Fundamental Theorem of Composite Numbers

Abstract: This paper presents a complete and non-overlapping partition of the composite numbers (OEIS A002808) into three mutually exclusive arithmetic subclasses: prime powers (OEIS A246547), squarefree composites (OEIS A120944), and mixed-power composites (OEIS A126706). This partition provides an algebraic framework for understanding the internal structure of composite numbers. The structural identity described here is referred to as the Fundamental Theorem of Composite Numbers (FTC).

Keywords: composite numbers, prime powers, squarefree numbers, number partitions, multiplicative structure, OEIS sequences.

2020 Mathematics Subject Classification: 11A41, 11A25, 11B83.