Various Arithmetic Functions and their Applications

TL;DR

This paper explores a wide range of arithmetic functions and integer sequences, presenting new problems, conjectures, and theoretical insights with applications across number theory.

Contribution

It introduces numerous new definitions, problems, and conjectures related to arithmetic functions and integer sequences, expanding the theoretical framework in number theory.

Findings

Over 300 sequences analyzed and classified.

New conjectures and problems proposed.

Mathematical criteria and formulas developed.

Abstract

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes squares cubes factorials, almost primes, mobile periodicals, functions, tables, prime square factorial bases, generalized factorials, generalized palindromes, so on.