These developed 19-21 December 2007, Tayya 7b05-7, seven dozen eleventh phase (Salcyra-Lectajinal Xrga, “life phase of the Virtual Solid Order”), St. Louis.

The tables at the top right,“Sexagesimal Totative Pairs”, “Hundal (Base 120) Totative Pairs”, “Kinoctoval (Base 360) Totative Pairs”, lists the digits coprime to bases 60, 120, and 360, respectively. The digits are paired with their additive complements. I was fascinated with composite totatives, something I regarded as a “flaw”, unhandled exceptions. The base 360 totative pair 143 + 217 intrigued me, as these were paired composite totatives. Eventually I came to regard composite totatives t = (r ± 1) as assets, and that composite totatives abound in very large bases. The table at bottom right, “Relationships between Totatives and Totative Regimes of Highly Composite Numbers”, studies the totient ratio of primorials (totient regimes of SHCNs), a study extended at s7836a08. These developed 29 December 2007-11 January 2008, Tayya 7b13-7b24, seven dozen eleventh phase (Salcyra-Lectajinal Xrga, “life phase of the Virtual Solid Order”), St. Louis.

This page last modified Friday 13 April 2012.