PSYCHEDELIC GEOMETRY Number Theory

POST UNDER CONSTRUCTION1) INTRODUCTION:Nowadays mathematicians have developed a huge number of generalizations of $latex \phi$, the Euler's Totient Function [54], this sets of arithmetical functions are rooted in many areas of mathematics, namely: Combinatorics, Group Theory, Matrix Algebra, and of

As I´m working on more than one small projects of programming sequences from The On-Line Encyclopedia of Integer Sequences, and as I always try to document my code the best I can: I like to add comments and help information to it, but after many hours of “copy and paste”, and being aware that when

Euler´s totient function: $latex \phi(n)$ is defined as the number of positive integers less than or equal to $latex n$, that are coprime to $latex n$, and using Iverson bracket, $latex \phi$ can be written as: (See reference [1])$latex \phi(n) =\sum_{i=1}^{n}{[gcd(i,n)=1]} $MULTIPLICATIVE BUT NOT C

I've been programming a small web application in PHP to get automatically the BibTeX citation of any sequence in the The On-Line Encyclopedia of Integer Sequences.If you follow this link: OEIS2BibTeX or just click on the above image, then you must enter the desired sequence ID to get the BibTeX cita

A BINOMIAL PLAY:Our contributor Raymond Rogers has sent an alternate proof for:$latex \displaystyle det{\bigg[ \binom{i+j+k}{i} \bigg]}_{0\leq i,j \leq n} =\binom{n+k+1}{k+1}$This expression is identical to the one found in the post Binomial Matrix (III), but here the matrices are indexed from zero

INTRO:The Bisection Method is a very well known root-finding algorithm that always comes at the very beginning of every book on Numerical Analysis.The algorithmn searches for a root in the interval, $latex [a_{0},b_{0}]$ in whose endpoints the continous problem function, $latex f(x)$, takes opposite

Integer Rounding Functions can be found in many Number Theory texts, but I wasn´t able to find something about its integrals.The following expresions can be derived just from their plots, adding and substracting areas. They hold if $latex \displaystyle \;x\geq 0$The Triangular Numbers function is us

The final result, in the preceeding post, can not be derived from a telescoping series [3], if $latex \displaystyle k$ is not integer (See comments at reference [1]).$latex \displaystyle \sum_{n=1}^\infty \frac{1}{n(n+k)}=\frac{H_k}{k} $This lack of generality, can be avoided, if we consider a more